Stable marriage problem
You are encouraged to solve this task according to the task description, using any language you may know.
Solve the Stable marriage problem using the Gale/Shapley algorithm.
Problem description
Given an equal number of men and women to be paired for marriage, each man ranks all the women in order of his preference and each women ranks all the men in order of her preference.
A stable set of engagements for marriage is one where no man prefers a women over the one he is engaged to, where that other woman also prefers that man over the one she is engaged to. I.e. with consulting marriages, there would be no reason for the engagements between the people to change.
Gale and Shapley proved that there is a stable set of engagements for any set of preferences and the first link above gives their algorithm for finding a set of stable engagements.
Task Specifics
Given ten males:
abe, bob, col, dan, ed, fred, gav, hal, ian, jon
And ten females:
abi, bea, cath, dee, eve, fay, gay, hope, ivy, jan
And a complete list of ranked preferences, where the most liked is to the left:
abe: abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay bob: cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay col: hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan dan: ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi ed: jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay fred: bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay gav: gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay hal: abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee ian: hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve jon: abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope abi: bob, fred, jon, gav, ian, abe, dan, ed, col, hal bea: bob, abe, col, fred, gav, dan, ian, ed, jon, hal cath: fred, bob, ed, gav, hal, col, ian, abe, dan, jon dee: fred, jon, col, abe, ian, hal, gav, dan, bob, ed eve: jon, hal, fred, dan, abe, gav, col, ed, ian, bob fay: bob, abe, ed, ian, jon, dan, fred, gav, col, hal gay: jon, gav, hal, fred, bob, abe, col, ed, dan, ian hope: gav, jon, bob, abe, ian, dan, hal, ed, col, fred ivy: ian, col, hal, gav, fred, bob, abe, ed, jon, dan jan: ed, hal, gav, abe, bob, jon, col, ian, fred, dan
- Use the Gale Shapley algorithm to find a stable set of engagements
- Perturb this set of engagements to form an unstable set of engagements then check this new set for stability.
References
- The Stable Marriage Problem. (Eloquent description and background information).
- Gale-Shapley Algorithm Demonstration.
- Another Gale-Shapley Algorithm Demonstration.
- Stable Marriage Problem - Numberphile (Video).
- Stable Marriage Problem (the math bit) (Video).
- The Stable Marriage Problem and School Choice. (Excellent exposition)
AutoHotkey
<lang autohotkey>; Given a complete list of ranked preferences, where the most liked is to the left: abe := ["abi", "eve", "cath", "ivy", "jan", "dee", "fay", "bea", "hope", "gay"] bob := ["cath", "hope", "abi", "dee", "eve", "fay", "bea", "jan", "ivy", "gay"] col := ["hope", "eve", "abi", "dee", "bea", "fay", "ivy", "gay", "cath", "jan"] dan := ["ivy", "fay", "dee", "gay", "hope", "eve", "jan", "bea", "cath", "abi"] ed := ["jan", "dee", "bea", "cath", "fay", "eve", "abi", "ivy", "hope", "gay"] fred := ["bea", "abi", "dee", "gay", "eve", "ivy", "cath", "jan", "hope", "fay"] gav := ["gay", "eve", "ivy", "bea", "cath", "abi", "dee", "hope", "jan", "fay"] hal := ["abi", "eve", "hope", "fay", "ivy", "cath", "jan", "bea", "gay", "dee"] ian := ["hope", "cath", "dee", "gay", "bea", "abi", "fay", "ivy", "jan", "eve"] jon := ["abi", "fay", "jan", "gay", "eve", "bea", "dee", "cath", "ivy", "hope"] abi := ["bob", "fred", "jon", "gav", "ian", "abe", "dan", "ed", "col", "hal"] bea := ["bob", "abe", "col", "fred", "gav", "dan", "ian", "ed", "jon", "hal"] cath := ["fred", "bob", "ed", "gav", "hal", "col", "ian", "abe", "dan", "jon"] dee := ["fred", "jon", "col", "abe", "ian", "hal", "gav", "dan", "bob", "ed"] eve := ["jon", "hal", "fred", "dan", "abe", "gav", "col", "ed", "ian", "bob"] fay := ["bob", "abe", "ed", "ian", "jon", "dan", "fred", "gav", "col", "hal"] gay := ["jon", "gav", "hal", "fred", "bob", "abe", "col", "ed", "dan", "ian"] hope := ["gav", "jon", "bob", "abe", "ian", "dan", "hal", "ed", "col", "fred"] ivy := ["ian", "col", "hal", "gav", "fred", "bob", "abe", "ed", "jon", "dan"] jan := ["ed", "hal", "gav", "abe", "bob", "jon", "col", "ian", "fred", "dan"]
- of ten males
males := ["abe", "bob", "col", "dan", "ed", "fred", "gav", "hal", "ian", "jon"]
- and ten females
females := ["abi", "bea", "cath", "dee", "eve", "fay", "gay", "hope", "ivy", "jan"]
- and an empty set of engagements
engagements := Object() freemales := males.Clone() ,s := "Engagements:`n"
- use the Gale Shapley algorithm to find a stable set of engagements
For i, male in freemales ; i=index of male (not needed) { j:=1 ; index of female While (engagements[female:=%male%[j]] != "" and index(%female%, male) > index(%female%, engagements[female])) j++ ; each male loops through all females in order of his preference until one accepts him If (engagements[female] != "") ; if she was previously engaged freemales.insert(engagements[female]) ; her old male goes to the bottom of the list ,s .= female . " dumped " . engagements[female] . "`n" engagements[female] := male ; the new engagement is registered ,s .= female . " accepted " . male . "`n" }
- summarize results
s .= "`nCouples:`n" For female, male in engagements s .= female . " is engaged to " . male . "`n" s .= Stable(engagements, females)
- then perturb this set of engagements to form an unstable set of engagements then check this new set for stability
s .= "`nWhat if cath and ivy swap?`n" engagements["cath"]:="abe", engagements["ivy"]:="bob"
- summarize results
s .= "`nCouples:`n" For female, male in engagements s .= female . " is engaged to " . male . "`n" s .= Stable(engagements, females)
Msgbox % clipboard := s Return
- Functions
Index(obj, value) { For key, val in obj If (val = value) Return, key, ErrorLevel := 0 Return, False, Errorlevel := 1 }
Stable(engagements, females) { For female, male in engagements { For j, female2 in females ; j=index of female (not needed) { If (index(%male%, female) > index(%male%, female2) and index(%female2%, male2:=engagements[female2]) > index(%female2%, male)) s .= male . " is engaged to " . female . " but would prefer " . female2 . " and " . female2 . " is engaged to " . male2 . " but would prefer " . male . "`n" } } If s Return "`nThese couples are not stable.`n" . s Else Return "`nThese couples are stable.`n" }</lang>
- Output:
Engagements: abi accepted abe cath accepted bob hope accepted col ivy accepted dan jan accepted ed bea accepted fred gay accepted gav eve accepted hal hope dumped col hope accepted ian abi dumped abe abi accepted jon dee accepted col ivy dumped dan ivy accepted abe fay accepted dan Couples: abi is engaged to jon bea is engaged to fred cath is engaged to bob dee is engaged to col eve is engaged to hal fay is engaged to dan gay is engaged to gav hope is engaged to ian ivy is engaged to abe jan is engaged to ed These couples are stable. What if cath and ivy swap? Couples: abi is engaged to jon bea is engaged to fred cath is engaged to abe dee is engaged to col eve is engaged to hal fay is engaged to dan gay is engaged to gav hope is engaged to ian ivy is engaged to bob jan is engaged to ed These couples are not stable. bob is engaged to ivy but would prefer abi and abi is engaged to jon but would prefer bob bob is engaged to ivy but would prefer bea and bea is engaged to fred but would prefer bob bob is engaged to ivy but would prefer cath and cath is engaged to abe but would prefer bob bob is engaged to ivy but would prefer fay and fay is engaged to dan but would prefer bob bob is engaged to ivy but would prefer hope and hope is engaged to ian but would prefer bob
Bracmat
<lang bracmat>( (abe.abi eve cath ivy jan dee fay bea hope gay)
(bob.cath hope abi dee eve fay bea jan ivy gay)
(col.hope eve abi dee bea fay ivy gay cath jan)
(dan.ivy fay dee gay hope eve jan bea cath abi)
(ed.jan dee bea cath fay eve abi ivy hope gay)
(fred.bea abi dee gay eve ivy cath jan hope fay)
(gav.gay eve ivy bea cath abi dee hope jan fay)
(hal.abi eve hope fay ivy cath jan bea gay dee)
(ian.hope cath dee gay bea abi fay ivy jan eve)
(jon.abi fay jan gay eve bea dee cath ivy hope)
: ?Mplan
: ?M
& (abi.bob fred jon gav ian abe dan ed col hal)
(bea.bob abe col fred gav dan ian ed jon hal)
(cath.fred bob ed gav hal col ian abe dan jon)
(dee.fred jon col abe ian hal gav dan bob ed)
(eve.jon hal fred dan abe gav col ed ian bob)
(fay.bob abe ed ian jon dan fred gav col hal)
(gay.jon gav hal fred bob abe col ed dan ian)
(hope.gav jon bob abe ian dan hal ed col fred)
(ivy.ian col hal gav fred bob abe ed jon dan)
(jan.ed hal gav abe bob jon col ian fred dan)
: ?W
& :?engaged & whl
' ( !Mplan
: ?A
(?m&~(!engaged:? (!m.?) ?).%?w ?ws)
( ?Z
& ( ( ~(!engaged:?a (?m`.!w) ?z)
& (!m.!w) !engaged
| !W:? (!w.? !m ? !m` ?) ?
& !a (!m.!w) !z
)
: ?engaged
|
)
& !Z !A (!m.!ws):?Mplan
)
)
& ( unstable
= m1 m2 w1 w2
. !arg
: ?
(?m1.?w1)
?
(?m2.?w2)
( ?
& ( !M:? (!m1.? !w2 ? !w1 ?) ?
& !W:? (!w2.? !m1 ? !m2 ?) ?
| !M:? (!m2.? !w1 ? !w2 ?) ?
& !W:? (!w1.? !m2 ? !m1 ?) ?
)
)
)
& ( unstable$!engaged&out$unstable
| out$stable )
& out$!engaged & !engaged:(?m1.?w1) (?m2.?w2) ?others & out$(swap !w1 for !w2) & ( unstable$((!m1.!w2) (!m2.!w1) !others)
& out$unstable | out$stable )
);</lang>
- Output:
stable (dan.fay) (col.dee) (hal.eve) (gav.gay) (fred.bea) (ed.jan) (abe.ivy) (ian.hope) (bob.cath) (jon.abi) swap fay for dee unstable
BBC BASIC
<lang bbcbasic> N = 10
DIM mname$(N), wname$(N), mpref$(N), wpref$(N), mpartner%(N), wpartner%(N)
DIM proposed&(N,N)
mname$() = "", "Abe","Bob","Col","Dan","Ed","Fred","Gav","Hal","Ian","Jon"
wname$() = "", "Abi","Bea","Cath","Dee","Eve","Fay","Gay","Hope","Ivy","Jan"
mpref$() = "", "AECIJDFBHG","CHADEFBJIG","HEADBFIGCJ","IFDGHEJBCA","JDBCFEAIHG",\
\ "BADGEICJHF","GEIBCADHJF","AEHFICJBGD","HCDGBAFIJE","AFJGEBDCIH"
wpref$() = "", "BFJGIADECH","BACFGDIEJH","FBEGHCIADJ","FJCAIHGDBE","JHFDAGCEIB",\
\ "BAEIJDFGCH","JGHFBACEDI","GJBAIDHECF","ICHGFBAEJD","EHGABJCIFD"
REM The Gale-Shapley algorithm:
REPEAT
FOR m% = 1 TO N
REPEAT
IF mpartner%(m%) EXIT REPEAT
FOR i% = 1 TO N
w% = ASCMID$(mpref$(m%),i%) - 64
IF proposed&(m%,w%) = 0 EXIT FOR
NEXT i%
IF i% > N EXIT REPEAT
proposed&(m%,w%) = 1
IF wpartner%(w%) = 0 THEN
mpartner%(m%) = w% : REM Get engaged
wpartner%(w%) = m%
ELSE
o% = wpartner%(w%)
IF INSTR(wpref$(w%), LEFT$(mname$(m%),1)) < \
\ INSTR(wpref$(w%), LEFT$(mname$(o%),1)) THEN
mpartner%(o%) = 0 : REM Split up
mpartner%(m%) = w% : REM Get engaged
wpartner%(w%) = m%
ENDIF
ENDIF
UNTIL TRUE
NEXT m%
UNTIL SUM(mpartner%()) = (N*(N+1))/2
FOR m% = 1 TO N
PRINT mname$(m%) " is engaged to " wname$(mpartner%(m%))
NEXT
PRINT "Relationships are ";
IF FNstable PRINT "stable." ELSE PRINT "unstable."
a% = RND(N)
REPEAT b% = RND(N) : UNTIL b%<>a%
PRINT '"Now swapping " mname$(a%) "'s and " mname$(b%) "'s partners:"
SWAP mpartner%(a%), mpartner%(b%)
PRINT mname$(a%) " is engaged to " wname$(mpartner%(a%))
PRINT mname$(b%) " is engaged to " wname$(mpartner%(b%))
PRINT "Relationships are ";
IF FNstable PRINT "stable." ELSE PRINT "unstable."
END
DEF FNstable
LOCAL m%, w%, o%, p%
FOR m% = 1 TO N
w% = mpartner%(m%)
FOR o% = 1 TO N
p% = wpartner%(o%)
IF INSTR(mpref$(m%), LEFT$(wname$(o%),1)) < \
\ INSTR(mpref$(m%), LEFT$(wname$(w%),1)) AND \
\ INSTR(wpref$(o%), LEFT$(mname$(m%),1)) < \
\ INSTR(wpref$(o%), LEFT$(mname$(p%),1)) THEN
= FALSE
ENDIF
NEXT o%
NEXT m%
= TRUE</lang>
Output:
Abe is engaged to Ivy Bob is engaged to Cath Col is engaged to Dee Dan is engaged to Fay Ed is engaged to Jan Fred is engaged to Bea Gav is engaged to Gay Hal is engaged to Eve Ian is engaged to Hope Jon is engaged to Abi Relationships are stable. Now swapping Hal's and Ian's partners: Hal is engaged to Hope Ian is engaged to Eve Relationships are unstable.
C
Oddly enough (or maybe it should be that way, only that I don't know): if the women were proposing instead of the men, the resulting pairs are exactly the same. <lang C>#include <stdio.h>
int verbose = 0; enum { clown = -1, abe, bob, col, dan, ed, fred, gav, hal, ian, jon, abi, bea, cath, dee, eve, fay, gay, hope, ivy, jan, }; const char *name[] = { "Abe", "Bob", "Col", "Dan", "Ed", "Fred", "Gav", "Hal", "Ian", "Jon", "Abi", "Bea", "Cath", "Dee", "Eve", "Fay", "Gay", "Hope", "Ivy", "Jan" }; int pref[jan + 1][jon + 1] = { { abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay }, { cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay }, { hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan }, { ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi }, { jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay }, { bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay }, { gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay }, { abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee }, { hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve }, { abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope },
{ bob, fred, jon, gav, ian, abe, dan, ed, col, hal }, { bob, abe, col, fred, gav, dan, ian, ed, jon, hal }, { fred, bob, ed, gav, hal, col, ian, abe, dan, jon }, { fred, jon, col, abe, ian, hal, gav, dan, bob, ed }, { jon, hal, fred, dan, abe, gav, col, ed, ian, bob }, { bob, abe, ed, ian, jon, dan, fred, gav, col, hal }, { jon, gav, hal, fred, bob, abe, col, ed, dan, ian }, { gav, jon, bob, abe, ian, dan, hal, ed, col, fred }, { ian, col, hal, gav, fred, bob, abe, ed, jon, dan }, { ed, hal, gav, abe, bob, jon, col, ian, fred, dan }, }; int pairs[jan + 1], proposed[jan + 1];
void engage(int man, int woman) { pairs[man] = woman; pairs[woman] = man; if (verbose) printf("%4s is engaged to %4s\n", name[man], name[woman]); }
void dump(int woman, int man) { pairs[man] = pairs[woman] = clown; if (verbose) printf("%4s dumps %4s\n", name[woman], name[man]); }
/* how high this person ranks that: lower is more preferred */ int rank(int this, int that) { int i; for (i = abe; i <= jon && pref[this][i] != that; i++); return i; }
void propose(int man, int woman) { int fiance = pairs[woman]; if (verbose) printf("%4s proposes to %4s\n", name[man], name[woman]);
if (fiance == clown) { engage(man, woman); } else if (rank(woman, man) < rank(woman, fiance)) { dump(woman, fiance); engage(man, woman); } }
int covet(int man1, int wife2) { if (rank(man1, wife2) < rank(man1, pairs[man1]) && rank(wife2, man1) < rank(wife2, pairs[wife2])) { printf( " %4s (w/ %4s) and %4s (w/ %4s) prefer each other" " over current pairing.\n", name[man1], name[pairs[man1]], name[wife2], name[pairs[wife2]] ); return 1; } return 0; }
int thy_neighbors_wife(int man1, int man2) { /* +: force checking all pairs; "||" would shortcircuit */ return covet(man1, pairs[man2]) + covet(man2, pairs[man1]); }
int unstable() { int i, j, bad = 0; for (i = abe; i < jon; i++) { for (j = i + 1; j <= jon; j++) if (thy_neighbors_wife(i, j)) bad = 1; } return bad; }
int main() { int i, unengaged; /* init: everyone marries the clown */ for (i = abe; i <= jan; i++) pairs[i] = proposed[i] = clown;
/* rounds */ do { unengaged = 0; for (i = abe; i <= jon; i++) { //for (i = abi; i <= jan; i++) { /* could let women propose */ if (pairs[i] != clown) continue; unengaged = 1; propose(i, pref[i][++proposed[i]]); } } while (unengaged);
printf("Pairing:\n"); for (i = abe; i <= jon; i++) printf(" %4s - %s\n", name[i], pairs[i] == clown ? "clown" : name[pairs[i]]);
printf(unstable() ? "Marriages not stable\n" /* draw sad face here */ : "Stable matchup\n");
printf("\nBut if Bob and Fred were to swap:\n"); i = pairs[bob]; engage(bob, pairs[fred]); engage(fred, i); printf(unstable() ? "Marriages not stable\n" : "Stable matchup\n");
return 0; }</lang>
- Output:
Pairing:
Abe - Ivy
Bob - Cath
Col - Dee
Dan - Fay
Ed - Jan
Fred - Bea
Gav - Gay
Hal - Eve
Ian - Hope
Jon - Abi
Stable matchup
But if Bob and Fred were to swap:
Fred (w/ Cath) and Ivy (w/ Abe) prefer each other over current pairing.
Bob (w/ Bea) and Fay (w/ Dan) prefer each other over current pairing.
Bob (w/ Bea) and Hope (w/ Ian) prefer each other over current pairing.
Bob (w/ Bea) and Abi (w/ Jon) prefer each other over current pairing.
Fred (w/ Cath) and Dee (w/ Col) prefer each other over current pairing.
Fred (w/ Cath) and Abi (w/ Jon) prefer each other over current pairing.
Marriages not stable
C++
<lang cpp>#include <algorithm>
- include <iostream>
- include <map>
- include <queue>
- include <string>
- include <vector>
using namespace std;
const char *men_data[][11] = {
{ "abe", "abi","eve","cath","ivy","jan","dee","fay","bea","hope","gay" },
{ "bob", "cath","hope","abi","dee","eve","fay","bea","jan","ivy","gay" },
{ "col", "hope","eve","abi","dee","bea","fay","ivy","gay","cath","jan" },
{ "dan", "ivy","fay","dee","gay","hope","eve","jan","bea","cath","abi" },
{ "ed", "jan","dee","bea","cath","fay","eve","abi","ivy","hope","gay" },
{ "fred", "bea","abi","dee","gay","eve","ivy","cath","jan","hope","fay" },
{ "gav", "gay","eve","ivy","bea","cath","abi","dee","hope","jan","fay" },
{ "hal", "abi","eve","hope","fay","ivy","cath","jan","bea","gay","dee" },
{ "ian", "hope","cath","dee","gay","bea","abi","fay","ivy","jan","eve" },
{ "jon", "abi","fay","jan","gay","eve","bea","dee","cath","ivy","hope" }
};
const char *women_data[][11] = {
{ "abi", "bob","fred","jon","gav","ian","abe","dan","ed","col","hal" },
{ "bea", "bob","abe","col","fred","gav","dan","ian","ed","jon","hal" },
{ "cath", "fred","bob","ed","gav","hal","col","ian","abe","dan","jon" },
{ "dee", "fred","jon","col","abe","ian","hal","gav","dan","bob","ed" },
{ "eve", "jon","hal","fred","dan","abe","gav","col","ed","ian","bob" },
{ "fay", "bob","abe","ed","ian","jon","dan","fred","gav","col","hal" },
{ "gay", "jon","gav","hal","fred","bob","abe","col","ed","dan","ian" },
{ "hope", "gav","jon","bob","abe","ian","dan","hal","ed","col","fred" },
{ "ivy", "ian","col","hal","gav","fred","bob","abe","ed","jon","dan" },
{ "jan", "ed","hal","gav","abe","bob","jon","col","ian","fred","dan" }
};
typedef vector<string> PrefList; typedef map<string, PrefList> PrefMap; typedef map<string, string> Couples;
// Does 'first' appear before 'second' in preference list? bool prefers(const PrefList &prefer, const string &first, const string &second) {
for (PrefList::const_iterator it = prefer.begin(); it != prefer.end(); ++it)
{
if (*it == first) return true;
if (*it == second) return false;
}
return false; // no preference
}
void check_stability(const Couples &engaged, const PrefMap &men_pref, const PrefMap &women_pref) {
cout << "Stablility:\n";
bool stable = true;
for (Couples::const_iterator it = engaged.begin(); it != engaged.end(); ++it)
{
const string &bride = it->first;
const string &groom = it->second;
const PrefList &preflist = men_pref.at(groom);
for (PrefList::const_iterator it = preflist.begin(); it != preflist.end(); ++it)
{
if (*it == bride) // he prefers his bride
break;
if (prefers(preflist, *it, bride) && // he prefers another woman
prefers(women_pref.at(*it), groom, engaged.at(*it))) // other woman prefers him
{
cout << "\t" << *it <<
" prefers " << groom <<
" over " << engaged.at(*it) <<
" and " << groom <<
" prefers " << *it <<
" over " << bride << "\n";
stable = false;
}
}
}
if (stable) cout << "\t(all marriages stable)\n";
}
int main() {
PrefMap men_pref, women_pref; queue<string> bachelors;
// init data structures
for (int i = 0; i < 10; ++i) // person
{
for (int j = 1; j < 11; ++j) // preference
{
men_pref[ men_data[i][0]].push_back( men_data[i][j]);
women_pref[women_data[i][0]].push_back(women_data[i][j]);
}
bachelors.push(men_data[i][0]);
}
Couples engaged; // <woman,man>
cout << "Matchmaking:\n";
while (!bachelors.empty())
{
const string &suitor = bachelors.front();
const PrefList &preflist = men_pref[suitor];
for (PrefList::const_iterator it = preflist.begin(); it != preflist.end(); ++it)
{
const string &bride = *it;
if (engaged.find(bride) == engaged.end()) // she's available
{
cout << "\t" << bride << " and " << suitor << "\n";
engaged[bride] = suitor; // hook up
break;
}
const string &groom = engaged[bride];
if (prefers(women_pref[bride], suitor, groom))
{
cout << "\t" << bride << " dumped " << groom << " for " << suitor << "\n";
bachelors.push(groom); // dump that zero
engaged[bride] = suitor; // get a hero
break;
}
}
bachelors.pop(); // pop at the end to not invalidate suitor reference
}
cout << "Engagements:\n";
for (Couples::const_iterator it = engaged.begin(); it != engaged.end(); ++it)
{
cout << "\t" << it->first << " and " << it->second << "\n";
}
check_stability(engaged, men_pref, women_pref);
cout << "Perturb:\n"; std::swap(engaged["abi"], engaged["bea"]); cout << "\tengage abi with " << engaged["abi"] << " and bea with " << engaged["bea"] << "\n";
check_stability(engaged, men_pref, women_pref);
}</lang>
- Output:
Matchmaking: abi and abe cath and bob hope and col ivy and dan jan and ed bea and fred gay and gav eve and hal hope dumped col for ian abi dumped abe for jon dee and col ivy dumped dan for abe fay and dan Engagements: abi and jon bea and fred cath and bob dee and col eve and hal fay and dan gay and gav hope and ian ivy and abe jan and ed Stablility: (all marriages stable) Perturb: engage abi with fred and bea with jon Stablility: bea prefers fred over jon and fred prefers bea over abi fay prefers jon over dan and jon prefers fay over bea gay prefers jon over gav and jon prefers gay over bea eve prefers jon over hal and jon prefers eve over bea
C#
(This is a straight-up translation of the Objective-C version.) <lang csharp>using System; using System.Collections.Generic;
namespace StableMarriage {
class Person
{
private int _candidateIndex;
public string Name { get; set; }
public List<Person> Prefs { get; set; }
public Person Fiance { get; set; }
public Person(string name) {
Name = name;
Prefs = null;
Fiance = null;
_candidateIndex = 0;
}
public bool Prefers(Person p) {
return Prefs.FindIndex(o => o == p) < Prefs.FindIndex(o => o == Fiance);
}
public Person NextCandidateNotYetProposedTo() {
if (_candidateIndex >= Prefs.Count) return null;
return Prefs[_candidateIndex++];
}
public void EngageTo(Person p) {
if (p.Fiance != null) p.Fiance.Fiance = null;
p.Fiance = this;
if (Fiance != null) Fiance.Fiance = null;
Fiance = p;
}
}
static class MainClass
{
static public bool IsStable(List<Person> men) {
List<Person> women = men[0].Prefs;
foreach (Person guy in men) {
foreach (Person gal in women) {
if (guy.Prefers(gal) && gal.Prefers(guy))
return false;
}
}
return true;
}
static void DoMarriage() {
Person abe = new Person("abe");
Person bob = new Person("bob");
Person col = new Person("col");
Person dan = new Person("dan");
Person ed = new Person("ed");
Person fred = new Person("fred");
Person gav = new Person("gav");
Person hal = new Person("hal");
Person ian = new Person("ian");
Person jon = new Person("jon");
Person abi = new Person("abi");
Person bea = new Person("bea");
Person cath = new Person("cath");
Person dee = new Person("dee");
Person eve = new Person("eve");
Person fay = new Person("fay");
Person gay = new Person("gay");
Person hope = new Person("hope");
Person ivy = new Person("ivy");
Person jan = new Person("jan");
abe.Prefs = new List<Person>() {abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay};
bob.Prefs = new List<Person>() {cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay};
col.Prefs = new List<Person>() {hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan};
dan.Prefs = new List<Person>() {ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi};
ed.Prefs = new List<Person>() {jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay};
fred.Prefs = new List<Person>() {bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay};
gav.Prefs = new List<Person>() {gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay};
hal.Prefs = new List<Person>() {abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee};
ian.Prefs = new List<Person>() {hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve};
jon.Prefs = new List<Person>() {abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope};
abi.Prefs = new List<Person>() {bob, fred, jon, gav, ian, abe, dan, ed, col, hal};
bea.Prefs = new List<Person>() {bob, abe, col, fred, gav, dan, ian, ed, jon, hal};
cath.Prefs = new List<Person>() {fred, bob, ed, gav, hal, col, ian, abe, dan, jon};
dee.Prefs = new List<Person>() {fred, jon, col, abe, ian, hal, gav, dan, bob, ed};
eve.Prefs = new List<Person>() {jon, hal, fred, dan, abe, gav, col, ed, ian, bob};
fay.Prefs = new List<Person>() {bob, abe, ed, ian, jon, dan, fred, gav, col, hal};
gay.Prefs = new List<Person>() {jon, gav, hal, fred, bob, abe, col, ed, dan, ian};
hope.Prefs = new List<Person>() {gav, jon, bob, abe, ian, dan, hal, ed, col, fred};
ivy.Prefs = new List<Person>() {ian, col, hal, gav, fred, bob, abe, ed, jon, dan};
jan.Prefs = new List<Person>() {ed, hal, gav, abe, bob, jon, col, ian, fred, dan};
List<Person> men = new List<Person>(abi.Prefs);
int freeMenCount = men.Count;
while (freeMenCount > 0) {
foreach (Person guy in men) {
if (guy.Fiance == null) {
Person gal = guy.NextCandidateNotYetProposedTo();
if (gal.Fiance == null) {
guy.EngageTo(gal);
freeMenCount--;
} else if (gal.Prefers(guy)) {
guy.EngageTo(gal);
}
}
}
}
foreach (Person guy in men) {
Console.WriteLine("{0} is engaged to {1}", guy.Name, guy.Fiance.Name);
}
Console.WriteLine("Stable = {0}", IsStable(men));
Console.WriteLine("\nSwitching fred & jon's partners");
Person jonsFiance = jon.Fiance;
Person fredsFiance = fred.Fiance;
fred.EngageTo(jonsFiance);
jon.EngageTo(fredsFiance);
Console.WriteLine("Stable = {0}", IsStable(men));
}
public static void Main(string[] args)
{
DoMarriage();
}
}
}</lang>
- Output:
bob is engaged to cath fred is engaged to bea jon is engaged to abi gav is engaged to gay ian is engaged to hope abe is engaged to ivy dan is engaged to fay ed is engaged to jan col is engaged to dee hal is engaged to eve Stable = True Switching fred & jon's partners Stable = False
CoffeeScript
<lang coffeescript>class Person
constructor: (@name, @preferences) ->
@mate = null
@best_mate_rank = 0
@rank = {}
for preference, i in @preferences
@rank[preference] = i
preferred_mate_name: =>
@preferences[@best_mate_rank]
reject: =>
@best_mate_rank += 1
set_mate: (mate) =>
@mate = mate
offer_mate: (free_mate, reject_mate_cb) =>
if @mate
if @covets(free_mate)
console.log "#{free_mate.name} steals #{@name} from #{@mate.name}"
reject_mate_cb @mate
free_mate.set_mate @
@set_mate free_mate
else
console.log "#{free_mate.name} cannot steal #{@name} from #{@mate.name}"
reject_mate_cb free_mate
else
console.log "#{free_mate.name} gets #{@name} first"
free_mate.set_mate @
@set_mate free_mate
happiness: =>
@rank[@mate.name]
covets: (other_mate) =>
@rank[other_mate.name] <= @rank[@mate.name]
persons_by_name = (persons) ->
hsh = {}
for person in persons
hsh[person.name] = person
hsh
mate_off = (guys, gals) ->
free_pursuers = (guy for guy in guys) guys_by_name = persons_by_name guys gals_by_name = persons_by_name gals
while free_pursuers.length > 0
free_pursuer = free_pursuers.shift()
gal_name = free_pursuer.preferred_mate_name()
gal = gals_by_name[gal_name]
reject_mate_cb = (guy) ->
guy.reject()
free_pursuers.push guy
gal.offer_mate free_pursuer, reject_mate_cb
report_on_mates = (guys) ->
console.log "\n----Marriage Report"
for guy, i in guys
throw Error("illegal marriage") if guy.mate.mate isnt guy
console.log guy.name, guy.mate.name, \
"(his choice #{guy.happiness()}, her choice #{guy.mate.happiness()} )"
report_potential_adulteries = (guys) ->
for guy1, i in guys
gal1 = guy1.mate
for j in [0...i]
guy2 = guys[j]
gal2 = guy2.mate
if guy1.covets(gal2) and gal2.covets(guy1)
console.log "#{guy1.name} and #{gal2.name} would stray"
if guy2.covets(gal1) and gal1.covets(guy2)
console.log "#{guy2.name} and #{gal1.name} would stray"
perturb = (guys) ->
# mess up marriages by swapping two couples...this is mainly to drive
# out that report_potential_adulteries will actually work
guy0 = guys[0]
guy1 = guys[1]
gal0 = guy0.mate
gal1 = guy1.mate
console.log "\nPerturbing with #{guy0.name}, #{gal0.name}, #{guy1.name}, #{gal1.name}"
guy0.set_mate gal1
guy1.set_mate gal0
gal1.set_mate guy0
gal0.set_mate guy1
Population = ->
guy_preferences = abe: ['abi', 'eve', 'cath', 'ivy', 'jan', 'dee', 'fay', 'bea', 'hope', 'gay'] bob: ['cath', 'hope', 'abi', 'dee', 'eve', 'fay', 'bea', 'jan', 'ivy', 'gay'] col: ['hope', 'eve', 'abi', 'dee', 'bea', 'fay', 'ivy', 'gay', 'cath', 'jan'] dan: ['ivy', 'fay', 'dee', 'gay', 'hope', 'eve', 'jan', 'bea', 'cath', 'abi'] ed: ['jan', 'dee', 'bea', 'cath', 'fay', 'eve', 'abi', 'ivy', 'hope', 'gay'] fred: ['bea', 'abi', 'dee', 'gay', 'eve', 'ivy', 'cath', 'jan', 'hope', 'fay'] gav: ['gay', 'eve', 'ivy', 'bea', 'cath', 'abi', 'dee', 'hope', 'jan', 'fay'] hal: ['abi', 'eve', 'hope', 'fay', 'ivy', 'cath', 'jan', 'bea', 'gay', 'dee'] ian: ['hope', 'cath', 'dee', 'gay', 'bea', 'abi', 'fay', 'ivy', 'jan', 'eve'] jon: ['abi', 'fay', 'jan', 'gay', 'eve', 'bea', 'dee', 'cath', 'ivy', 'hope'] gal_preferences = abi: ['bob', 'fred', 'jon', 'gav', 'ian', 'abe', 'dan', 'ed', 'col', 'hal'] bea: ['bob', 'abe', 'col', 'fred', 'gav', 'dan', 'ian', 'ed', 'jon', 'hal'] cath: ['fred', 'bob', 'ed', 'gav', 'hal', 'col', 'ian', 'abe', 'dan', 'jon'] dee: ['fred', 'jon', 'col', 'abe', 'ian', 'hal', 'gav', 'dan', 'bob', 'ed'] eve: ['jon', 'hal', 'fred', 'dan', 'abe', 'gav', 'col', 'ed', 'ian', 'bob'] fay: ['bob', 'abe', 'ed', 'ian', 'jon', 'dan', 'fred', 'gav', 'col', 'hal'] gay: ['jon', 'gav', 'hal', 'fred', 'bob', 'abe', 'col', 'ed', 'dan', 'ian'] hope: ['gav', 'jon', 'bob', 'abe', 'ian', 'dan', 'hal', 'ed', 'col', 'fred'] ivy: ['ian', 'col', 'hal', 'gav', 'fred', 'bob', 'abe', 'ed', 'jon', 'dan'] jan: ['ed', 'hal', 'gav', 'abe', 'bob', 'jon', 'col', 'ian', 'fred', 'dan']
guys = (new Person(name, preferences) for name, preferences of guy_preferences) gals = (new Person(name, preferences) for name, preferences of gal_preferences) [guys, gals]
do ->
[guys, gals] = Population() mate_off guys, gals report_on_mates guys report_potential_adulteries guys perturb guys report_on_mates guys report_potential_adulteries guys</lang>
- Output:
> coffee stable_marriage.coffee abe gets abi first bob gets cath first col gets hope first dan gets ivy first ed gets jan first fred gets bea first gav gets gay first hal cannot steal abi from abe ian steals hope from col jon steals abi from abe hal gets eve first col cannot steal eve from hal abe cannot steal eve from hal col cannot steal abi from jon abe cannot steal cath from bob col gets dee first abe steals ivy from dan dan gets fay first ----Marriage Report abe ivy (his choice 3, her choice 6 ) bob cath (his choice 0, her choice 1 ) col dee (his choice 3, her choice 2 ) dan fay (his choice 1, her choice 5 ) ed jan (his choice 0, her choice 0 ) fred bea (his choice 0, her choice 3 ) gav gay (his choice 0, her choice 1 ) hal eve (his choice 1, her choice 1 ) ian hope (his choice 0, her choice 4 ) jon abi (his choice 0, her choice 2 ) Perturbing with abe, ivy, bob, cath ----Marriage Report abe cath (his choice 2, her choice 7 ) bob ivy (his choice 8, her choice 5 ) col dee (his choice 3, her choice 2 ) dan fay (his choice 1, her choice 5 ) ed jan (his choice 0, her choice 0 ) fred bea (his choice 0, her choice 3 ) gav gay (his choice 0, her choice 1 ) hal eve (his choice 1, her choice 1 ) ian hope (his choice 0, her choice 4 ) jon abi (his choice 0, her choice 2 ) bob and cath would stray bob and fay would stray bob and bea would stray bob and hope would stray bob and abi would stray
ColdFusion
<lang cfm> PERSON.CFC
component displayName="Person" accessors="true" {
property name="Name" type="string"; property name="MrOrMrsGoodEnough" type="Person"; property name="UnrealisticExpectations" type="array"; property name="PersonalHistory" type="array";
public Person function init( required String name ) {
setName( arguments.name );
setPersonalHistory([ getName() & " is on the market." ]);
this.HotnessScale = 0;
return this;
}
public Boolean function hasSettled() {
// if we have settled, return true;
return isInstanceOf( getMrOrMrsGoodEnough(), "Person" );
}
public Person function getBestOfWhatIsLeft() {
// increment the hotness scale...1 is best, 10 is...well...VERY settling.
this.HotnessScale++;
// get the match from the current rung in the barrel
var bestChoice = getUnrealisticExpectations()[ this.HotnessScale ];
return bestChoice;
}
public Boolean function wouldRatherBeWith( required Person person ) {
// only compare if we've already settled on a potential mate
if( isInstanceOf( this.getMrOrMrsGoodEnough(), "Person" ) ) {
// if the new person's hotness is greater (numerically smaller) than our current beau...
return getHotness( this, arguments.person ) < getHotness( this, this.getMrOrMrsGoodEnough() );
}
return false;
}
public Void function settle( required Person person ) {
if( person.hasSettled() ) {
// this is the match we want. Force a break up of a previous relationship (sorry!)
dumpLikeATonOfBricks( person );
}
person.setMrOrMrsGoodEnough( this );
if( hasSettled() ) {
// this is the match we want, so write a dear john to our current match
dumpLikeATonOfBricks( this );
}
logHookup( arguments.person );
// we've found the mate of our dreams!
setMrOrMrsGoodEnough( arguments.person );
}
public Void function swing( required Person person ) {
// get our spouses
var mySpouse = getMrOrMrsGoodEnough();
var notMySpouse = arguments.person.getMrOrMrsGoodEnough();
// swap em'
setMrOrMrsGoodEnough( notMySpouse );
person.setMrOrMrsGoodEnough( mySpouse );
}
public Void function dumpLikeATonOfBricks( required Person person ) {
logBreakup( arguments.person );
person.getMrOrMrsGoodEnough().setMrOrMrsGoodEnough( JavaCast( "null", "" ) );
}
public String function psychoAnalyze() {
logNuptuals();
logRegrets();
var personalJourney = "";
for( var entry in getPersonalHistory() ) {
personalJourney = personalJourney & entry & "
";
}
return personalJourney;
}
private Numeric function getHotness( required Person pursuer, required Person pursued ) {
var pursuersExpectations = pursuer.getUnrealisticExpectations();
var hotnessFactor = 1;
for( var hotnessFactor=1; hotnessFactor<=arrayLen( pursuersExpectations ); hotnessFactor++ ) {
if( pursuersExpectations[ hotnessFactor ].getName()==arguments.pursued.getName() ) {
return hotnessFactor;
}
}
}
private Void function logRegrets() {
var spouse = getMrOrMrsGoodEnough();
var spouseHotness = getHotness( this, spouse );
var myHotness = getHotness( spouse, this );
if( spouseHotness == 1 && myHotness == 1 ) {
arrayAppend( getPersonalHistory(), "Yes, yes, the beautiful people always find happy endings: #getName()# (her ###myHotness#), #spouse.getName()# (his ###spouseHotness#)");
}
else if( spouseHotness == myHotness ) {
arrayAppend( getPersonalHistory(), "#getName()# (her ###myHotness#) was made for #spouse.getName()# (his ###spouseHotness#). How precious.");
}
else if( spouseHotness > myHotness ) {
arrayAppend( getPersonalHistory(), "#getName()# (her ###myHotness#) could have done better than #spouse.getName()# (his ###spouseHotness#). Poor slob.");
}
else {
arrayAppend( getPersonalHistory(), "#getName()# (her ###myHotness#) is a lucky bastard to have landed #spouse.getName()# (his ###spouseHotness#).");
}
}
private Void function logNuptuals() {
arrayAppend( getPersonalHistory(), "#getName()# has settled for #getMrOrMrsGoodEnough().getName()#." );
}
private Void function logHookup( required Person person ) {
var winnerHotness = getHotness( this, arguments.person );
var myHotness = getHotness( arguments.person, this );
arrayAppend( getPersonalHistory(), "#getName()# (her ###myHotness#) is checking out #arguments.person.getName()# (his ###winnerHotness#), but wants to keep his options open.");
}
private Void function logBreakup( required Person person ) {
var scrub = person.getMrOrMrsGoodEnough();
var scrubHotness = getHotness( person, scrub );
var myHotness = getHotness( person, this );
arrayAppend( getPersonalHistory(), "#getName()# is so hot (her ###myHotness#) that #person.getName()# is dumping #scrub.getName()# (her ###scrubHotness#)");
}
} </lang> <lang cfm> INDEX.CFM
<cfscript>
/**
* Let's get these crazy kids married!
* @men.hint The men who want to get married
*/
function doCreepyMassMarriages( required Array men ) {
marriagesAreStable = false;
while( !marriagesAreStable ) {
marriagesAreStable = true;
for( man in men ) {
if( !man.hasSettled() ) {
marriagesAreStable = false;
sexyLady = man.getBestOfWhatIsLeft();
if( !sexyLady.hasSettled() || sexyLady.wouldRatherBeWith( man ) ) {
man.settle( sexyLady );
}
}
}
}
return men;
}
/**
* We played God...now let's see if society is going to survive
* @men.hint The married men
* @women.hint The married women
*/
function isSocietyStable( required Array men, required Array women ) {
// loop over married men
for( var man in arguments.men ) {
// loop over married women
for( var woman in arguments.women ) {
// if the man does not prefer this woman to his current spouse, and the women
// doesn't prefer the man to her current spouse, this is the best possible match
if( man.wouldRatherBeWith( woman ) && woman.wouldRatherBeWith( man ) ) {
return false;
}
}
}
return true;
}
// the men abe = new Person( "Abe" ); bob = new Person( "Bob" ); col = new Person( "Col" ); dan = new Person( "Dan" ); ed = new Person( "Ed" ); fred = new Person( "Fred" ); gav = new Person( "Gav" ); hal = new Person( "Hal" ); ian = new Person( "Ian" ); jon = new Person( "Jon" );
men = [ abe, bob, col, dan, ed, fred, gav, hal, ian, jon ];
// the women abi = new Person( "Abi" ); bea = new Person( "Bea" ); cath = new Person( "Cath" ); dee = new Person( "Dee" ); eve = new Person( "Eve" ); fay = new Person( "Fay" ); gay = new Person( "Gay" ); hope = new Person( "Hope" ); ivy = new Person( "Ivy" ); jan = new Person( "Jan" );
women = [ abi, bea, cath, dee, eve, fay, gay, hope, ivy, jan ];
// set unrealistic expectations for the men abe.setUnrealisticExpectations([ abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay ]); bob.setUnrealisticExpectations([ cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay ]); col.setUnrealisticExpectations([ hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan ]); dan.setUnrealisticExpectations([ ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi ]); ed.setUnrealisticExpectations([ jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay ]); fred.setUnrealisticExpectations([ bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay ]); gav.setUnrealisticExpectations([ gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay ]); hal.setUnrealisticExpectations([ abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee ]); ian.setUnrealisticExpectations([ hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve ]); jon.setUnrealisticExpectations([ abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope ]); // set unrealistic expectations for the women abi.setUnrealisticExpectations([ bob, fred, jon, gav, ian, abe, dan, ed, col, hal ]); bea.setUnrealisticExpectations([ bob, abe, col, fred, gav, dan, ian, ed, jon, hal ]); cath.setUnrealisticExpectations([ fred, bob, ed, gav, hal, col, ian, abe, dan, jon ]); dee.setUnrealisticExpectations([ fred, jon, col, abe, ian, hal, gav, dan, bob, ed ]); eve.setUnrealisticExpectations([ jon, hal, fred, dan, abe, gav, col, ed, ian, bob ]); fay.setUnrealisticExpectations([ bob, abe, ed, ian, jon, dan, fred, gav, col, hal ]); gay.setUnrealisticExpectations([ jon, gav, hal, fred, bob, abe, col, ed, dan, ian ]); hope.setUnrealisticExpectations([ gav, jon, bob, abe, ian, dan, hal, ed, col, fred ]); ivy.setUnrealisticExpectations([ ian, col, hal, gav, fred, bob, abe, ed, jon, dan ]); jan.setUnrealisticExpectations([ ed, hal, gav, abe, bob, jon, col, ian, fred, dan ]);
// here comes the bride, duhn, duhn, duh-duhn
possiblyHappilyMarriedMen = doCreepyMassMarriages( men );
// let's see who shacked up!
for( man in possiblyHappilyMarriedMen ) {
writeoutput( man.psychoAnalyze() & "
" );
}
// check if society is stable
if( isSocietyStable( men, women ) ) {
writeoutput( "Hey, look at that. Creepy social engineering works. Sort of...
" );
}
// what happens if couples start swingin'?
jon.swing( fred );
writeoutput( "Swapping Jon and Fred's wives...will society survive?
" );
// check if society is still stable after the swingers
if( !isSocietyStable( men, women ) ) {
writeoutput( "Nope, now everything is broken. Sharing spouses doesn't work, kids.
" );
}
</cfscript> </lang>
- Output:
Abe is on the market. Abe (her #6) is checking out Abi (his #1), but wants to keep his options open. Abe (her #5) is checking out Eve (his #2), but wants to keep his options open. Abe is so hot (her #7) that Ivy is dumping Dan (her #10) Abe (her #7) is checking out Ivy (his #4), but wants to keep his options open. Abe has settled for Ivy. Abe (her #7) is lucky to have landed Ivy (his #4). Bob is on the market. Bob (her #2) is checking out Cath (his #1), but wants to keep his options open. Bob has settled for Cath. Bob (her #2) is lucky to have landed Cath (his #1). Col is on the market. Col (her #9) is checking out Hope (his #1), but wants to keep his options open. Col (her #3) is checking out Dee (his #4), but wants to keep his options open. Col has settled for Dee. Col (her #3) could have done better than Dee (his #4). Dan is on the market. Dan (her #10) is checking out Ivy (his #1), but wants to keep his options open. Dan (her #6) is checking out Fay (his #2), but wants to keep his options open. Dan has settled for Fay. Dan (her #6) is lucky to have landed Fay (his #2). Ed is on the market. Ed (her #1) is checking out Jan (his #1), but wants to keep his options open. Ed has settled for Jan. Yes, yes, the beautiful people always find happy endings: Ed (her #1), Jan (his #1) Fred is on the market. Fred (her #4) is checking out Bea (his #1), but wants to keep his options open. Fred has settled for Bea. Fred (her #4) is lucky to have landed Bea (his #1). Gav is on the market. Gav (her #2) is checking out Gay (his #1), but wants to keep his options open. Gav has settled for Gay. Gav (her #2) is lucky to have landed Gay (his #1). Hal is on the market. Hal is so hot (her #2) that Eve is dumping Abe (her #5) Hal (her #2) is checking out Eve (his #2), but wants to keep his options open. Hal has settled for Eve. Hal (her #2) was made for Eve (his #2). How precious. Ian is on the market. Ian is so hot (her #5) that Hope is dumping Col (her #9) Ian (her #5) is checking out Hope (his #1), but wants to keep his options open. Ian has settled for Hope. Ian (her #5) is lucky to have landed Hope (his #1). Jon is on the market. Jon is so hot (her #3) that Abi is dumping Abe (her #6) Jon (her #3) is checking out Abi (his #1), but wants to keep his options open. Jon has settled for Abi. Jon (her #3) is lucky to have landed Abi (his #1). // Is society stable? Hey, look at that. Creepy social engineering works. Sort of... Swapping Jon and Fred's wives...will society survive? // How about now? Still stable? Nope, now everything is broken. Sharing spouses doesn't work, kids.
D
From the Python and Java versions: <lang d>import std.stdio, std.array, std.algorithm, std.string;
string[string] matchmaker(string[][string] guyPrefers,
string[][string] girlPrefers) /*@safe*/ {
string[string] engagedTo;
string[] freeGuys = guyPrefers.keys;
while (freeGuys.length) {
const string thisGuy = freeGuys[0];
freeGuys.popFront();
const auto thisGuyPrefers = guyPrefers[thisGuy];
foreach (girl; thisGuyPrefers) {
if (girl !in engagedTo) { // girl is free
engagedTo[girl] = thisGuy;
break;
} else {
string otherGuy = engagedTo[girl];
string[] thisGirlPrefers = girlPrefers[girl];
if (thisGirlPrefers.countUntil(thisGuy) <
thisGirlPrefers.countUntil(otherGuy)) {
// this girl prefers this guy to
// the guy she's engagedTo to.
engagedTo[girl] = thisGuy;
freeGuys ~= otherGuy;
break;
}
// else no change, keep looking for this guy
}
}
}
return engagedTo;
}
bool check(bool doPrint=false)(string[string] engagedTo,
string[][string] guyPrefers,
string[][string] galPrefers) @safe {
enum MSG = "%s likes %s better than %s and %s " ~
"likes %s better than their current partner";
string[string] inverseEngaged;
foreach (k, v; engagedTo)
inverseEngaged[v] = k;
foreach (she, he; engagedTo) {
auto sheLikes = galPrefers[she];
auto sheLikesBetter = sheLikes[0 .. sheLikes.countUntil(he)];
auto heLikes = guyPrefers[he];
auto heLikesBetter = heLikes[0 .. heLikes.countUntil(she)];
foreach (guy; sheLikesBetter) {
auto guysGirl = inverseEngaged[guy];
auto guyLikes = guyPrefers[guy];
if (guyLikes.countUntil(guysGirl) >
guyLikes.countUntil(she)) {
static if (doPrint)
writefln(MSG, she, guy, he, guy, she);
return false;
}
}
foreach (gal; heLikesBetter) {
auto girlsGuy = engagedTo[gal];
auto galLikes = galPrefers[gal];
if (galLikes.countUntil(girlsGuy) >
galLikes.countUntil(he)) {
static if (doPrint)
writefln(MSG, he, gal, she, gal, he);
return false;
}
}
}
return true;
}
void main() /*@safe*/ {
auto guyData = "abe abi eve cath ivy jan dee fay bea hope gay
bob cath hope abi dee eve fay bea jan ivy gay
col hope eve abi dee bea fay ivy gay cath jan
dan ivy fay dee gay hope eve jan bea cath abi
ed jan dee bea cath fay eve abi ivy hope gay
fred bea abi dee gay eve ivy cath jan hope fay
gav gay eve ivy bea cath abi dee hope jan fay
hal abi eve hope fay ivy cath jan bea gay dee
ian hope cath dee gay bea abi fay ivy jan eve
jon abi fay jan gay eve bea dee cath ivy hope";
auto galData = "abi bob fred jon gav ian abe dan ed col hal
bea bob abe col fred gav dan ian ed jon hal
cath fred bob ed gav hal col ian abe dan jon
dee fred jon col abe ian hal gav dan bob ed
eve jon hal fred dan abe gav col ed ian bob
fay bob abe ed ian jon dan fred gav col hal
gay jon gav hal fred bob abe col ed dan ian
hope gav jon bob abe ian dan hal ed col fred
ivy ian col hal gav fred bob abe ed jon dan
jan ed hal gav abe bob jon col ian fred dan";
string[][string] guyPrefers, galPrefers;
foreach (line; guyData.splitLines())
guyPrefers[split(line)[0]] = split(line)[1..$];
foreach (line; galData.splitLines())
galPrefers[split(line)[0]] = split(line)[1..$];
writeln("Engagements:");
auto engagedTo = matchmaker(guyPrefers, galPrefers);
writeln("\nCouples:");
string[] parts;
foreach (k; engagedTo.keys.sort())
writefln("%s is engagedTo to %s", k, engagedTo[k]);
writeln();
bool c = check!(true)(engagedTo, guyPrefers, galPrefers);
writeln("Marriages are ", c ? "stable" : "unstable");
writeln("\n\nSwapping two fiances to introduce an error");
auto gals = galPrefers.keys.sort();
swap(engagedTo[gals[0]], engagedTo[gals[1]]);
foreach (gal; gals[0 .. 2])
writefln(" %s is now engagedTo to %s", gal, engagedTo[gal]);
writeln();
c = check!(true)(engagedTo, guyPrefers, galPrefers);
writeln("Marriages are ", c ? "stable" : "unstable");
}</lang>
- Output:
Engagements: Couples: abi is engagedTo to jon bea is engagedTo to fred cath is engagedTo to bob dee is engagedTo to col eve is engagedTo to hal fay is engagedTo to dan gay is engagedTo to gav hope is engagedTo to ian ivy is engagedTo to abe jan is engagedTo to ed Marriages are stable Swapping two fiances to introduce an error abi is now engagedTo to fred bea is now engagedTo to jon fred likes bea better than abi and bea likes fred better than their current partner Marriages are unstable
Stronger Version
<lang d>import std.stdio, std.algorithm, std.array;
enum F { abi, bea, cath, dee, eve, fay, gay, hope, ivy, jan } enum M { abe, bob, col, dan, ed, fred, gav, hal, ian, jon }
alias PrefMapF = M[][F]; alias PrefMapM = F[][M]; alias Couples = M[F];
immutable PrefMapF womenPref; immutable PrefMapM menPref;
static this() pure nothrow @safe {
with (F) with (M) {
womenPref = [
abi: [bob, fred, jon, gav, ian, abe, dan, ed, col, hal],
bea: [bob, abe, col, fred, gav, dan, ian, ed, jon, hal],
cath: [fred, bob, ed, gav, hal, col, ian, abe, dan, jon],
dee: [fred, jon, col, abe, ian, hal, gav, dan, bob, ed],
eve: [jon, hal, fred, dan, abe, gav, col, ed, ian, bob],
fay: [bob, abe, ed, ian, jon, dan, fred, gav, col, hal],
gay: [jon, gav, hal, fred, bob, abe, col, ed, dan, ian],
hope: [gav, jon, bob, abe, ian, dan, hal, ed, col, fred],
ivy: [ian, col, hal, gav, fred, bob, abe, ed, jon, dan],
jan: [ed, hal, gav, abe, bob, jon, col, ian, fred, dan]
];
menPref = [
abe: [abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay],
bob: [cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay],
col: [hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan],
dan: [ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi],
ed: [jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay],
fred: [bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay],
gav: [gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay],
hal: [abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee],
ian: [hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve],
jon: [abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope]
];
}
}
/// Does 'first' appear before 'second' in preference list? bool prefers(T)(in T[] preference, in T first, in T second) pure nothrow @safe @nogc if (is(T == F) || is(T == M)) {
//const found = preference.findAmong([first, second]); immutable T[2] two = [first, second]; const found = preference.findAmong(two[]); return !(found.empty || found.front == second);
}
void checkStability(in Couples engaged, in PrefMapM menPref,
in PrefMapF womenPref) @safe {
"Stablility:".writeln;
bool stable = true;
foreach (immutable bride, immutable groom; engaged) {
const prefList = menPref[groom];
foreach (immutable pr; prefList) {
if (pr == bride) // He prefers his bride.
break;
if (prefers(prefList, pr, bride) &&
// He prefers another woman.
prefers(womenPref[pr], groom, engaged[pr])) {
// Other woman prefers him.
writeln("\t", pr, " prefers ", groom, " over ",
engaged[pr], " and ", groom, " prefers ",
pr, " over ", bride);
stable = false;
}
}
}
if (stable)
"\t(all marriages stable)".writeln;
}
void main() /*@safe*/ {
auto bachelors = menPref.keys.sort().release;// No queue in Phobos. Couples engaged;
"Matchmaking:".writeln;
while (!bachelors.empty) {
immutable suitor = bachelors[0];
bachelors.popFront;
immutable prefList = menPref[suitor];
foreach (immutable bride; prefList) {
if (bride !in engaged) { // She's available.
writeln("\t", bride, " and ", suitor);
engaged[bride] = suitor; // Hook up.
break;
}
immutable groom = engaged[bride];
if (prefers(womenPref[bride], suitor, groom)) {
writeln("\t", bride, " dumped ", groom,
" for ", suitor);
bachelors ~= groom; // Dump that zero.
engaged[bride] = suitor; // Get a hero.
break;
}
}
}
"Engagements:".writeln;
foreach (immutable first, immutable second; engaged)
writeln("\t", first, " and ", second);
checkStability(engaged, menPref, womenPref);
"Perturb:".writeln;
engaged[F.abi].swap(engaged[F.bea]);
writeln("\tengage abi with ", engaged[F.abi],
" and bea with ", engaged[F.bea]);
checkStability(engaged, menPref, womenPref);
} </lang>
- Output:
Matchmaking:
abi and abe
cath and bob
hope and col
ivy and dan
jan and ed
bea and fred
gay and gav
eve and hal
hope dumped col for ian
abi dumped abe for jon
dee and col
ivy dumped dan for abe
fay and dan
Engagements:
abi and jon
ivy and abe
eve and hal
jan and ed
bea and fred
fay and dan
cath and bob
gay and gav
hope and ian
dee and col
Stablility:
(all marriages stable)
Perturb:
engage abi with fred and bea with jon
Stablility:
bea prefers fred over jon and fred prefers bea over abi
fay prefers jon over dan and jon prefers fay over bea
gay prefers jon over gav and jon prefers gay over bea
eve prefers jon over hal and jon prefers eve over bea
F#
<lang fsharp>let menPrefs =
Map.ofList
["abe", ["abi";"eve";"cath";"ivy";"jan";"dee";"fay";"bea";"hope";"gay"];
"bob", ["cath";"hope";"abi";"dee";"eve";"fay";"bea";"jan";"ivy";"gay"];
"col", ["hope";"eve";"abi";"dee";"bea";"fay";"ivy";"gay";"cath";"jan"];
"dan", ["ivy";"fay";"dee";"gay";"hope";"eve";"jan";"bea";"cath";"abi"];
"ed", ["jan";"dee";"bea";"cath";"fay";"eve";"abi";"ivy";"hope";"gay"];
"fred", ["bea";"abi";"dee";"gay";"eve";"ivy";"cath";"jan";"hope";"fay"];
"gav", ["gay";"eve";"ivy";"bea";"cath";"abi";"dee";"hope";"jan";"fay"];
"hal", ["abi";"eve";"hope";"fay";"ivy";"cath";"jan";"bea";"gay";"dee"];
"ian", ["hope";"cath";"dee";"gay";"bea";"abi";"fay";"ivy";"jan";"eve"];
"jon", ["abi";"fay";"jan";"gay";"eve";"bea";"dee";"cath";"ivy";"hope"];
]
let womenPrefs =
Map.ofList
["abi", ["bob";"fred";"jon";"gav";"ian";"abe";"dan";"ed";"col";"hal"];
"bea", ["bob";"abe";"col";"fred";"gav";"dan";"ian";"ed";"jon";"hal"];
"cath", ["fred";"bob";"ed";"gav";"hal";"col";"ian";"abe";"dan";"jon"];
"dee", ["fred";"jon";"col";"abe";"ian";"hal";"gav";"dan";"bob";"ed"];
"eve", ["jon";"hal";"fred";"dan";"abe";"gav";"col";"ed";"ian";"bob"];
"fay", ["bob";"abe";"ed";"ian";"jon";"dan";"fred";"gav";"col";"hal"];
"gay", ["jon";"gav";"hal";"fred";"bob";"abe";"col";"ed";"dan";"ian"];
"hope", ["gav";"jon";"bob";"abe";"ian";"dan";"hal";"ed";"col";"fred"];
"ivy", ["ian";"col";"hal";"gav";"fred";"bob";"abe";"ed";"jon";"dan"];
"jan", ["ed";"hal";"gav";"abe";"bob";"jon";"col";"ian";"fred";"dan"];
]
let men = menPrefs |> Map.toList |> List.map fst |> List.sort let women = womenPrefs |> Map.toList |> List.map fst |> List.sort
type Configuration =
{
proposed: Map<string,string list>; // man -> list of women
wifeOf: Map<string, string>; // man -> woman
husbandOf: Map<string, string>; // woman -> man
}
// query functions
let isFreeMan config man = config.wifeOf.TryFind man = None
let isFreeWoman config woman = config.husbandOf.TryFind woman = None
let hasProposedTo config man woman =
defaultArg (config.proposed.TryFind(man)) [] |> List.exists ((=) woman)
// helper let negate f = fun x -> not (f x)
// returns those 'women' who 'man' has not proposed to before let notProposedBy config man women = List.filter (negate (hasProposedTo config man)) women
let prefers (prefs:Map<string,string list>) w m1 m2 =
let order = prefs.[w] let m1i = List.findIndex ((=) m1) order let m2i = List.findIndex ((=) m2) order m1i < m2i
let womanPrefers = prefers womenPrefs let manPrefers = prefers menPrefs
// returns the women that m likes better than his current fiancée let preferredWomen config m =
let w = config.wifeOf.[m] women |> List.filter (fun w' -> manPrefers m w' w) // '
// whether there is a woman who m likes better than his current fiancée // and who also likes him better than her current fiancé let prefersAWomanWhoAlsoPrefersHim config m =
preferredWomen config m |> List.exists (fun w -> womanPrefers w m config.husbandOf.[w])
let isStable config =
not (List.exists (prefersAWomanWhoAlsoPrefersHim config) men)
// modifiers (return new configurations)
let engage config man woman =
{ config with wifeOf = config.wifeOf.Add(man, woman);
husbandOf = config.husbandOf.Add(woman, man) }
let breakOff config man =
let woman = config.wifeOf.[man]
{ config with wifeOf = config.wifeOf.Remove(man);
husbandOf = config.husbandOf.Remove(woman) }
let propose config m w =
// remember the proposition
let proposedByM = defaultArg (config.proposed.TryFind m) []
let proposed' = config.proposed.Add(m, w::proposedByM) // '
let config = { config with proposed = proposed'} // '
// actually try to engage
if isFreeWoman config w then engage config m w
else
let m' = config.husbandOf.[w] // '
if womanPrefers w m m' then // '
let config = breakOff config m' // '
engage config m w
else
config
// do one step of the algorithm; returns None if no more steps are possible let step config : Configuration option =
let freeMen = men |> List.filter (isFreeMan config)
let menWhoCanPropose =
freeMen |>
List.filter (fun man -> (notProposedBy config man women) <> [] )
match menWhoCanPropose with
| [] -> None
| m::_ -> let unproposedByM = menPrefs.[m] |> notProposedBy config m
// w is automatically the highest ranked because menPrefs.[m] is the source
let w = List.head unproposedByM
Some( propose config m w )
let rec loop config =
match step config with | None -> config | Some config' -> loop config' // '
// find solution and print it
let solution = loop { proposed = Map.empty<string, string list>;
wifeOf = Map.empty<string, string>;
husbandOf = Map.empty<string, string> }
for woman, man in Map.toList solution.husbandOf do
printfn "%s is engaged to %s" woman man
printfn "Solution is stable: %A" (isStable solution)
// create unstable configuration by perturbing the solution
let perturbed =
let gal0 = women.[0]
let gal1 = women.[1]
let guy0 = solution.husbandOf.[gal0]
let guy1 = solution.husbandOf.[gal1]
{ solution with wifeOf = solution.wifeOf.Add( guy0, gal1 ).Add( guy1, gal0 );
husbandOf = solution.husbandOf.Add( gal0, guy1 ).Add( gal1, guy0 ) }
printfn "Perturbed is stable: %A" (isStable perturbed)</lang>
- Output:
abi is engaged to jon bea is engaged to fred cath is engaged to bob dee is engaged to col eve is engaged to hal fay is engaged to dan gay is engaged to gav hope is engaged to ian ivy is engaged to abe jan is engaged to ed Solution is stable: true Perturbed is stable: false
Go
<lang go>package main
import "fmt"
// Asymetry in the algorithm suggests different data structures for the // map value types of the proposers and the recipients. Proposers go down // their list of preferences in order, and do not need random access. // Recipients on the other hand must compare their preferences to arbitrary // proposers. A slice is adequate for proposers, but a map allows direct // lookups for recipients and avoids looping code. type proposers map[string][]string
var mPref = proposers{
"abe": []string{
"abi", "eve", "cath", "ivy", "jan",
"dee", "fay", "bea", "hope", "gay"},
"bob": []string{
"cath", "hope", "abi", "dee", "eve",
"fay", "bea", "jan", "ivy", "gay"},
"col": []string{
"hope", "eve", "abi", "dee", "bea",
"fay", "ivy", "gay", "cath", "jan"},
"dan": []string{
"ivy", "fay", "dee", "gay", "hope",
"eve", "jan", "bea", "cath", "abi"},
"ed": []string{
"jan", "dee", "bea", "cath", "fay",
"eve", "abi", "ivy", "hope", "gay"},
"fred": []string{
"bea", "abi", "dee", "gay", "eve",
"ivy", "cath", "jan", "hope", "fay"},
"gav": []string{
"gay", "eve", "ivy", "bea", "cath",
"abi", "dee", "hope", "jan", "fay"},
"hal": []string{
"abi", "eve", "hope", "fay", "ivy",
"cath", "jan", "bea", "gay", "dee"},
"ian": []string{
"hope", "cath", "dee", "gay", "bea",
"abi", "fay", "ivy", "jan", "eve"},
"jon": []string{
"abi", "fay", "jan", "gay", "eve",
"bea", "dee", "cath", "ivy", "hope"},
}
type recipients map[string]map[string]int
var wPref = recipients{
"abi": map[string]int{
"bob": 1, "fred": 2, "jon": 3, "gav": 4, "ian": 5,
"abe": 6, "dan": 7, "ed": 8, "col": 9, "hal": 10},
"bea": map[string]int{
"bob": 1, "abe": 2, "col": 3, "fred": 4, "gav": 5,
"dan": 6, "ian": 7, "ed": 8, "jon": 9, "hal": 10},
"cath": map[string]int{
"fred": 1, "bob": 2, "ed": 3, "gav": 4, "hal": 5,
"col": 6, "ian": 7, "abe": 8, "dan": 9, "jon": 10},
"dee": map[string]int{
"fred": 1, "jon": 2, "col": 3, "abe": 4, "ian": 5,
"hal": 6, "gav": 7, "dan": 8, "bob": 9, "ed": 10},
"eve": map[string]int{
"jon": 1, "hal": 2, "fred": 3, "dan": 4, "abe": 5,
"gav": 6, "col": 7, "ed": 8, "ian": 9, "bob": 10},
"fay": map[string]int{
"bob": 1, "abe": 2, "ed": 3, "ian": 4, "jon": 5,
"dan": 6, "fred": 7, "gav": 8, "col": 9, "hal": 10},
"gay": map[string]int{
"jon": 1, "gav": 2, "hal": 3, "fred": 4, "bob": 5,
"abe": 6, "col": 7, "ed": 8, "dan": 9, "ian": 10},
"hope": map[string]int{
"gav": 1, "jon": 2, "bob": 3, "abe": 4, "ian": 5,
"dan": 6, "hal": 7, "ed": 8, "col": 9, "fred": 10},
"ivy": map[string]int{
"ian": 1, "col": 2, "hal": 3, "gav": 4, "fred": 5,
"bob": 6, "abe": 7, "ed": 8, "jon": 9, "dan": 10},
"jan": map[string]int{
"ed": 1, "hal": 2, "gav": 3, "abe": 4, "bob": 5,
"jon": 6, "col": 7, "ian": 8, "fred": 9, "dan": 10},
}
func main() {
// get parings by Gale/Shapley algorithm
ps := pair(mPref, wPref)
// show results
fmt.Println("\nresult:")
if !validateStable(ps, mPref, wPref) {
return
}
// perturb
for {
i := 0
var w2, m2 [2]string
for w, m := range ps {
w2[i] = w
m2[i] = m
if i == 1 {
break
}
i++
}
fmt.Println("\nexchanging partners of", m2[0], "and", m2[1])
ps[w2[0]] = m2[1]
ps[w2[1]] = m2[0]
// validate perturbed parings
if !validateStable(ps, mPref, wPref) {
return
}
// if those happened to be stable as well, perturb more
}
}
type parings map[string]string // map[recipient]proposer (or map[w]m)
// Pair implements the Gale/Shapley algorithm. func pair(pPref proposers, rPref recipients) parings {
// code is destructive on the maps, so work with copies
pFree := proposers{}
for k, v := range pPref {
pFree[k] = append([]string{}, v...)
}
rFree := recipients{}
for k, v := range rPref {
rFree[k] = v
}
// struct only used in this function.
// preferences must be saved in case engagement is broken.
type save struct {
proposer string
pPref []string
rPref map[string]int
}
proposals := map[string]save{} // key is recipient (w)
// WP pseudocode comments prefaced with WP: m is proposer, w is recipient.
// WP: while ∃ free man m who still has a woman w to propose to
for len(pFree) > 0 { // while there is a free proposer,
var proposer string
var ppref []string
for proposer, ppref = range pFree {
break // pick a proposer at random, whatever range delivers first.
}
if len(ppref) == 0 {
continue // if proposer has no possible recipients, skip
}
// WP: w = m's highest ranked such woman to whom he has not yet proposed
recipient := ppref[0] // highest ranged is first in list.
ppref = ppref[1:] // pop from list
var rpref map[string]int
var ok bool
// WP: if w is free
if rpref, ok = rFree[recipient]; ok {
// WP: (m, w) become engaged
// (common code follows if statement)
} else {
// WP: else some pair (m', w) already exists
s := proposals[recipient] // get proposal saved preferences
// WP: if w prefers m to m'
if s.rPref[proposer] < s.rPref[s.proposer] {
fmt.Println("engagement broken:", recipient, s.proposer)
// WP: m' becomes free
pFree[s.proposer] = s.pPref // return proposer to the map
// WP: (m, w) become engaged
rpref = s.rPref
// (common code follows if statement)
} else {
// WP: else (m', w) remain engaged
pFree[proposer] = ppref // update preferences in map
continue
}
}
fmt.Println("engagement:", recipient, proposer)
proposals[recipient] = save{proposer, ppref, rpref}
delete(pFree, proposer)
delete(rFree, recipient)
}
// construct return value
ps := parings{}
for recipient, s := range proposals {
ps[recipient] = s.proposer
}
return ps
}
func validateStable(ps parings, pPref proposers, rPref recipients) bool {
for r, p := range ps {
fmt.Println(r, p)
}
for r, p := range ps {
for _, rp := range pPref[p] {
if rp == r {
break
}
rprefs := rPref[rp]
if rprefs[p] < rprefs[ps[rp]] {
fmt.Println("unstable.")
fmt.Printf("%s and %s would prefer each other over"+
" their current pairings.\n", p, rp)
return false
}
}
}
fmt.Println("stable.")
return true
}</lang>
- Output:
engagement: hope col engagement: bea fred engagement: ivy dan engagement: cath bob engagement: abi abe engagement broken: abi abe engagement: abi jon engagement: gay gav engagement: eve abe engagement: jan ed engagement broken: hope col engagement: hope ian engagement: dee col engagement broken: eve abe engagement: eve hal engagement broken: ivy dan engagement: ivy abe engagement: fay dan result: fay dan dee col cath bob hope ian eve hal jan ed abi jon gay gav ivy abe bea fred stable. exchanging partners of fred and dan ivy abe bea dan fay fred dee col cath bob hope ian eve hal jan ed abi jon gay gav unstable. dan and fay would prefer each other over their current pairings.
Groovy
(more or less) Uses explicit maps for preference ranking rather than list position. Uses Man and Woman enumerated types instead of string names, in order to take advantage of compile time type and constant checking to help keep the playas straight without a scorecard.
"Stable Matching" Solution: <lang groovy>import static Man.* import static Woman.*
Map<Woman,Man> match(Map<Man,Map<Woman,Integer>> guysGalRanking, Map<Woman,Map<Man,Integer>> galsGuyRanking) {
Map<Woman,Man> engagedTo = new TreeMap()
List<Man> freeGuys = (Man.values()).clone()
while(freeGuys) {
Man thisGuy = freeGuys[0]
freeGuys -= thisGuy
List<Woman> guyChoices = Woman.values().sort{ she -> - guysGalRanking[thisGuy][she] }
for(Woman girl in guyChoices) {
if(! engagedTo[girl]) {
engagedTo[girl] = thisGuy
break
} else {
Man thatGuy = engagedTo[girl]
if (galsGuyRanking[girl][thisGuy] > galsGuyRanking[girl][thatGuy]) {
engagedTo[girl] = thisGuy
freeGuys << thatGuy
break
}
}
}
}
engagedTo
}</lang>
"Stability Checking" Solution: (Could do more to eliminate common code. Maybe later.) <lang groovy>boolean isStable(Map<Woman,Man> matches, Map<Man,Map<Woman,Integer>> guysGalRanking, Map<Woman,Map<Man,Integer>> galsGuyRanking) {
matches.collect{ girl, guy ->
int guysRank = galsGuyRanking[girl][guy]
List<Man> sheLikesBetter = Man.values().findAll{ he -> galsGuyRanking[girl][he] > guysRank }
for(Man otherGuy : sheLikesBetter) {
Woman otherGuyFiancee = matches.find{ pair -> pair.value == otherGuy }.key
if(guysGalRanking[otherGuy][girl] > guysGalRanking[otherGuy][otherGuyFiancee]) {
println """O. M. G. ... ${otherGuy} likes ${girl} better than ${otherGuyFiancee}, and ${girl} likes ${otherGuy} better than ${guy}!
I am TOTALLY 'shipping ${girl} and ${otherGuy} now!"""
return false
}
}
int galsRank = guysGalRanking[guy][girl]
List<Woman> heLikesBetter = Woman.values().findAll{ she -> guysGalRanking[guy][she] > galsRank }
for(Woman otherGal : heLikesBetter) {
Man otherGalFiance = matches[otherGal]
if(galsGuyRanking[otherGal][guy] > galsGuyRanking[otherGal][otherGalFiance]) {
println """O. M. G. ... ${otherGal} likes ${guy} better than ${otherGalFiance}, and ${guy} likes ${otherGal} better than ${girl}!
I am TOTALLY 'shipping ${guy} and ${otherGal} now!"""
return false
}
}
true
}.every()
}</lang>
Test (Stable and Perturbed): <lang groovy>enum Man {
abe, bob, col, dan, ed, fred, gav, hal, ian, jon
}
enum Woman {
abi, bea, cath, dee, eve, fay, gay, hope, ivy, jan
}
Map<Man,Map<Woman,Integer>> mansWomanRanking = [
(abe): [(abi):10, (eve):9, (cath):8, (ivy):7, (jan):6, (dee):5, (fay):4, (bea):3, (hope):2, (gay):1], (bob): [(cath):10, (hope):9, (abi):8, (dee):7, (eve):6, (fay):5, (bea):4, (jan):3, (ivy):2, (gay):1], (col): [(hope):10, (eve):9, (abi):8, (dee):7, (bea):6, (fay):5, (ivy):4, (gay):3, (cath):2, (jan):1], (dan): [(ivy):10, (fay):9, (dee):8, (gay):7, (hope):6, (eve):5, (jan):4, (bea):3, (cath):2, (abi):1], (ed): [(jan):10, (dee):9, (bea):8, (cath):7, (fay):6, (eve):5, (abi):4, (ivy):3, (hope):2, (gay):1], (fred):[(bea):10, (abi):9, (dee):8, (gay):7, (eve):6, (ivy):5, (cath):4, (jan):3, (hope):2, (fay):1], (gav): [(gay):10, (eve):9, (ivy):8, (bea):7, (cath):6, (abi):5, (dee):4, (hope):3, (jan):2, (fay):1], (hal): [(abi):10, (eve):9, (hope):8, (fay):7, (ivy):6, (cath):5, (jan):4, (bea):3, (gay):2, (dee):1], (ian): [(hope):10, (cath):9, (dee):8, (gay):7, (bea):6, (abi):5, (fay):4, (ivy):3, (jan):2, (eve):1], (jon): [(abi):10, (fay):9, (jan):8, (gay):7, (eve):6, (bea):5, (dee):4, (cath):3, (ivy):2, (hope):1],
]
Map<Woman,List<Man>> womansManRanking = [
(abi): [(bob):10, (fred):9, (jon):8, (gav):7, (ian):6, (abe):5, (dan):4, (ed):3, (col):2, (hal):1], (bea): [(bob):10, (abe):9, (col):8, (fred):7, (gav):6, (dan):5, (ian):4, (ed):3, (jon):2, (hal):1], (cath):[(fred):10, (bob):9, (ed):8, (gav):7, (hal):6, (col):5, (ian):4, (abe):3, (dan):2, (jon):1], (dee): [(fred):10, (jon):9, (col):8, (abe):7, (ian):6, (hal):5, (gav):4, (dan):3, (bob):2, (ed):1], (eve): [(jon):10, (hal):9, (fred):8, (dan):7, (abe):6, (gav):5, (col):4, (ed):3, (ian):2, (bob):1], (fay): [(bob):10, (abe):9, (ed):8, (ian):7, (jon):6, (dan):5, (fred):4, (gav):3, (col):2, (hal):1], (gay): [(jon):10, (gav):9, (hal):8, (fred):7, (bob):6, (abe):5, (col):4, (ed):3, (dan):2, (ian):1], (hope):[(gav):10, (jon):9, (bob):8, (abe):7, (ian):6, (dan):5, (hal):4, (ed):3, (col):2, (fred):1], (ivy): [(ian):10, (col):9, (hal):8, (gav):7, (fred):6, (bob):5, (abe):4, (ed):3, (jon):2, (dan):1], (jan): [(ed):10, (hal):9, (gav):8, (abe):7, (bob):6, (jon):5, (col):4, (ian):3, (fred):2, (dan):1],
]
// STABLE test Map<Woman,Man> matches = match(mansWomanRanking, womansManRanking) matches.each { w, m ->
println "${w} (his '${mansWomanRanking[m][w]}' girl) is engaged to ${m} (her '${womansManRanking[w][m]}' guy)"
} assert matches.keySet() == Woman.values() as Set assert matches.values() as Set == Man.values() as Set println
assert isStable(matches, mansWomanRanking, womansManRanking)
// PERTURBED test println 'Swapping partners now ...' def temp = matches[abi] matches[abi] = matches[bea] matches[bea] = temp matches.each { w, m ->
println "${w} (his '${mansWomanRanking[m][w]}' girl) is engaged to ${m} (her '${womansManRanking[w][m]}' guy)"
} println
assert ! isStable(matches, mansWomanRanking, womansManRanking)</lang>
- Output:
abi (his '10' girl) is engaged to jon (her '8' guy)
bea (his '10' girl) is engaged to fred (her '7' guy)
cath (his '10' girl) is engaged to bob (her '9' guy)
dee (his '7' girl) is engaged to col (her '8' guy)
eve (his '9' girl) is engaged to hal (her '9' guy)
fay (his '9' girl) is engaged to dan (her '5' guy)
gay (his '10' girl) is engaged to gav (her '9' guy)
hope (his '10' girl) is engaged to ian (her '6' guy)
ivy (his '7' girl) is engaged to abe (her '4' guy)
jan (his '10' girl) is engaged to ed (her '10' guy)
Swapping partners now ...
abi (his '9' girl) is engaged to fred (her '9' guy)
bea (his '5' girl) is engaged to jon (her '2' guy)
cath (his '10' girl) is engaged to bob (her '9' guy)
dee (his '7' girl) is engaged to col (her '8' guy)
eve (his '9' girl) is engaged to hal (her '9' guy)
fay (his '9' girl) is engaged to dan (her '5' guy)
gay (his '10' girl) is engaged to gav (her '9' guy)
hope (his '10' girl) is engaged to ian (her '6' guy)
ivy (his '7' girl) is engaged to abe (her '4' guy)
jan (his '10' girl) is engaged to ed (her '10' guy)
O. M. G. ... bea likes fred better than jon, and fred likes bea better than abi!
I am TOTALLY 'shipping fred and bea now!
O. M. G. ... fred likes bea better than abi, and bea likes fred better than jon!
I am TOTALLY 'shipping bea and fred now!
O. M. G. ... jon likes eve better than bea, and eve likes jon better than hal!
I am TOTALLY 'shipping eve and jon now!
O. M. G. ... jon likes fay better than bea, and fay likes jon better than dan!
I am TOTALLY 'shipping fay and jon now!
O. M. G. ... jon likes gay better than bea, and gay likes jon better than gav!
I am TOTALLY 'shipping gay and jon now!
Haskell
<lang haskell>import Data.List import Control.Monad import Control.Arrow import Data.Maybe
mp = map ((head &&& tail). splitNames)
["abe: abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay", "bob: cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay", "col: hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan", "dan: ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi", "ed: jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay", "fred: bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay", "gav: gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay", "hal: abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee", "ian: hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve", "jon: abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope"]
fp = map ((head &&& tail). splitNames)
["abi: bob, fred, jon, gav, ian, abe, dan, ed, col, hal",
"bea: bob, abe, col, fred, gav, dan, ian, ed, jon, hal",
"cath: fred, bob, ed, gav, hal, col, ian, abe, dan, jon",
"dee: fred, jon, col, abe, ian, hal, gav, dan, bob, ed",
"eve: jon, hal, fred, dan, abe, gav, col, ed, ian, bob",
"fay: bob, abe, ed, ian, jon, dan, fred, gav, col, hal",
"gay: jon, gav, hal, fred, bob, abe, col, ed, dan, ian",
"hope: gav, jon, bob, abe, ian, dan, hal, ed, col, fred",
"ivy: ian, col, hal, gav, fred, bob, abe, ed, jon, dan",
"jan: ed, hal, gav, abe, bob, jon, col, ian, fred, dan"]
splitNames = map (takeWhile(`notElem`",:")). words
pref x y xs = fromJust (elemIndex x xs) < fromJust (elemIndex y xs)
task ms fs = do
let jos = fst $ unzip ms runGS es js ms = do let (m:js') = js
(v:vm') = case lookup m ms of Just xs -> xs _ -> [] vv = fromJust $ lookup v fs m2 = case lookup v es of Just e -> e _ -> "" ms1 = insert (m,vm') $ delete (m,v:vm') ms
if null js then do
putStrLn "" putStrLn "=== Couples ===" return es
else if null m2 then
do putStrLn $ v ++ " with " ++ m runGS ( insert (v,m) es ) js' ms1
else if pref m m2 vv then
do putStrLn $ v ++ " dumped " ++ m2 ++ " for " ++ m runGS ( insert (v,m) $ delete (v,m2) es ) (if not $ null vm' then js'++[m2] else js') ms1
else runGS es (if not $ null js' then js'++[m] else js') ms1
cs <- runGS [] jos ms
mapM_ (\(f,m) -> putStrLn $ f ++ " with " ++ m ) cs
putStrLn ""
checkStab cs
putStrLn ""
putStrLn "Introducing error: "
let [r1@(a,b), r2@(p,q)] = take 2 cs
r3 = (a,q)
r4 = (p,b)
errcs = insert r4. insert r3. delete r2 $ delete r1 cs
putStrLn $ "\tSwapping partners of " ++ a ++ " and " ++ p
putStrLn $ (\((a,b),(p,q)) -> "\t" ++ a ++ " is now with " ++ b ++ " and " ++ p ++ " with " ++ q) (r3,r4)
putStrLn ""
checkStab errcs
checkStab es = do
let fmt (a,b,c,d) = a ++ " and " ++ b ++ " like each other better than their current partners " ++ c ++ " and " ++ d ies = uncurry(flip zip) $ unzip es -- es = [(fem,m)] & ies = [(m,fem)] slb = map (\(f,m)-> (f,m, map (id &&& fromJust. flip lookup ies). fst.break(==m). fromJust $ lookup f fp) ) es hlb = map (\(f,m)-> (m,f, map (id &&& fromJust. flip lookup es ). fst.break(==f). fromJust $ lookup m mp) ) es tslb = concatMap (filter snd. (\(f,m,ls) ->
map (\(m2,f2) -> ((f,m2,f2,m), pref f f2 $ fromJust $ lookup m2 mp)) ls)) slb
thlb = concatMap (filter snd. (\(m,f,ls) ->
map (\(f2,m2) -> ((m,f2,m2,f), pref m m2 $ fromJust $ lookup f2 fp)) ls)) hlb
res = tslb ++ thlb if not $ null res then do putStrLn "Marriages are unstable, e.g.:" putStrLn.fmt.fst $ head res
else putStrLn "Marriages are stable"</lang>
- Output:
*Main> task mp fp
abi with abe
cath with bob
hope with col
ivy with dan
jan with ed
bea with fred
gay with gav
hope dumped col for ian
abi dumped abe for jon
eve with hal
dee with col
ivy dumped dan for abe
fay with dan
=== Couples ===
abi with jon
bea with fred
cath with bob
dee with col
eve with hal
fay with dan
gay with gav
hope with ian
ivy with abe
jan with ed
Marriages are stable
Introducing error:
Swapping partners of abi and bea
abi is now with fred and bea with jon
Marriages are unstable, e.g.:
bea and fred like each other better than their current partners abi and jon
Icon and Unicon
<lang Icon>link printf
procedure main()
smd := IsStable(ShowEngaged(StableMatching(setup()))) IsStable(ShowEngaged(Swap(\smd,smd.women[1],smd.women[2])))
end
procedure index(L,x) #: return index of value or fail
return ( L[i := 1 to *L] === x, i)
end
procedure ShowEngaged(smd) #: Show who's hooked up
printf("\nEngagements:\n")
every w := !smd.women do
printf("%s is engaged to %s\n",w,smd.engaged[w])
return smd
end
procedure Swap(smd,x0,x1) #: swap two couples by m or w
printf("\nSwapping %s and %s\n",x0,x1)
e := smd.engaged
e[x0] :=: e[x1] # swap partners
e[e[x0]] := e[e[x1]]
return smd
end
procedure IsStable(smd) #: validate stability
stable := 1 # assumption
printf("\n")
every mp := smd.prefs[m := !smd.men] & # man & pref
w := mp[index(mp,smd.engaged[m])-1 to 1 by -1] do { # better choices
wp := smd.prefs[w] # her choices
if index(wp,smd.engaged[w]) > index(wp,m) then {
printf("Engagement of %s to %s is unstable.\n",w,m)
stable := &null # broken
}
}
if \stable then {
printf("Engagments are all stable.\n")
return smd
}
end
procedure StableMatching(smd) #: match making
freemen := copy(smd.men) # Initialize all m memberof M
freewomen := set(smd.women) # ... and w memberof W to free
every (prefmen := table())[m := !freemen] := copy(smd.prefs[m])
smd.engaged := engaged := table()
printf("\nMatching:\n")
while m := get(freemen) do { # next freeman
while w := get(prefmen[m]) do { # . with prpoposals left
if member(freewomen,w) then { # . . is she free?
engaged[m] := w # . . . (m, w)
engaged[w] := m
delete(freewomen,w)
printf("%s accepted %s's proposal\n",w,m)
break
}
else { # . . no, she's engaged
m0 := engaged[w] # to m0
if index(smd.prefs[w],m) < index(smd.prefs[w],m0) then {
engaged[m] := w # (m, w) become engaged
engaged[w] := m
delete(freewomen,w)
engaged[m0] := &null # m' becomes free
put(freemen,m0)
printf("%s chose %s over %s\n",w,m,m0)
break
}
else next # she's happier as is
}
}
}
return smd
end
record sm_data(men,women,prefs,engaged) #: everyones data
procedure setup() #: setup everyones data
X := sm_data() X.men := ["abe","bob","col","dan","ed","fred","gav","hal","ian","jon"] X.women := ["abi","bea","cath","dee","eve","fay","gay","hope","ivy","jan"] if *X.men ~= *(M := set(X.men)) then runerr(500,X.men) # duplicate? if *X.women ~= *(W := set(X.women)) then runerr(500,X.women) # duplicate? if *(B := M**W) ~= 0 then runerr(500,B) # intersect? X.prefs := p := table() p["abe"] := ["abi","eve","cath","ivy","jan","dee","fay","bea","hope","gay"] p["bob"] := ["cath","hope","abi","dee","eve","fay","bea","jan","ivy","gay"] p["col"] := ["hope","eve","abi","dee","bea","fay","ivy","gay","cath","jan"] p["dan"] := ["ivy","fay","dee","gay","hope","eve","jan","bea","cath","abi"] p["ed"] := ["jan","dee","bea","cath","fay","eve","abi","ivy","hope","gay"] p["fred"] := ["bea","abi","dee","gay","eve","ivy","cath","jan","hope","fay"] p["gav"] := ["gay","eve","ivy","bea","cath","abi","dee","hope","jan","fay"] p["hal"] := ["abi","eve","hope","fay","ivy","cath","jan","bea","gay","dee"] p["ian"] := ["hope","cath","dee","gay","bea","abi","fay","ivy","jan","eve"] p["jon"] := ["abi","fay","jan","gay","eve","bea","dee","cath","ivy","hope"] p["abi"] := ["bob","fred","jon","gav","ian","abe","dan","ed","col","hal"] p["bea"] := ["bob","abe","col","fred","gav","dan","ian","ed","jon","hal"] p["cath"] := ["fred","bob","ed","gav","hal","col","ian","abe","dan","jon"] p["dee"] := ["fred","jon","col","abe","ian","hal","gav","dan","bob","ed"] p["eve"] := ["jon","hal","fred","dan","abe","gav","col","ed","ian","bob"] p["fay"] := ["bob","abe","ed","ian","jon","dan","fred","gav","col","hal"] p["gay"] := ["jon","gav","hal","fred","bob","abe","col","ed","dan","ian"] p["hope"] := ["gav","jon","bob","abe","ian","dan","hal","ed","col","fred"] p["ivy"] := ["ian","col","hal","gav","fred","bob","abe","ed","jon","dan"] p["jan"] := ["ed","hal","gav","abe","bob","jon","col","ian","fred","dan"] return X
end</lang>
printf.icn provides formatting
- Output:
Matching: abi accepted abe's proposal cath accepted bob's proposal hope accepted col's proposal ivy accepted dan's proposal jan accepted ed's proposal bea accepted fred's proposal gay accepted gav's proposal eve accepted hal's proposal hope chose ian over col abi chose jon over abe dee accepted col's proposal ivy chose abe over dan fay accepted dan's proposal Engagements: abi is engaged to jon bea is engaged to fred cath is engaged to bob dee is engaged to col eve is engaged to hal fay is engaged to dan gay is engaged to gav hope is engaged to ian ivy is engaged to abe jan is engaged to ed Engagments are all stable. Swapping abi and bea Engagements: abi is engaged to fred bea is engaged to jon cath is engaged to bob dee is engaged to col eve is engaged to hal fay is engaged to dan gay is engaged to gav hope is engaged to ian ivy is engaged to abe jan is engaged to ed Engagement of bea to fred is unstable.
J
<lang j>Mraw=: ;: ;._2 noun define -. ':,'
abe: abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay bob: cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay col: hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan dan: ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi ed: jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay fred: bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay gav: gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay hal: abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee ian: hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve jon: abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope
)
Fraw=: ;: ;._2 noun define -. ':,'
abi: bob, fred, jon, gav, ian, abe, dan, ed, col, hal bea: bob, abe, col, fred, gav, dan, ian, ed, jon, hal cath: fred, bob, ed, gav, hal, col, ian, abe, dan, jon dee: fred, jon, col, abe, ian, hal, gav, dan, bob, ed eve: jon, hal, fred, dan, abe, gav, col, ed, ian, bob fay: bob, abe, ed, ian, jon, dan, fred, gav, col, hal gay: jon, gav, hal, fred, bob, abe, col, ed, dan, ian hope: gav, jon, bob, abe, ian, dan, hal, ed, col, fred ivy: ian, col, hal, gav, fred, bob, abe, ed, jon, dan jan: ed, hal, gav, abe, bob, jon, col, ian, fred, dan
)
GuyNames=: {."1 Mraw GalNames=: {."1 Fraw
Mprefs=: GalNames i. }."1 Mraw Fprefs=: GuyNames i. }."1 Fraw
propose=: dyad define
engaged=. x
'guy gal'=. y
if. gal e. engaged do.
fiance=. engaged i. gal
if. guy <&((gal{Fprefs)&i.) fiance do.
engaged=. gal guy} _ fiance} engaged
end.
else.
engaged=. gal guy} engaged
end.
engaged
)
matchMake=: monad define
engaged=. _"0 GuyNames NB. initially no one is engaged
fallback=. 0"0 engaged NB. and each guy will first propose to his favorite
whilst. _ e. engaged do.
for_guy. I. _ = engaged do.
next=. guy{fallback
gal=. (<guy,next){Mprefs
engaged=. engaged propose guy,gal
fallback=. (next+1) guy} fallback
end.
end.
GuyNames,:engaged{GalNames
)
checkStable=: monad define
'guys gals'=. (GuyNames,:GalNames) i."1 y
satisfied=. ] >: (<0 1) |: ]
guyshappy=. satisfied (guys{Mprefs) i."1 0/ gals
galshappy=. satisfied (gals{Fprefs) i."1 0/ guys
unstable=. 4$.$.-. guyshappy +. |:galshappy
if. bad=. 0 < #unstable do.
smoutput 'Engagements preferred by both members to their current ones:'
smoutput y {~"1 0"2 1 unstable
end.
assert-.bad
)</lang>
For most of this, males and females are both represented by indices. Rows of Mprefs are indexed by a male index and each contains a list female indices, in priority order. Rows of Fprefs are indexed by a female index and each contains a list male indices in priority order. These indices select the corresponding names from GuyNames and GalNames.
In matchMake (and propose), engaged identifies the gal each guy is engaged to (or _ if that guy is not engaged). And, fallback identifies the column which has the next gal, in Mprefs, for that guy to propose to.
Example use:
<lang j> matchMake ┌───┬────┬───┬───┬───┬────┬───┬───┬────┬───┐ │abe│bob │col│dan│ed │fred│gav│hal│ian │jon│ ├───┼────┼───┼───┼───┼────┼───┼───┼────┼───┤ │ivy│cath│dee│fay│jan│bea │gay│eve│hope│abi│ └───┴────┴───┴───┴───┴────┴───┴───┴────┴───┘</lang>
Stability check:
<lang j> 0 105 A."_1 matchMake NB. swap abi and bea ┌───┬────┬───┬───┬───┬────┬───┬───┬────┬───┐ │abe│bob │col│dan│ed │fred│gav│hal│ian │jon│ ├───┼────┼───┼───┼───┼────┼───┼───┼────┼───┤ │ivy│cath│dee│fay│jan│abi │gay│eve│hope│bea│ └───┴────┴───┴───┴───┴────┴───┴───┴────┴───┘
checkStable 0 105 A."_1 matchMake
Engagements preferred by both members to their current ones: ┌────┬───┐ │fred│bea│ ├────┼───┤ │jon │fay│ ├────┼───┤ │jon │gay│ ├────┼───┤ │jon │eve│ └────┴───┘ |assertion failure: assert | assert-.bad</lang> As an aside, note that the guys fared much better than the gals here, with over half of the guys getting their first preference and only one gal getting her first preference. The worst match for any guy was fourth preference where the worst for any gal was seventh preference.
Java
This is not a direct translation of Python, but it's fairly close (especially the stability check). <lang java5>import java.util.*;
public class Stable {
static List<String> guys = Arrays.asList(
new String[]{
"abe", "bob", "col", "dan", "ed", "fred", "gav", "hal", "ian", "jon"});
static List<String> girls = Arrays.asList(
new String[]{
"abi", "bea", "cath", "dee", "eve", "fay", "gay", "hope", "ivy", "jan"});
static Map<String, List<String>> guyPrefers =
new HashMap<String, List<String>>(){{
put("abe",
Arrays.asList("abi", "eve", "cath", "ivy", "jan", "dee", "fay",
"bea", "hope", "gay"));
put("bob",
Arrays.asList("cath", "hope", "abi", "dee", "eve", "fay", "bea",
"jan", "ivy", "gay"));
put("col",
Arrays.asList("hope", "eve", "abi", "dee", "bea", "fay", "ivy",
"gay", "cath", "jan"));
put("dan",
Arrays.asList("ivy", "fay", "dee", "gay", "hope", "eve", "jan",
"bea", "cath", "abi"));
put("ed",
Arrays.asList("jan", "dee", "bea", "cath", "fay", "eve", "abi",
"ivy", "hope", "gay"));
put("fred",
Arrays.asList("bea", "abi", "dee", "gay", "eve", "ivy", "cath",
"jan", "hope", "fay"));
put("gav",
Arrays.asList("gay", "eve", "ivy", "bea", "cath", "abi", "dee",
"hope", "jan", "fay"));
put("hal",
Arrays.asList("abi", "eve", "hope", "fay", "ivy", "cath", "jan",
"bea", "gay", "dee"));
put("ian",
Arrays.asList("hope", "cath", "dee", "gay", "bea", "abi", "fay",
"ivy", "jan", "eve"));
put("jon",
Arrays.asList("abi", "fay", "jan", "gay", "eve", "bea", "dee",
"cath", "ivy", "hope"));
}};
static Map<String, List<String>> girlPrefers =
new HashMap<String, List<String>>(){{
put("abi",
Arrays.asList("bob", "fred", "jon", "gav", "ian", "abe", "dan",
"ed", "col", "hal"));
put("bea",
Arrays.asList("bob", "abe", "col", "fred", "gav", "dan", "ian",
"ed", "jon", "hal"));
put("cath",
Arrays.asList("fred", "bob", "ed", "gav", "hal", "col", "ian",
"abe", "dan", "jon"));
put("dee",
Arrays.asList("fred", "jon", "col", "abe", "ian", "hal", "gav",
"dan", "bob", "ed"));
put("eve",
Arrays.asList("jon", "hal", "fred", "dan", "abe", "gav", "col",
"ed", "ian", "bob"));
put("fay",
Arrays.asList("bob", "abe", "ed", "ian", "jon", "dan", "fred",
"gav", "col", "hal"));
put("gay",
Arrays.asList("jon", "gav", "hal", "fred", "bob", "abe", "col",
"ed", "dan", "ian"));
put("hope",
Arrays.asList("gav", "jon", "bob", "abe", "ian", "dan", "hal",
"ed", "col", "fred"));
put("ivy",
Arrays.asList("ian", "col", "hal", "gav", "fred", "bob", "abe",
"ed", "jon", "dan"));
put("jan",
Arrays.asList("ed", "hal", "gav", "abe", "bob", "jon", "col",
"ian", "fred", "dan"));
}};
public static void main(String[] args){
Map<String, String> matches = match(guys, guyPrefers, girlPrefers);
for(Map.Entry<String, String> couple:matches.entrySet()){
System.out.println(
couple.getKey() + " is engaged to " + couple.getValue());
}
if(checkMatches(guys, girls, matches, guyPrefers, girlPrefers)){
System.out.println("Marriages are stable");
}else{
System.out.println("Marriages are unstable");
}
String tmp = matches.get(girls.get(0));
matches.put(girls.get(0), matches.get(girls.get(1)));
matches.put(girls.get(1), tmp);
System.out.println(
girls.get(0) +" and " + girls.get(1) + " have switched partners");
if(checkMatches(guys, girls, matches, guyPrefers, girlPrefers)){
System.out.println("Marriages are stable");
}else{
System.out.println("Marriages are unstable");
}
}
private static Map<String, String> match(List<String> guys,
Map<String, List<String>> guyPrefers,
Map<String, List<String>> girlPrefers){
Map<String, String> engagedTo = new TreeMap<String, String>();
List<String> freeGuys = new LinkedList<String>();
freeGuys.addAll(guys);
while(!freeGuys.isEmpty()){
String thisGuy = freeGuys.remove(0); //get a load of THIS guy
List<String> thisGuyPrefers = guyPrefers.get(thisGuy);
for(String girl:thisGuyPrefers){
if(engagedTo.get(girl) == null){//girl is free
engagedTo.put(girl, thisGuy); //awww
break;
}else{
String otherGuy = engagedTo.get(girl);
List<String> thisGirlPrefers = girlPrefers.get(girl);
if(thisGirlPrefers.indexOf(thisGuy) <
thisGirlPrefers.indexOf(otherGuy)){
//this girl prefers this guy to the guy she's engaged to
engagedTo.put(girl, thisGuy);
freeGuys.add(otherGuy);
break;
}//else no change...keep looking for this guy
}
}
}
return engagedTo;
}
private static boolean checkMatches(List<String> guys, List<String> girls,
Map<String, String> matches, Map<String, List<String>> guyPrefers,
Map<String, List<String>> girlPrefers) {
if(!matches.keySet().containsAll(girls)){
return false;
}
if(!matches.values().containsAll(guys)){
return false;
}
Map<String, String> invertedMatches = new TreeMap<String, String>();
for(Map.Entry<String, String> couple:matches.entrySet()){
invertedMatches.put(couple.getValue(), couple.getKey());
}
for(Map.Entry<String, String> couple:matches.entrySet()){
List<String> shePrefers = girlPrefers.get(couple.getKey());
List<String> sheLikesBetter = new LinkedList<String>();
sheLikesBetter.addAll(shePrefers.subList(0, shePrefers.indexOf(couple.getValue())));
List<String> hePrefers = guyPrefers.get(couple.getValue());
List<String> heLikesBetter = new LinkedList<String>();
heLikesBetter.addAll(hePrefers.subList(0, hePrefers.indexOf(couple.getKey())));
for(String guy : sheLikesBetter){
String guysFinace = invertedMatches.get(guy);
List<String> thisGuyPrefers = guyPrefers.get(guy);
if(thisGuyPrefers.indexOf(guysFinace) >
thisGuyPrefers.indexOf(couple.getKey())){
System.out.printf("%s likes %s better than %s and %s"
+ " likes %s better than their current partner\n",
couple.getKey(), guy, couple.getValue(),
guy, couple.getKey());
return false;
}
}
for(String girl : heLikesBetter){
String girlsFinace = matches.get(girl);
List<String> thisGirlPrefers = girlPrefers.get(girl);
if(thisGirlPrefers.indexOf(girlsFinace) >
thisGirlPrefers.indexOf(couple.getValue())){
System.out.printf("%s likes %s better than %s and %s"
+ " likes %s better than their current partner\n",
couple.getValue(), girl, couple.getKey(),
girl, couple.getValue());
return false;
}
}
}
return true;
}
}</lang>
- Output:
abi is engaged to jon bea is engaged to fred cath is engaged to bob dee is engaged to col eve is engaged to hal fay is engaged to dan gay is engaged to gav hope is engaged to ian ivy is engaged to abe jan is engaged to ed Marriages are stable abi and bea have switched partners fred likes bea better than abi and bea likes fred better than their current partner Marriages are unstable
JavaScript
<lang javascript>function Person(name) {
var candidateIndex = 0;
this.name = name; this.fiance = null; this.candidates = [];
this.rank = function(p) {
for (i = 0; i < this.candidates.length; i++)
if (this.candidates[i] === p) return i;
return this.candidates.length + 1;
}
this.prefers = function(p) {
return this.rank(p) < this.rank(this.fiance);
}
this.nextCandidate = function() {
if (candidateIndex >= this.candidates.length) return null;
return this.candidates[candidateIndex++];
}
this.engageTo = function(p) {
if (p.fiance) p.fiance.fiance = null;
p.fiance = this;
if (this.fiance) this.fiance.fiance = null;
this.fiance = p;
}
this.swapWith = function(p) {
console.log("%s & %s swap partners", this.name, p.name);
var thisFiance = this.fiance;
var pFiance = p.fiance;
this.engageTo(pFiance);
p.engageTo(thisFiance);
}
}
function isStable(guys, gals) {
for (var i = 0; i < guys.length; i++)
for (var j = 0; j < gals.length; j++)
if (guys[i].prefers(gals[j]) && gals[j].prefers(guys[i]))
return false;
return true;
}
function engageEveryone(guys) {
var done;
do {
done = true;
for (var i = 0; i < guys.length; i++) {
var guy = guys[i];
if (!guy.fiance) {
done = false;
var gal = guy.nextCandidate();
if (!gal.fiance || gal.prefers(guy))
guy.engageTo(gal);
}
}
} while (!done);
}
function doMarriage() {
var abe = new Person("Abe");
var bob = new Person("Bob");
var col = new Person("Col");
var dan = new Person("Dan");
var ed = new Person("Ed");
var fred = new Person("Fred");
var gav = new Person("Gav");
var hal = new Person("Hal");
var ian = new Person("Ian");
var jon = new Person("Jon");
var abi = new Person("Abi");
var bea = new Person("Bea");
var cath = new Person("Cath");
var dee = new Person("Dee");
var eve = new Person("Eve");
var fay = new Person("Fay");
var gay = new Person("Gay");
var hope = new Person("Hope");
var ivy = new Person("Ivy");
var jan = new Person("Jan");
abe.candidates = [abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay]; bob.candidates = [cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay]; col.candidates = [hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan]; dan.candidates = [ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi]; ed.candidates = [jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay]; fred.candidates = [bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay]; gav.candidates = [gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay]; hal.candidates = [abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee]; ian.candidates = [hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve]; jon.candidates = [abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope]; abi.candidates = [bob, fred, jon, gav, ian, abe, dan, ed, col, hal]; bea.candidates = [bob, abe, col, fred, gav, dan, ian, ed, jon, hal]; cath.candidates = [fred, bob, ed, gav, hal, col, ian, abe, dan, jon]; dee.candidates = [fred, jon, col, abe, ian, hal, gav, dan, bob, ed]; eve.candidates = [jon, hal, fred, dan, abe, gav, col, ed, ian, bob]; fay.candidates = [bob, abe, ed, ian, jon, dan, fred, gav, col, hal]; gay.candidates = [jon, gav, hal, fred, bob, abe, col, ed, dan, ian]; hope.candidates = [gav, jon, bob, abe, ian, dan, hal, ed, col, fred]; ivy.candidates = [ian, col, hal, gav, fred, bob, abe, ed, jon, dan]; jan.candidates = [ed, hal, gav, abe, bob, jon, col, ian, fred, dan];
var guys = [abe, bob, col, dan, ed, fred, gav, hal, ian, jon]; var gals = [abi, bea, cath, dee, eve, fay, gay, hope, ivy, jan];
engageEveryone(guys);
for (var i = 0; i < guys.length; i++) {
console.log("%s is engaged to %s", guys[i].name, guys[i].fiance.name);
}
console.log("Stable = %s", isStable(guys, gals) ? "Yes" : "No");
jon.swapWith(fred);
console.log("Stable = %s", isStable(guys, gals) ? "Yes" : "No");
}
doMarriage(); </lang>
- Output:
Abe is engaged to Ivy Bob is engaged to Cath Col is engaged to Dee Dan is engaged to Fay Ed is engaged to Jan Fred is engaged to Bea Gav is engaged to Gay Hal is engaged to Eve Ian is engaged to Hope Jon is engaged to Abi Stable = Yes Jon & Fred swap partners Stable = No
Lua
<lang lua>local Person = {} Person.__index = Person
function Person.new(inName)
local o = {
name = inName,
prefs = nil,
fiance = nil,
_candidateIndex = 1,
}
return setmetatable(o, Person)
end
function Person:indexOf(other)
for i, p in pairs(self.prefs) do
if p == other then return i end
end
return 999
end
function Person:prefers(other)
return self:indexOf(other) < self:indexOf(self.fiance)
end
function Person:nextCandidateNotYetProposedTo()
if self._candidateIndex >= #self.prefs then return nil end local c = self.prefs[self._candidateIndex]; self._candidateIndex = self._candidateIndex + 1 return c;
end
function Person:engageTo(other)
if other.fiance then
other.fiance.fiance = nil
end
other.fiance = self
if self.fiance then
self.fiance.fiance = nil
end
self.fiance = other;
end
local function isStable(men)
local women = men[1].prefs
local stable = true
for _, guy in pairs(men) do
for _, gal in pairs(women) do
if guy:prefers(gal) and gal:prefers(guy) then
stable = false
print(guy.name .. ' and ' .. gal.name ..
' prefer each other over their partners ' ..
guy.fiance.name .. ' and ' .. gal.fiance.name)
end
end
end
return stable
end
local abe = Person.new("Abe") local bob = Person.new("Bob") local col = Person.new("Col") local dan = Person.new("Dan") local ed = Person.new("Ed") local fred = Person.new("Fred") local gav = Person.new("Gav") local hal = Person.new("Hal") local ian = Person.new("Ian") local jon = Person.new("Jon")
local abi = Person.new("Abi") local bea = Person.new("Bea") local cath = Person.new("Cath") local dee = Person.new("Dee") local eve = Person.new("Eve") local fay = Person.new("Fay") local gay = Person.new("Gay") local hope = Person.new("Hope") local ivy = Person.new("Ivy") local jan = Person.new("Jan")
abe.prefs = { abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay } bob.prefs = { cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay } col.prefs = { hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan } dan.prefs = { ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi } ed.prefs = { jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay } fred.prefs = { bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay } gav.prefs = { gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay } hal.prefs = { abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee } ian.prefs = { hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve } jon.prefs = { abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope }
abi.prefs = { bob, fred, jon, gav, ian, abe, dan, ed, col, hal } bea.prefs = { bob, abe, col, fred, gav, dan, ian, ed, jon, hal } cath.prefs = { fred, bob, ed, gav, hal, col, ian, abe, dan, jon } dee.prefs = { fred, jon, col, abe, ian, hal, gav, dan, bob, ed } eve.prefs = { jon, hal, fred, dan, abe, gav, col, ed, ian, bob } fay.prefs = { bob, abe, ed, ian, jon, dan, fred, gav, col, hal } gay.prefs = { jon, gav, hal, fred, bob, abe, col, ed, dan, ian } hope.prefs = { gav, jon, bob, abe, ian, dan, hal, ed, col, fred } ivy.prefs = { ian, col, hal, gav, fred, bob, abe, ed, jon, dan } jan.prefs = { ed, hal, gav, abe, bob, jon, col, ian, fred, dan }
local men = abi.prefs local freeMenCount = #men while freeMenCount > 0 do
for _, guy in pairs(men) do
if not guy.fiance then
local gal = guy:nextCandidateNotYetProposedTo()
if not gal.fiance then
guy:engageTo(gal)
freeMenCount = freeMenCount - 1
elseif gal:prefers(guy) then
guy:engageTo(gal)
end
end
end
end
print(' ') for _, guy in pairs(men) do
print(guy.name .. ' is engaged to ' .. guy.fiance.name)
end print('Stable: ', isStable(men))
print(' ') print('Switching ' .. fred.name .. "'s & " .. jon.name .. "'s partners") jon.fiance, fred.fiance = fred.fiance, jon.fiance print('Stable: ', isStable(men)) </lang>
- Output:
Bob is engaged to Cath Fred is engaged to Bea Jon is engaged to Abi Gav is engaged to Gay Ian is engaged to Hope Abe is engaged to Ivy Dan is engaged to Fay Ed is engaged to Jan Col is engaged to Dee Hal is engaged to Eve Stable: true Switching Fred's & Jon's partners Jon and Eve prefer each other over their partners Bea and Hal Jon and Fay prefer each other over their partners Bea and Dan Jon and Gay prefer each other over their partners Bea and Gav Stable: false
Objective-C
(The C# version is essentially the same as this.) <lang objc>//-------------------------------------------------------------------- // Person class
@interface Person : NSObject {
NSUInteger _candidateIndex;
} @property (nonatomic, strong) NSString* name; @property (nonatomic, strong) NSArray* prefs; @property (nonatomic, weak) Person* fiance; @end
@implementation Person + (instancetype)named:(NSString *)name {
return [[self alloc] initWithName:name];
} - (instancetype)initWithName:(NSString *)name {
if ((self = [super init])) {
_name = name;
_prefs = nil;
_fiance = nil;
_candidateIndex = 0;
}
return self;
} - (BOOL)prefers:(Person *)p {
return [_prefs indexOfObject:p] < [_prefs indexOfObject:_fiance];
} - (Person *)nextCandidateNotYetProposedTo {
if (_candidateIndex >= _prefs.count) return nil; return _prefs[_candidateIndex++];
} - (void)engageTo:(Person *)p {
if (p.fiance) p.fiance.fiance = nil; p.fiance = self; if (self.fiance) self.fiance.fiance = nil; self.fiance = p;
} - (NSString *)description {
return _name;
} @end
//--------------------------------------------------------------------
BOOL isStable(NSArray *men) {
NSArray *women = ((Person *)men[0]).prefs;
for (Person *guy in men) {
for (Person *gal in women) {
if ([guy prefers:gal] && [gal prefers:guy])
return NO;
}
}
return YES;
}
//--------------------------------------------------------------------
void doMarriage() {
Person *abe = [Person named:@"abe"];
Person *bob = [Person named:@"bob"];
Person *col = [Person named:@"col"];
Person *dan = [Person named:@"dan"];
Person *ed = [Person named:@"ed"];
Person *fred = [Person named:@"fred"];
Person *gav = [Person named:@"gav"];
Person *hal = [Person named:@"hal"];
Person *ian = [Person named:@"ian"];
Person *jon = [Person named:@"jon"];
Person *abi = [Person named:@"abi"];
Person *bea = [Person named:@"bea"];
Person *cath = [Person named:@"cath"];
Person *dee = [Person named:@"dee"];
Person *eve = [Person named:@"eve"];
Person *fay = [Person named:@"fay"];
Person *gay = [Person named:@"gay"];
Person *hope = [Person named:@"hope"];
Person *ivy = [Person named:@"ivy"];
Person *jan = [Person named:@"jan"];
abe.prefs = @[ abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay ];
bob.prefs = @[ cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay ];
col.prefs = @[ hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan ];
dan.prefs = @[ ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi ];
ed.prefs = @[ jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay ];
fred.prefs = @[ bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay ];
gav.prefs = @[ gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay ];
hal.prefs = @[ abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee ];
ian.prefs = @[ hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve ];
jon.prefs = @[ abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope ];
abi.prefs = @[ bob, fred, jon, gav, ian, abe, dan, ed, col, hal ];
bea.prefs = @[ bob, abe, col, fred, gav, dan, ian, ed, jon, hal ];
cath.prefs = @[ fred, bob, ed, gav, hal, col, ian, abe, dan, jon ];
dee.prefs = @[ fred, jon, col, abe, ian, hal, gav, dan, bob, ed ];
eve.prefs = @[ jon, hal, fred, dan, abe, gav, col, ed, ian, bob ];
fay.prefs = @[ bob, abe, ed, ian, jon, dan, fred, gav, col, hal ];
gay.prefs = @[ jon, gav, hal, fred, bob, abe, col, ed, dan, ian ];
hope.prefs = @[ gav, jon, bob, abe, ian, dan, hal, ed, col, fred ];
ivy.prefs = @[ ian, col, hal, gav, fred, bob, abe, ed, jon, dan ];
jan.prefs = @[ ed, hal, gav, abe, bob, jon, col, ian, fred, dan ];
NSArray *men = abi.prefs;
NSUInteger freeMenCount = men.count;
while (freeMenCount > 0) {
for (Person *guy in men) {
if (guy.fiance == nil) {
Person *gal = [guy nextCandidateNotYetProposedTo];
if (gal.fiance == nil) {
[guy engageTo:gal];
freeMenCount--;
} else if ([gal prefers:guy]) {
[guy engageTo:gal];
}
}
}
}
for (Person *guy in men) {
printf("%s is engaged to %s\n", [guy.name UTF8String], [guy.fiance.name UTF8String]);
}
printf("Stable = %d\n", (int)isStable(men));
printf("\nSwitching fred & jon's partners\n");
[fred engageTo:abi];
[jon engageTo:bea];
printf("Stable = %d\n", (int)isStable(men));
}
//--------------------------------------------------------------------
int main(int argc, const char * argv[]) {
@autoreleasepool {
doMarriage();
}
return 0;
}</lang>
- Output:
bob is engaged to cath fred is engaged to bea jon is engaged to abi gav is engaged to gay ian is engaged to hope abe is engaged to ivy dan is engaged to fay ed is engaged to jan col is engaged to dee hal is engaged to eve Stable = 1 Switching fred & jon's partners Stable = 0
OCaml
<lang ocaml>let men = [
"abe", ["abi";"eve";"cath";"ivy";"jan";"dee";"fay";"bea";"hope";"gay"]; "bob", ["cath";"hope";"abi";"dee";"eve";"fay";"bea";"jan";"ivy";"gay"]; "col", ["hope";"eve";"abi";"dee";"bea";"fay";"ivy";"gay";"cath";"jan"]; "dan", ["ivy";"fay";"dee";"gay";"hope";"eve";"jan";"bea";"cath";"abi"]; "ed", ["jan";"dee";"bea";"cath";"fay";"eve";"abi";"ivy";"hope";"gay"]; "fred", ["bea";"abi";"dee";"gay";"eve";"ivy";"cath";"jan";"hope";"fay"]; "gav", ["gay";"eve";"ivy";"bea";"cath";"abi";"dee";"hope";"jan";"fay"]; "hal", ["abi";"eve";"hope";"fay";"ivy";"cath";"jan";"bea";"gay";"dee"]; "ian", ["hope";"cath";"dee";"gay";"bea";"abi";"fay";"ivy";"jan";"eve"]; "jon", ["abi";"fay";"jan";"gay";"eve";"bea";"dee";"cath";"ivy";"hope"];
]
let women = [
"abi", ["bob";"fred";"jon";"gav";"ian";"abe";"dan";"ed";"col";"hal"]; "bea", ["bob";"abe";"col";"fred";"gav";"dan";"ian";"ed";"jon";"hal"]; "cath", ["fred";"bob";"ed";"gav";"hal";"col";"ian";"abe";"dan";"jon"]; "dee", ["fred";"jon";"col";"abe";"ian";"hal";"gav";"dan";"bob";"ed"]; "eve", ["jon";"hal";"fred";"dan";"abe";"gav";"col";"ed";"ian";"bob"]; "fay", ["bob";"abe";"ed";"ian";"jon";"dan";"fred";"gav";"col";"hal"]; "gay", ["jon";"gav";"hal";"fred";"bob";"abe";"col";"ed";"dan";"ian"]; "hope", ["gav";"jon";"bob";"abe";"ian";"dan";"hal";"ed";"col";"fred"]; "ivy", ["ian";"col";"hal";"gav";"fred";"bob";"abe";"ed";"jon";"dan"]; "jan", ["ed";"hal";"gav";"abe";"bob";"jon";"col";"ian";"fred";"dan"];
]
type woman_name = string type man_name = string
type man =
{ m_name: man_name;
mutable free: bool;
women_rank: woman_name list;
has_proposed: (woman_name, unit) Hashtbl.t (* a set *)
}
type woman =
{ w_name: woman_name;
men_rank: man_name list;
mutable engaged: man_name option
}
let prefers w m1 m2 =
(* returns true if w has a lower (better) rank for m1 than m2 *) let rec aux = function | [] -> invalid_arg "rank_cmp" | x::_ when x = m1 -> true | x::_ when x = m2 -> false | _::xs -> aux xs in aux w.men_rank
let take_while f lst =
let rec aux acc = function | x::xs when f x -> aux (x::acc) xs | _ -> List.rev acc in aux [] lst
let more_ranked_than name =
take_while ((<>) name)
let build_structs ~men ~women =
List.map (fun (name, rank) ->
{ m_name = name;
women_rank = rank;
free = true;
has_proposed = Hashtbl.create 42 }
) men,
List.map (fun (name, rank) ->
{ w_name = name;
men_rank = rank;
engaged = None }
) women
let _stable_matching ms ws =
let men_by_name = Hashtbl.create 42 in
List.iter (fun m -> Hashtbl.add men_by_name m.m_name m) ms;
let women_by_name = Hashtbl.create 42 in
List.iter (fun w -> Hashtbl.add women_by_name w.w_name w) ws;
try
while true do
(*TODO free men who still has some w to propose to *)
let m = List.find (fun m -> m.free) ms in
(* highest ranked woman who the man has not proposed to yet *)
let w_name =
List.find (fun w -> not (Hashtbl.mem m.has_proposed w)) m.women_rank in
Hashtbl.add m.has_proposed w_name ();
let w = Hashtbl.find women_by_name w_name in
match w.engaged with
| None -> (* w is free *)
(* (m, w) become engaged *)
w.engaged <- Some m.m_name;
m.free <- false
| Some m'_name -> (* some pair (m', w) already exists *)
if prefers w m.m_name m'_name
then begin (* w prefers m to m' *)
w.engaged <- Some m.m_name;
let m' = Hashtbl.find men_by_name m'_name in
m'.free <- true;
m.free <- false
end
done;
assert false
with Not_found -> ()
let stable_matching ~men ~women =
let ms, ws = build_structs ~men ~women in _stable_matching ms ws; let some = function Some v -> v | None -> "" in List.map (fun w -> w.w_name, some w.engaged) ws
let is_stable ~men ~women eng =
let ms, ws = build_structs ~men ~women in
not (List.exists (fun (wn, mn) ->
let m = List.find (fun m -> m.m_name = mn) ms in
let prefered_women = more_ranked_than wn m.women_rank in
List.exists (fun pref_w ->
let w = List.find (fun w -> w.w_name = pref_w) ws in
let eng_m = List.assoc pref_w eng in
let prefered_men = more_ranked_than eng_m w.men_rank in
List.mem m.m_name prefered_men (* exists unstable engagement *)
) prefered_women
) eng)
let perturb_engagements eng =
Random.self_init(); let eng = Array.of_list eng in let len = Array.length eng in for n = 1 to 3 do let i = Random.int len and j = Random.int len in let w1, m1 = eng.(i) and w2, m2 = eng.(j) in eng.(i) <- (w1, m2); eng.(j) <- (w2, m1); done; Array.to_list eng
let print engs =
List.iter (fun (w,m) -> Printf.printf " %4s is engaged with %s\n" w m) engs; Printf.printf "# Engagements %s stable\n" (if is_stable ~men ~women engs then "are" else "are not")
let () =
let engagements = stable_matching ~men ~women in print engagements; print_endline "========================"; let engagements = perturb_engagements engagements in print engagements;
- </lang>
- Output:
fay is engaged with dan ivy is engaged with abe cath is engaged with bob eve is engaged with hal abi is engaged with jon dee is engaged with col hope is engaged with ian gay is engaged with gav bea is engaged with fred jan is engaged with ed # Engagements are stable ======================== fay is engaged with abe ivy is engaged with dan cath is engaged with hal eve is engaged with bob abi is engaged with jon dee is engaged with col hope is engaged with ed gay is engaged with gav bea is engaged with fred jan is engaged with ian # Engagements are not stable
Perl
<lang Perl>#!/usr/bin/env perl use strict; use warnings; use feature qw/say/; use List::Util qw(first);
my %Likes = (
M => {
abe => [qw/ abi eve cath ivy jan dee fay bea hope gay /],
bob => [qw/ cath hope abi dee eve fay bea jan ivy gay /],
col => [qw/ hope eve abi dee bea fay ivy gay cath jan /],
dan => [qw/ ivy fay dee gay hope eve jan bea cath abi /],
ed => [qw/ jan dee bea cath fay eve abi ivy hope gay /],
fred => [qw/ bea abi dee gay eve ivy cath jan hope fay /],
gav => [qw/ gay eve ivy bea cath abi dee hope jan fay /],
hal => [qw/ abi eve hope fay ivy cath jan bea gay dee /],
ian => [qw/ hope cath dee gay bea abi fay ivy jan eve /],
jon => [qw/ abi fay jan gay eve bea dee cath ivy hope /],
},
W => {
abi => [qw/ bob fred jon gav ian abe dan ed col hal /],
bea => [qw/ bob abe col fred gav dan ian ed jon hal /],
cath => [qw/ fred bob ed gav hal col ian abe dan jon /],
dee => [qw/ fred jon col abe ian hal gav dan bob ed /],
eve => [qw/ jon hal fred dan abe gav col ed ian bob /],
fay => [qw/ bob abe ed ian jon dan fred gav col hal /],
gay => [qw/ jon gav hal fred bob abe col ed dan ian /],
hope => [qw/ gav jon bob abe ian dan hal ed col fred /],
ivy => [qw/ ian col hal gav fred bob abe ed jon dan /],
jan => [qw/ ed hal gav abe bob jon col ian fred dan /],
},
);
my %Engaged; my %Proposed;
match_them(); check_stability(); perturb(); check_stability();
sub match_them {
say 'Matchmaking:';
while(my $man = unmatched_man()) {
my $woman = preferred_choice($man);
$Proposed{$man}{$woman} = 1;
if(! $Engaged{W}{$woman}) {
engage($man, $woman);
say "\t$woman and $man";
}
else {
if(woman_prefers($woman, $man)) {
my $engaged_man = $Engaged{W}{$woman};
engage($man, $woman);
undef $Engaged{M}{$engaged_man};
say "\t$woman dumped $engaged_man for $man";
}
}
}
}
sub check_stability {
say 'Stablility:';
my $stable = 1;
foreach my $m (men()) {
foreach my $w (women()) {
if(man_prefers($m, $w) && woman_prefers($w, $m)) {
say "\t$w prefers $m to $Engaged{W}{$w} and $m prefers $w to $Engaged{M}{$m}";
$stable = 0;
}
}
}
if($stable) {
say "\t(all marriages stable)";
}
}
sub unmatched_man {
return first { ! $Engaged{M}{$_} } men();
}
sub preferred_choice {
my $man = shift;
return first { ! $Proposed{$man}{$_} } @{ $Likes{M}{$man} };
}
sub engage {
my ($man, $woman) = @_;
$Engaged{W}{$woman} = $man;
$Engaged{M}{$man} = $woman;
}
sub prefers {
my $sex = shift;
return sub {
my ($person, $prospect) = @_;
my $choices = join ' ', @{ $Likes{$sex}{$person} };
return index($choices, $prospect) < index($choices, $Engaged{$sex}{$person});
}
}
BEGIN {
*woman_prefers = prefers('W');
*man_prefers = prefers('M');
}
sub perturb {
say 'Perturb:';
say "\tengage abi with fred and bea with jon";
engage('fred' => 'abi');
engage('jon' => 'bea');
}
sub men { keys %{ $Likes{M} } } sub women { keys %{ $Likes{W} } }</lang>
- Output:
Matchmaking:
abi and abe
ivy and dan
abi dumped abe for jon
eve and abe
eve dumped abe for hal
cath and abe
gay and gav
jan and ed
hope and ian
dee and col
cath dumped abe for bob
ivy dumped dan for abe
fay and dan
bea and fred
Stablility:
(all marriages stable)
Perturb:
engage abi with fred and bea with jon
Stablility:
eve prefers jon to hal and jon prefers eve to bea
gay prefers jon to gav and jon prefers gay to bea
fay prefers jon to dan and jon prefers fay to bea
bea prefers fred to jon and fred prefers bea to abi
Perl 6
<lang perl6>my %he-likes =
abe => < abi eve cath ivy jan dee fay bea hope gay >, bob => < cath hope abi dee eve fay bea jan ivy gay >, col => < hope eve abi dee bea fay ivy gay cath jan >, dan => < ivy fay dee gay hope eve jan bea cath abi >, ed => < jan dee bea cath fay eve abi ivy hope gay >, fred => < bea abi dee gay eve ivy cath jan hope fay >, gav => < gay eve ivy bea cath abi dee hope jan fay >, hal => < abi eve hope fay ivy cath jan bea gay dee >, ian => < hope cath dee gay bea abi fay ivy jan eve >, jon => < abi fay jan gay eve bea dee cath ivy hope >,
my %she-likes =
abi => < bob fred jon gav ian abe dan ed col hal >, bea => < bob abe col fred gav dan ian ed jon hal >, cath => < fred bob ed gav hal col ian abe dan jon >, dee => < fred jon col abe ian hal gav dan bob ed >, eve => < jon hal fred dan abe gav col ed ian bob >, fay => < bob abe ed ian jon dan fred gav col hal >, gay => < jon gav hal fred bob abe col ed dan ian >, hope => < gav jon bob abe ian dan hal ed col fred >, ivy => < ian col hal gav fred bob abe ed jon dan >, jan => < ed hal gav abe bob jon col ian fred dan >,
my \guys = %he-likes.keys; my \gals = %she-likes.keys;
my %fiancé; my %fiancée; my %proposed;
sub she-prefers ($her, $hottie) { .index($hottie) < .index(%fiancé{$her}) given ~%she-likes{$her} } sub he-prefers ($him, $hottie) { .index($hottie) < .index(%fiancée{$him}) given ~%he-likes{$him} }
match'em; check-stability;
perturb'em; check-stability;
sub match'em { #'
say 'Matchmaking:';
while unmatched-guy() -> $guy {
my $gal = preferred-choice($guy);
%proposed{"$guy $gal"} = '❤';
if not %fiancé{$gal} {
engage($guy, $gal);
say "\t$gal and $guy";
}
elsif she-prefers($gal, $guy) {
my $engaged-guy = %fiancé{$gal}; engage($guy, $gal); %fiancée{$engaged-guy} = ; say "\t$gal dumped $engaged-guy for $guy"; }
}
}
sub check-stability {
my @instabilities = gather for guys X gals -> $m, $w {
if he-prefers($m, $w) and she-prefers($w, $m) { take "\t$w prefers $m to %fiancé{$w} and $m prefers $w to %fiancée{$m}"; }
}
say 'Stablility:';
if @instabilities {
.say for @instabilities;
}
else {
say "\t(all marriages stable)";
}
}
sub unmatched-guy { guys.first: { not %fiancée{$_} } }
sub preferred-choice($guy) { %he-likes{$guy}.first: { not %proposed{"$guy $_" } } }
sub engage($guy, $gal) {
%fiancé{$gal} = $guy;
%fiancée{$guy} = $gal;
}
sub perturb'em { #'
say 'Perturb:';
say "\tengage abi with fred and bea with jon";
engage('fred', 'abi');
engage('jon', 'bea');
}</lang>
- Output:
Matchmaking: abi and abe cath and bob hope and col ivy and dan jan and ed bea and fred gay and gav eve and hal hope dumped col for ian dee and col abi dumped abe for jon ivy dumped dan for abe fay and dan Stablility: (all marriages stable) Perturb: engage abi with fred and bea with jon Stablility: bea prefers fred to jon and fred prefers bea to abi eve prefers jon to hal and jon prefers eve to bea fay prefers jon to dan and jon prefers fay to bea gay prefers jon to gav and jon prefers gay to bea
PicoLisp
<lang PicoLisp>(setq
*Boys (list
(de abe abi eve cath ivy jan dee fay bea hope gay)
(de bob cath hope abi dee eve fay bea jan ivy gay)
(de col hope eve abi dee bea fay ivy gay cath jan)
(de dan ivy fay dee gay hope eve jan bea cath abi)
(de ed jan dee bea cath fay eve abi ivy hope gay)
(de fred bea abi dee gay eve ivy cath jan hope fay)
(de gav gay eve ivy bea cath abi dee hope jan fay)
(de hal abi eve hope fay ivy cath jan bea gay dee)
(de ian hope cath dee gay bea abi fay ivy jan eve)
(de jon abi fay jan gay eve bea dee cath ivy hope) )
*Girls (list
(de bi bob fred jon gav ian abe dan ed col hal)
(de bea bob abe col fred gav dan ian ed jon hal)
(de cath fred bob ed gav hal col ian abe dan jon)
(de dee fred jon col abe ian hal gav dan bob ed)
(de eve jon hal fred dan abe gav col ed ian bob)
(de fay bob abe ed ian jon dan fred gav col hal)
(de gay jon gav hal fred bob abe col ed dan ian)
(de hope gav jon bob abe ian dan hal ed col fred)
(de ivy ian col hal gav fred bob abe ed jon dan)
(de jan ed hal gav abe bob jon col ian fred dan) )
*Couples NIL )
(bind *Boys
(while
(find
'((Boy) (and (val Boy) (not (asoq Boy *Couples))))
*Boys )
(let (Boy @ Girl (pop Boy) Pair (find '((P) (== Girl (cdr P))) *Couples))
(nond
(Pair (push '*Couples (cons Boy Girl))) # Girl is free
((memq Boy (memq (car Pair) (val Girl))) # Girl prefers Boy
(set Pair Boy) ) ) ) ) )
(for Pair *Couples
(prinl (cdr Pair) " is engaged to " (car Pair)) )
(de checkCouples ()
(unless
(filter
'((Pair)
(let (Boy (car Pair) Girl (cdr Pair))
(find
'((B)
(and
(memq Boy (cdr (memq B (val Girl)))) # Girl prefers B
(memq
(cdr (asoq B *Couples)) # and B prefers Girl
(cdr (memq Girl (val B))) )
(prinl
Girl " likes " B " better than " Boy " and "
B " likes " Girl " better than "
(cdr (asoq B *Couples)) ) ) )
(val Girl) ) ) )
*Couples )
(prinl "All marriages are stable") ) )
(checkCouples) (prinl) (prinl "Engage fred with abi and jon with bea") (con (asoq 'fred *Couples) 'abi) (con (asoq 'jon *Couples) 'bea) (checkCouples)</lang>
- Output:
dee is engaged to col fay is engaged to dan eve is engaged to hal gay is engaged to gav bea is engaged to fred jan is engaged to ed ivy is engaged to abe hope is engaged to ian cath is engaged to bob abi is engaged to jon All marriages are stable Engage fred with abi and jon with bea fay likes jon better than dan and jon likes fay better than bea eve likes jon better than hal and jon likes eve better than bea gay likes jon better than gav and jon likes gay better than bea bea likes fred better than jon and fred likes bea better than abi
Prolog
XPCE is used for its integrated messaging system. <lang Prolog>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % facts prefere(abe,[ abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay]). prefere( bob,[ cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay]). prefere( col,[ hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan]). prefere( dan,[ ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi]). prefere( ed,[ jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay]). prefere( fred,[ bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay]). prefere( gav,[ gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay]). prefere( hal,[ abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee]). prefere( ian,[ hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve]). prefere( jon,[ abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope]).
prefere( abi,[ bob, fred, jon, gav, ian, abe, dan, ed, col, hal]). prefere( bea,[ bob, abe, col, fred, gav, dan, ian, ed, jon, hal]). prefere( cath,[ fred, bob, ed, gav, hal, col, ian, abe, dan, jon]). prefere( dee,[ fred, jon, col, abe, ian, hal, gav, dan, bob, ed]). prefere( eve,[ jon, hal, fred, dan, abe, gav, col, ed, ian, bob]). prefere( fay,[ bob, abe, ed, ian, jon, dan, fred, gav, col, hal]). prefere( gay,[ jon, gav, hal, fred, bob, abe, col, ed, dan, ian]). prefere( hope,[ gav, jon, bob, abe, ian, dan, hal, ed, col, fred]). prefere( ivy,[ ian, col, hal, gav, fred, bob, abe, ed, jon, dan]). prefere( jan,[ ed, hal, gav, abe, bob, jon, col, ian, fred, dan]).
man(abe).
man(bob).
man(col).
man(dan).
man(ed).
man(fred).
man(gav).
man(hal).
man(ian).
man(jon).
woman(abi). woman(bea). woman(cath). woman(dee). woman(eve). woman(fay). woman(gay). woman(hope). woman(ivy). woman(jan).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % rules
stable_mariage :- new(LstMan, chain), forall(man(X), ( prefere(X, Lst), new(P, man(X, Lst)), send(LstMan, append, P))),
new(LstWoman, chain), forall(woman(X), ( prefere(X, Lst), new(P, woman(X, Lst)), send(LstWoman, append, P))), send(LstMan, for_all, message(@arg1, init_liste, LstWoman)), send(LstWoman, for_all, message(@arg1, init_liste, LstMan)),
round(LstMan, LstWoman), new(LstCouple, chain), % creation of the couple. send(LstWoman, for_all, and(message(@prolog, create_couple, @arg1, LstCouple), message(@pce, write_ln, @arg1?name, with, @arg1?elu?name))),
nl,
% test of the stability of couples stability(LstCouple), nl,
% Perturbation of couples get(LstCouple, size, Len), get_two_random_couples(Len, V1, V2),
get(LstCouple, nth0, V1, C1), get(LstCouple, nth0, V2, C2), new(NC1, tuple(C1?first, C2?second)), new(NC2, tuple(C2?first, C1?second)), send(LstCouple, nth0, V1, NC1), send(LstCouple, nth0, V2, NC2),
send(@pce, write_ln, 'perturbation of couples'), send(@pce, write_ln, NC1?second, with, NC1?first), send(@pce, write_ln, NC2?second, with, NC2?first), nl,
stability(LstCouple).
get_two_random_couples(Len, C1, C2) :- C1 is random(Len), repeat, C2 is random(Len), C1 \= C2.
create_couple(Woman, LstCouple ) :- send(LstCouple, append, new(_, tuple(Woman?elu?name, Woman?name))).
% iterations of the algorithm round(LstMan, LstWoman) :- send(LstMan, for_some, message(@arg1, propose)), send(LstWoman, for_some, message(@arg1, dispose)), ( \+send(LstWoman, for_all, @arg1?status == maybe) -> round(LstMan, LstWoman) ; true ).
- -pce_begin_class(person, object, "description of a person").
variable(name, object, both, "name of the person"). variable(preference, chain, both, "list of priority"). variable(status, object, both, "statut of engagement : maybe / free").
initialise(P, Name, Pref) :-> send(P, send_super, initialise), send(P, slot, name, Name), send(P, slot, preference, Pref), send(P, slot, status, free).
% reception of the list of partners init_liste(P, Lst) :-> % we replace the list of name of partners % with the list of persons partners. new(NLP, chain), get(P, slot, preference, LP), send(LP, for_all, message(@prolog, find_person,@arg1, Lst, NLP)), send(P, slot, preference, NLP).
- - pce_end_class(person).
find_person(Name, LstPerson, LstPref) :- get(LstPerson, find, @arg1?name == Name, Elem), send(LstPref, append, Elem).
- -pce_begin_class(man, person, "description of a man").
initialise(P, Name, Pref) :-> send(P, send_super, initialise, Name, Pref).
% a man propose "la botte" to a woman propose(P) :-> get(P, slot, status, free), get(P, slot, preference, XPref), get(XPref, delete_head, Pref), send(P, slot, preference, XPref), send(Pref, proposition, P).
refuse(P) :-> send(P, slot, status, free).
accept(P) :-> send(P, slot, status, maybe).
- - pce_end_class(man).
- -pce_begin_class(woman, person, "description of a woman").
variable(elu, object, both, "name of the elu"). variable(contact, chain, both, "men that have contact this woman").
initialise(P, Name, Pref) :-> send(P, send_super, initialise, Name, Pref), send(P, slot, contact, new(_, chain)), send(P, slot, elu, @nil).
% a woman decide Maybe/No dispose(P) :-> get(P, slot, contact, Contact), get(P, slot, elu, Elu),
( Elu \= @nil -> send(Contact, append, Elu) ; true),
new(R, chain), send(Contact, for_all, message(P, fetch, @arg1, R)), send(R, sort, ?(@arg1?first, compare, @arg2?first)), get(R, delete_head, Tete), send(Tete?second, accept), send(P, slot, status, maybe), send(P, slot, elu, Tete?second), send(R, for_some, message(@arg1?second, refuse)), send(P, slot, contact, new(_, chain)) .
% looking for the person of the given name Contact
% Adding it in the chain Chain
fetch(P, Contact, Chain) :->
get(P, slot, preference, Lst),
get(Lst, find, @arg1?name == Contact?name, Elem),
get(Lst, index, Elem, Ind),
send(Chain, append, new(_, tuple(Ind, Contact))).
% a woman receive a proposition from a man proposition(P, Name) :-> get(P, slot, contact, C), send(C, append, Name), send(P, slot, contact, C).
- - pce_end_class(woman).
% computation of the stability od couple stability(LstCouple) :- chain_list(LstCouple, LstPceCouple), maplist(transform, LstPceCouple, PrologLstCouple), study_couples(PrologLstCouple, [], UnstableCouple), ( UnstableCouple = [] -> writeln('Couples are stable') ; sort(UnstableCouple, SortUnstableCouple), writeln('Unstable couples are'), maplist(print_unstable_couple, SortUnstableCouple), nl ).
print_unstable_couple((C1, C2)) :-
format('~w and ~w~n', [C1, C2]).
transform(PceCouple, couple(First, Second)):- get(PceCouple?first, value, First), get(PceCouple?second, value, Second).
study_couples([], UnstableCouple, UnstableCouple).
study_couples([H | T], CurrentUnstableCouple, UnstableCouple):- include(unstable_couple(H), T, Lst), ( Lst \= [] -> maplist(build_one_couple(H), Lst, Lst1), append(CurrentUnstableCouple, Lst1,CurrentUnstableCouple1) ; CurrentUnstableCouple1 = CurrentUnstableCouple ), study_couples(T, CurrentUnstableCouple1, UnstableCouple).
build_one_couple(C1, C2, (C1, C2)).
unstable_couple(couple(X1, Y1), couple(X2, Y2)) :- prefere(X1, PX1), prefere(X2, PX2), prefere(Y1, PY1), prefere(Y2, PY2),
% index of women for X1 nth0(IY12, PX1, Y2), nth0(IY11, PX1, Y1), % index of men for Y2 nth0(IX21, PY2, X1), nth0(IX22, PY2, X2),
% index of women for X2 nth0(IY21, PX2, Y1), nth0(IY22, PX2, Y2), % index of men for Y1 nth0(IX11, PY1, X1), nth0(IX12, PY1, X2),
% A couple is unstable ( (IY12 < IY11 , IX21 < IX22); (IY21 < IY22 , IX12 < IX11)). </lang>
- Output:
?- stable_mariage. abi with jon bea with fred cath with bob dee with col eve with hal fay with dan gay with gav hope with ian ivy with abe jan with ed Couples are stable perturbation of couples gay with jon abi with gav Unstable couples are couple(gav,abi) and couple(abe,ivy) couple(jon,gay) and couple(dan,fay) couple(jon,gay) and couple(gav,abi) true
A more Prolog-ish version (working with SWI-Prolog) could be : <lang Prolog>:- dynamic person/4, prop/2. % person(Name, Preference, Status, Candidate) % prop(Name, List_of_Candidates) (for a woman)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % facts prefere(abe,[ abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay]). prefere( bob,[ cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay]). prefere( col,[ hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan]). prefere( dan,[ ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi]). prefere( ed,[ jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay]). prefere( fred,[ bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay]). prefere( gav,[ gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay]). prefere( hal,[ abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee]). prefere( ian,[ hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve]). prefere( jon,[ abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope]).
prefere( abi,[ bob, fred, jon, gav, ian, abe, dan, ed, col, hal]). prefere( bea,[ bob, abe, col, fred, gav, dan, ian, ed, jon, hal]). prefere( cath,[ fred, bob, ed, gav, hal, col, ian, abe, dan, jon]). prefere( dee,[ fred, jon, col, abe, ian, hal, gav, dan, bob, ed]). prefere( eve,[ jon, hal, fred, dan, abe, gav, col, ed, ian, bob]). prefere( fay,[ bob, abe, ed, ian, jon, dan, fred, gav, col, hal]). prefere( gay,[ jon, gav, hal, fred, bob, abe, col, ed, dan, ian]). prefere( hope,[ gav, jon, bob, abe, ian, dan, hal, ed, col, fred]). prefere( ivy,[ ian, col, hal, gav, fred, bob, abe, ed, jon, dan]). prefere( jan,[ ed, hal, gav, abe, bob, jon, col, ian, fred, dan]).
man(abe).
man(bob).
man(col).
man(dan).
man(ed).
man(fred).
man(gav).
man(hal).
man(ian).
man(jon).
woman(abi). woman(bea). woman(cath). woman(dee). woman(eve). woman(fay). woman(gay). woman(hope). woman(ivy). woman(jan).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % rules stable_mariage :- %initialization retractall(person(_,_,_,_)), retractall(prop(_,_)), forall(prefere(P, Pref), assert(person(P, Pref, free, none))), bagof(X, man(X), LstMen), bagof(Y, woman(Y), LstWomen), forall(member(Z, LstWomen), assert(prop(Z, []))),
% compute the mariages iteration(LstMen, LstWomen, LstCouple), maplist(print_couple,LstCouple), nl,
% test of the stability of couples stability(LstCouple), nl,
% Perturbation of couples length(LstCouple, Len), get_two_random_couples(Len, V1, V2),
nth0(V1, LstCouple, C1), select(C1, LstCouple, Lst1), ( V2 > 0 -> V22 is V2 - 1; V22 = V2), nth0(V22, Lst1, C2), select(C2, Lst1, Lst2), C1 = couple(M1, W1), C2 = couple(M2, W2),
writeln('perturbation of couples'), format('~w with ~w~n', [W1, M2]), format('~w with ~w~n', [W2, M1]), nl, stability([couple(M1, W2), couple(M2, W1)| Lst2]).
% the algorithm
iteration(Men, Women, LstCouples) :-
% Men propose
bagof(M, X^Y^(member(M, Men),person(M, X, free, Y)), LM),
forall(member(X, LM),
( retract(person(X, [W|Pref], free, Elu)),
assert(person(X, Pref, free, Elu)),
retract(prop(W, Prop)),
assert(prop(W, [X| Prop])))),
% women dispose bagof(W, L^(prop(W, L), L \= []), LW), forall(member(W, LW), ( retract(prop(W, Prop)), retract(person(W, Pref, _, Elu)), ( Elu = none -> Prop1 = Prop; Prop1 = [Elu|Prop]), order_prop(Pref, Prop1, [M | Prop2]), retract(person(M, PrefM, _, _)), assert(person(M, PrefM, maybe, W)), forall(member(Y, Prop2), ( retract(person(Y, Pref1, _, _TE)), assert(person(Y, Pref1, free, none)))), assert(prop(W, [])), assert(person(W, Pref, maybe, M)) )),
% finished ? ( bagof(X, T^Z^(member(X, Women), person(X, T, free, Z)), _LW1) -> iteration(Men, Women, LstCouples) ; make_couple(Women, LstCouples) ).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % compute order preference of candidates. order_prop(Pref, Prop, Res) :- maplist(index(Pref), Prop, Rtemp), sort(Rtemp, Rtemp1), maplist(simplifie,Rtemp1, Res).
index(Lst, Value, [Ind, Value]) :- nth0(Ind, Lst, Value).
simplifie([_, V], V).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% print_couple(couple(M, W)) :- format('~w with ~w~n', [W, M]).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % creation of couples make_couple([], []).
make_couple([W | LW], [couple(M, W) | LC]) :- make_couple(LW, LC), person(W, _, _, M).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % miscellaneous get_two_random_couples(Len, C1, C2) :- C1 is random(Len), repeat, C2 is random(Len), C1 \= C2.
print_unstable_couple((C1, C2)) :- format('~w and ~w~n', [C1, C2]).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% test the stability of couples
stability(LstCouple) :-
study_couples(LstCouple, [], CoupleInstable),
( CoupleInstable = []
->
writeln('Couples are stable')
;
sort(CoupleInstable, SortCoupleInstable),
writeln('Unstable couples are'),
maplist(print_unstable_couple, SortCoupleInstable),
nl
).
% compute the stability od couple
study_couples([], UnstableCouple, UnstableCouple).
study_couples([H | T], CurrentUnstableCouple, UnstableCouple):- include(unstable_couple(H), T, Lst), ( Lst \= [] -> maplist(build_one_couple(H), Lst, Lst1), append(CurrentUnstableCouple, Lst1,CurrentUnstableCouple1) ; CurrentUnstableCouple1 = CurrentUnstableCouple ), study_couples(T, CurrentUnstableCouple1, UnstableCouple).
build_one_couple(C1, C2, (C1, C2)).
unstable_couple(couple(X1, Y1), couple(X2, Y2)) :- prefere(X1, PX1), prefere(X2, PX2), prefere(Y1, PY1), prefere(Y2, PY2),
% index of women for X1 nth0(IY12, PX1, Y2), nth0(IY11, PX1, Y1), % index of men for Y2 nth0(IX21, PY2, X1), nth0(IX22, PY2, X2),
% index of women for X2 nth0(IY21, PX2, Y1), nth0(IY22, PX2, Y2), % index of men for Y1 nth0(IX11, PY1, X1), nth0(IX12, PY1, X2),
% A couple is unstable ( (IY12 < IY11 , IX21 < IX22); (IY21 < IY22 , IX12 < IX11)).</lang>
PureBasic
This approach uses a messaging system to pass messages between prospective partners. <lang PureBasic>#coupleCount = 10
DataSection
;guys Data.s "abe: abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay" Data.s "bob: cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay" Data.s "col: hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan" Data.s "dan: ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi" Data.s "ed: jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay" Data.s "fred: bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay" Data.s "gav: gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay" Data.s "hal: abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee" Data.s "ian: hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve" Data.s "jon: abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope" ;gals Data.s "abi: bob, fred, jon, gav, ian, abe, dan, ed, col, hal" Data.s "bea: bob, abe, col, fred, gav, dan, ian, ed, jon, hal" Data.s "cath: fred, bob, ed, gav, hal, col, ian, abe, dan, jon" Data.s "dee: fred, jon, col, abe, ian, hal, gav, dan, bob, ed" Data.s "eve: jon, hal, fred, dan, abe, gav, col, ed, ian, bob" Data.s "fay: bob, abe, ed, ian, jon, dan, fred, gav, col, hal" Data.s "gay: jon, gav, hal, fred, bob, abe, col, ed, dan, ian" Data.s "hope: gav, jon, bob, abe, ian, dan, hal, ed, col, fred" Data.s "ivy: ian, col, hal, gav, fred, bob, abe, ed, jon, dan" Data.s "jan: ed, hal, gav, abe, bob, jon, col, ian, fred, dan"
EndDataSection
Structure message
source.s ;person that message is from
dest.s ;person that message is for
action.s ;{'P', 'A', 'D', 'B'} for proposal, accept, decline, break-up
EndStructure
Structure person
name.s isEngagedTo.s List prefs.s()
EndStructure
Global NewList messages.message()
Procedure setupPersons(List persons.person(), count)
Protected i, j, start, pref$
For i = 1 To count
Read.s pref$
pref$ = LCase(pref$)
start = FindString(pref$, ":", 1)
AddElement(persons())
persons()\name = Left(pref$, start - 1)
pref$ = Trim(Right(pref$, Len(pref$) - start))
For j = 1 To count
AddElement(persons()\prefs())
persons()\prefs() = Trim(StringField(pref$, j, ","))
Next
Next
EndProcedure
Procedure sendMessage(source.s, dest.s, action.s)
LastElement(messages()) AddElement(messages()) With messages() \source = source \dest = dest \action = action EndWith ResetList(messages())
EndProcedure
Procedure selectPerson(name.s, List persons.person())
ForEach persons()
If persons()\name = name
Break
EndIf
Next
EndProcedure
Procedure rankPerson(name.s, List prefs.s())
ForEach prefs()
If prefs() = name
ProcedureReturn #coupleCount - ListIndex(prefs()) ;higher is better
EndIf
Next
ProcedureReturn -1 ;no rank, shouldn't occur
EndProcedure
Procedure stabilityCheck(List guys.person(), List gals.person())
Protected isStable = #True
ForEach guys()
rankPerson(guys()\isEngagedTo, guys()\prefs())
While PreviousElement(guys()\prefs())
selectPerson(guys()\prefs(), gals())
If rankPerson(guys()\name, gals()\prefs()) > rankPerson(gals()\isEngagedTo, gals()\prefs())
Print(" " + gals()\name + " loves " + guys()\name + " more than " + gals()\isEngagedTo + ",")
PrintN(" And " + guys()\name + " loves " + gals()\name + " more than " + guys()\isEngagedTo + ".")
isStable = #False
EndIf
Wend
Next
If isStable
PrintN(#CRLF$ + "Marriage stability check PASSED.")
Else
PrintN(#CRLF$ + "Marriage stability check FAILED.")
EndIf
EndProcedure
NewList guys.person() NewList gals.person() setupPersons(guys(), #coupleCount) setupPersons(gals(), #coupleCount)
- make initial round of proposals
ForEach guys()
FirstElement(guys()\prefs()) sendMessage(guys()\name, guys()\prefs(), "P")
Next
- dispatch messages
Define source.s, dest.s, action.s ForEach messages()
source = messages()\source
dest = messages()\dest
action = messages()\action
DeleteElement(messages())
Select action
Case "P" ;propose ;only message received by gals
selectPerson(dest, gals())
selectPerson(source, guys())
If rankPerson(guys()\name, gals()\prefs()) < rankPerson(gals()\isEngagedTo, gals()\prefs())
sendMessage(dest, source, "D") ;decline proposal
ElseIf rankPerson(guys()\name, gals()\prefs()) > rankPerson(gals()\isEngagedTo, gals()\prefs())
If gals()\isEngagedTo
sendMessage(dest, gals()\isEngagedTo, "B") ;break-up engagement
EndIf
gals()\isEngagedTo = source
sendMessage(dest, source, "A") ;accept proposal
EndIf
Case "A", "D", "B" ;messages received by guys
selectPerson(dest, guys())
If action = "A" ;proposal accepted
guys()\isEngagedTo = source
Else
If action = "B" ;broke-up
guys()\isEngagedTo = ""
EndIf
NextElement(guys()\prefs())
sendMessage(dest, guys()\prefs(),"P") ;propose to next pref
EndIf
EndSelect
Next
If OpenConsole()
PrintN("Marriages:")
ForEach guys()
PrintN(" " + guys()\name + " And " + guys()\isEngagedTo + ".")
Next
stabilityCheck(guys(), gals())
Define *person_1.person, *person_2.person
PrintN(#CRLF$ + "Introducing an error by swapping partners of abi and bea.")
selectPerson("abi", gals()): *person_1 = @gals()
selectPerson("bea", gals()): *person_2 = @gals()
Swap *person_1\isEngagedTo, *person_2\isEngagedTo
selectPerson(*person_1\isEngagedTo, guys()): *person_1 = @guys()
selectPerson(*person_1\isEngagedTo, guys()): *person_2 = @guys()
Swap *person_1\isEngagedTo, *person_2\isEngagedTo
PrintN(" " + *person_1\name + " is now with " + *person_1\isEngagedTo + ".")
PrintN(" " + *person_2\name + " is now with " + *person_2\isEngagedTo + ".")
PrintN("")
stabilityCheck(guys(), gals())
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf</lang>
- Output:
Marriages: abe And ivy. bob And cath. col And dee. dan And fay. ed And jan. fred And bea. gav And gay. hal And eve. ian And hope. jon And abi. Marriage stability check PASSED. Introducing an error by swapping partners of abi and bea. fred is now with abi. jon is now with bea. bea loves fred more than jon, And fred loves bea more than abi. eve loves jon more than hal, And jon loves eve more than bea. gay loves jon more than gav, And jon loves gay more than bea. fay loves jon more than dan, And jon loves fay more than bea. Marriage stability check FAILED.
Python
<lang python>import copy
guyprefers = {
'abe': ['abi', 'eve', 'cath', 'ivy', 'jan', 'dee', 'fay', 'bea', 'hope', 'gay'], 'bob': ['cath', 'hope', 'abi', 'dee', 'eve', 'fay', 'bea', 'jan', 'ivy', 'gay'], 'col': ['hope', 'eve', 'abi', 'dee', 'bea', 'fay', 'ivy', 'gay', 'cath', 'jan'], 'dan': ['ivy', 'fay', 'dee', 'gay', 'hope', 'eve', 'jan', 'bea', 'cath', 'abi'], 'ed': ['jan', 'dee', 'bea', 'cath', 'fay', 'eve', 'abi', 'ivy', 'hope', 'gay'], 'fred': ['bea', 'abi', 'dee', 'gay', 'eve', 'ivy', 'cath', 'jan', 'hope', 'fay'], 'gav': ['gay', 'eve', 'ivy', 'bea', 'cath', 'abi', 'dee', 'hope', 'jan', 'fay'], 'hal': ['abi', 'eve', 'hope', 'fay', 'ivy', 'cath', 'jan', 'bea', 'gay', 'dee'], 'ian': ['hope', 'cath', 'dee', 'gay', 'bea', 'abi', 'fay', 'ivy', 'jan', 'eve'], 'jon': ['abi', 'fay', 'jan', 'gay', 'eve', 'bea', 'dee', 'cath', 'ivy', 'hope']}
galprefers = {
'abi': ['bob', 'fred', 'jon', 'gav', 'ian', 'abe', 'dan', 'ed', 'col', 'hal'], 'bea': ['bob', 'abe', 'col', 'fred', 'gav', 'dan', 'ian', 'ed', 'jon', 'hal'], 'cath': ['fred', 'bob', 'ed', 'gav', 'hal', 'col', 'ian', 'abe', 'dan', 'jon'], 'dee': ['fred', 'jon', 'col', 'abe', 'ian', 'hal', 'gav', 'dan', 'bob', 'ed'], 'eve': ['jon', 'hal', 'fred', 'dan', 'abe', 'gav', 'col', 'ed', 'ian', 'bob'], 'fay': ['bob', 'abe', 'ed', 'ian', 'jon', 'dan', 'fred', 'gav', 'col', 'hal'], 'gay': ['jon', 'gav', 'hal', 'fred', 'bob', 'abe', 'col', 'ed', 'dan', 'ian'], 'hope': ['gav', 'jon', 'bob', 'abe', 'ian', 'dan', 'hal', 'ed', 'col', 'fred'], 'ivy': ['ian', 'col', 'hal', 'gav', 'fred', 'bob', 'abe', 'ed', 'jon', 'dan'], 'jan': ['ed', 'hal', 'gav', 'abe', 'bob', 'jon', 'col', 'ian', 'fred', 'dan']}
guys = sorted(guyprefers.keys()) gals = sorted(galprefers.keys())
def check(engaged):
inverseengaged = dict((v,k) for k,v in engaged.items())
for she, he in engaged.items():
shelikes = galprefers[she]
shelikesbetter = shelikes[:shelikes.index(he)]
helikes = guyprefers[he]
helikesbetter = helikes[:helikes.index(she)]
for guy in shelikesbetter:
guysgirl = inverseengaged[guy]
guylikes = guyprefers[guy]
if guylikes.index(guysgirl) > guylikes.index(she):
print("%s and %s like each other better than "
"their present partners: %s and %s, respectively"
% (she, guy, he, guysgirl))
return False
for gal in helikesbetter:
girlsguy = engaged[gal]
gallikes = galprefers[gal]
if gallikes.index(girlsguy) > gallikes.index(he):
print("%s and %s like each other better than "
"their present partners: %s and %s, respectively"
% (he, gal, she, girlsguy))
return False
return True
def matchmaker():
guysfree = guys[:]
engaged = {}
guyprefers2 = copy.deepcopy(guyprefers)
galprefers2 = copy.deepcopy(galprefers)
while guysfree:
guy = guysfree.pop(0)
guyslist = guyprefers2[guy]
gal = guyslist.pop(0)
fiance = engaged.get(gal)
if not fiance:
# She's free
engaged[gal] = guy
print(" %s and %s" % (guy, gal))
else:
# The bounder proposes to an engaged lass!
galslist = galprefers2[gal]
if galslist.index(fiance) > galslist.index(guy):
# She prefers new guy
engaged[gal] = guy
print(" %s dumped %s for %s" % (gal, fiance, guy))
if guyprefers2[fiance]:
# Ex has more girls to try
guysfree.append(fiance)
else:
# She is faithful to old fiance
if guyslist:
# Look again
guysfree.append(guy)
return engaged
print('\nEngagements:')
engaged = matchmaker()
print('\nCouples:') print(' ' + ',\n '.join('%s is engaged to %s' % couple
for couple in sorted(engaged.items())))
print() print('Engagement stability check PASSED'
if check(engaged) else 'Engagement stability check FAILED')
print('\n\nSwapping two fiances to introduce an error') engaged[gals[0]], engaged[gals[1]] = engaged[gals[1]], engaged[gals[0]] for gal in gals[:2]:
print(' %s is now engaged to %s' % (gal, engaged[gal]))
print() print('Engagement stability check PASSED'
if check(engaged) else 'Engagement stability check FAILED')</lang>
- Output:
Engagements: abe and abi bob and cath col and hope dan and ivy ed and jan fred and bea gav and gay hope dumped col for ian abi dumped abe for jon hal and eve col and dee ivy dumped dan for abe dan and fay Couples: abi is engaged to jon, bea is engaged to fred, cath is engaged to bob, dee is engaged to col, eve is engaged to hal, fay is engaged to dan, gay is engaged to gav, hope is engaged to ian, ivy is engaged to abe, jan is engaged to ed Engagement stability check PASSED Swapping two fiances to introduce an error abi is now engaged to fred bea is now engaged to jon fay and jon like each other better than their present partners: dan and bea, respectively Engagement stability check FAILED
Ruby
<lang ruby>class Person
def initialize(name) @name = name @fiance = nil @preferences = [] @proposals = [] end attr_reader :name, :proposals attr_accessor :fiance, :preferences
def to_s @name end
def free @fiance = nil end
def single? @fiance == nil end
def engage(person) self.fiance = person person.fiance = self end
def better_choice?(person) @preferences.index(person) < @preferences.index(@fiance) end
def propose_to(person)
puts "#{self} proposes to #{person}" if $DEBUG
@proposals << person
person.respond_to_proposal_from(self)
end
def respond_to_proposal_from(person)
if single?
puts "#{self} accepts proposal from #{person}" if $DEBUG
engage(person)
elsif better_choice?(person)
puts "#{self} dumps #{@fiance} for #{person}" if $DEBUG
@fiance.free
engage(person)
else
puts "#{self} rejects proposal from #{person}" if $DEBUG
end
end
end
- initialize data
prefs = {
'abe' => %w[abi eve cath ivy jan dee fay bea hope gay], 'bob' => %w[cath hope abi dee eve fay bea jan ivy gay], 'col' => %w[hope eve abi dee bea fay ivy gay cath jan], 'dan' => %w[ivy fay dee gay hope eve jan bea cath abi], 'ed' => %w[jan dee bea cath fay eve abi ivy hope gay], 'fred' => %w[bea abi dee gay eve ivy cath jan hope fay], 'gav' => %w[gay eve ivy bea cath abi dee hope jan fay], 'hal' => %w[abi eve hope fay ivy cath jan bea gay dee], 'ian' => %w[hope cath dee gay bea abi fay ivy jan eve], 'jon' => %w[abi fay jan gay eve bea dee cath ivy hope], 'abi' => %w[bob fred jon gav ian abe dan ed col hal], 'bea' => %w[bob abe col fred gav dan ian ed jon hal], 'cath' => %w[fred bob ed gav hal col ian abe dan jon], 'dee' => %w[fred jon col abe ian hal gav dan bob ed], 'eve' => %w[jon hal fred dan abe gav col ed ian bob], 'fay' => %w[bob abe ed ian jon dan fred gav col hal], 'gay' => %w[jon gav hal fred bob abe col ed dan ian], 'hope' => %w[gav jon bob abe ian dan hal ed col fred], 'ivy' => %w[ian col hal gav fred bob abe ed jon dan], 'jan' => %w[ed hal gav abe bob jon col ian fred dan],
}
@men = Hash[
%w[abe bob col dan ed fred gav hal ian jon].collect do |name| [name, Person.new(name)] end
]
@women = Hash[
%w[abi bea cath dee eve fay gay hope ivy jan].collect do |name| [name, Person.new(name)] end
]
@men.each {|name, man| man.preferences = @women.values_at(*prefs[name])} @women.each {|name, woman| woman.preferences = @men.values_at(*prefs[name])}
- perform the matching
def match_couples(men, women)
men.each_value {|man| man.free}
women.each_value {|woman| woman.free}
while m = men.values.find {|man| man.single?} do
puts "considering single man #{m}" if $DEBUG
w = m.preferences.find {|woman| not m.proposals.include?(woman)}
m.propose_to(w)
end
end
match_couples @men, @women
@men.each_value.collect {|man| puts "#{man} + #{man.fiance}"}
- check for stability
class Person
def more_preferable_people
( @preferences.partition {|p| better_choice?(p)} ).first
end
end
require 'set'
def stability(men)
unstable = Set.new
men.each_value do |man|
woman = man.fiance
puts "considering #{man} and #{woman}" if $DEBUG
man.more_preferable_people.each do |other_woman|
if other_woman.more_preferable_people.include?(man)
puts "an unstable pairing: #{man} and #{other_woman}" if $DEBUG
unstable << [man, other_woman]
end
end
woman.more_preferable_people.each do |other_man|
if other_man.more_preferable_people.include?(woman)
puts "an unstable pairing: #{woman} and #{other_man}" if $DEBUG
unstable << [other_man, woman]
end
end
end
if unstable.empty?
puts "these couples are stable"
else
puts "uh oh"
unstable.each do |a,b|
puts "#{a} is engaged to #{a.fiance} but would prefer #{b}, and #{b} is engaged to #{b.fiance} but would prefer #{a}"
end
end
end
stability @men
- perturb
puts "\nwhat if abe and bob swap..."
def swap(m1, m2)
w1 = m1.fiance w2 = m2.fiance m1.fiance = w2 w1.fiance = m2 m2.fiance = w1 w2.fiance = m1
end
swap *@men.values_at('abe','bob')
@men.each_value.collect {|man| puts "#{man} + #{man.fiance}"} stability @men</lang>
- Output:
abe + ivy bob + cath col + dee dan + fay ed + jan fred + bea gav + gay hal + eve ian + hope jon + abi these couples are stable what if abe and bob swap... abe + cath bob + ivy col + dee dan + fay ed + jan fred + bea gav + gay hal + eve ian + hope jon + abi uh oh bob is engaged to ivy but would prefer cath, and cath is engaged to abe but would prefer bob bob is engaged to ivy but would prefer hope, and hope is engaged to ian but would prefer bob bob is engaged to ivy but would prefer abi, and abi is engaged to jon but would prefer bob bob is engaged to ivy but would prefer fay, and fay is engaged to dan but would prefer bob bob is engaged to ivy but would prefer bea, and bea is engaged to fred but would prefer bob
Hmm, turns out Bob is a popular guy...
Racket
<lang Racket>
- lang racket
(define MEN
'([abe abi eve cath ivy jan dee fay bea hope gay ] [bob cath hope abi dee eve fay bea jan ivy gay ] [col hope eve abi dee bea fay ivy gay cath jan ] [dan ivy fay dee gay hope eve jan bea cath abi ] [ed jan dee bea cath fay eve abi ivy hope gay ] [fred bea abi dee gay eve ivy cath jan hope fay ] [gav gay eve ivy bea cath abi dee hope jan fay ] [hal abi eve hope fay ivy cath jan bea gay dee ] [ian hope cath dee gay bea abi fay ivy jan eve ] [jon abi fay jan gay eve bea dee cath ivy hope]))
(define WOMEN
'([abi bob fred jon gav ian abe dan ed col hal ] [bea bob abe col fred gav dan ian ed jon hal ] [cath fred bob ed gav hal col ian abe dan jon ] [dee fred jon col abe ian hal gav dan bob ed ] [eve jon hal fred dan abe gav col ed ian bob ] [fay bob abe ed ian jon dan fred gav col hal ] [gay jon gav hal fred bob abe col ed dan ian ] [hope gav jon bob abe ian dan hal ed col fred] [ivy ian col hal gav fred bob abe ed jon dan ] [jan ed hal gav abe bob jon col ian fred dan ]))
- x is better than y according to the l order
(define (better? x y l) (memq y (cdr (memq x l))))
(define (stable-matching Mprefs Wprefs)
(define M (map car Mprefs))
(define engagements (make-hasheq))
(define preferences (make-hasheq))
(define (engage! m w)
(hash-set! engagements m w)
(hash-set! engagements w m))
(for ([m Mprefs]) (hash-set! preferences (car m) (cdr m)))
(for ([w Wprefs]) (hash-set! preferences (car w) (cdr w)))
(let loop ()
(define m+w
(for/or ([m M])
(and (not (hash-ref engagements m #f)) ; m is free
(let ([p (hash-ref preferences m)]) ; can propose
(and (pair? p)
(let ([w (car p)])
(hash-set! preferences m (cdr p)) ; drop w from m
(cons m w)))))))
(when m+w
(define m (car m+w))
(define w (cdr m+w))
(define m* (hash-ref engagements w #f)) ; m* is w's prev engagement
(cond [(not m*) (engage! m w)] ; w is free
[(better? m m* (hash-ref preferences w)) ; w prefers m over m*
(engage! m w)
(hash-set! engagements m* #f)]) ; m* becomes free
(loop)))
engagements)
(define (find-unstable Mprefs Wprefs matches)
(for*/or ([m (map car Mprefs)] [w (map car Wprefs)])
(define w* (hash-ref matches m))
(define m* (hash-ref matches w))
(and (not (eq? m m*))
(better? w w* (cdr (assq m Mprefs)))
(better? m m* (cdr (assq w Wprefs)))
(cons m w))))
(define (check-stability)
(let ([u (find-unstable MEN WOMEN matches)])
(if u
(printf "Unstable: ~a and ~a prefer each other over partners.\n"
(car u) (cdr u))
(printf "The match is stable.\n"))))
(define matches (stable-matching MEN WOMEN)) (printf "Found matches:\n") (for ([m (map car MEN)]) (printf " ~a, ~a\n" m (hash-ref matches m))) (check-stability) (let ([M (map car (take (shuffle MEN) 2))])
(printf "Swapping wives of ~a and ~a\n" (car M) (cadr M)) (define (swap! x y) (define t (hash-ref matches x)) (hash-set! matches x (hash-ref matches y)) (hash-set! matches y t)) (swap! (car M) (cadr M)) (swap! (hash-ref matches (car M)) (hash-ref matches (cadr M))))
(check-stability) </lang>
Sample run:
Found matches: abe, ivy bob, cath col, dee dan, fay ed, jan fred, bea gav, gay hal, eve ian, hope jon, abi The match is stable. Swapping wives of bob and gav Unstable: bob and abi prefer each other over partners.
Seed7
<lang seed7>$ include "seed7_05.s7i";
const type: preferences is hash [string] array string; const type: engaged is hash [string] string;
const func integer: pos (in array string: area, in string: searched) is func
result
var integer: pos is 1;
begin
while pos <= length(area) and area[pos] <> searched do
incr(pos);
end while;
if pos > length(area) then
pos := 0;
end if;
end func;
const func engaged: matchmaker (in preferences: guyPrefers, in preferences: girlPrefers) is func
result
var engaged: engagedTo is engaged.value;
local
var array string: freeGuys is 0 times "";
var string: guy is "";
var string: girl is "";
var string: fiance is "";
var array string: guyPreferencList is 0 times "";
var array string: girlPreferenceList is 0 times "";
var boolean: searching is TRUE;
begin
freeGuys := sort(keys(guyPrefers));
while length(freeGuys) <> 0 do
guy := freeGuys[1];
freeGuys := freeGuys[2 ..];
guyPreferencList := guyPrefers[guy];
searching := TRUE;
while searching and length(guyPreferencList) <> 0 do
girl := guyPreferencList[1];
guyPreferencList := guyPreferencList[2 ..];
if girl not in engagedTo then
engagedTo @:= [girl] guy;
writeln(" " <& girl <& " and " <& guy);
searching := FALSE;
else
fiance := engagedTo[girl];
girlPreferenceList := girlPrefers[girl];
if pos(girlPreferenceList, guy) < pos(girlPreferenceList, fiance) then
# She prefers new guy
engagedTo @:= [girl] guy;
freeGuys &:= fiance;
writeln(" " <& girl <& " dumped " <& fiance <& " for " <& guy);
searching := FALSE;
end if;
end if;
end while;
end while;
end func;
const func boolean: check (in engaged: engagedTo,
in preferences: guyPrefers, in preferences: girlPrefers) is func
result
var boolean: stable is TRUE;
local
var string: he is "";
var string: she is "";
var string: guy is "";
var string: girl is "";
var engaged: inverseEngaged is engaged.value;
var array string: sheLikes is 0 times "";
var array string: sheLikesBetter is 0 times "";
var array string: heLikes is 0 times "";
var array string: heLikesBetter is 0 times "";
var string: guysGirl is "";
var array string: guyLikes is 0 times "";
var string: girlsGuy is "";
var array string: girlLikes is 0 times "";
begin
for he key she range engagedTo do
inverseEngaged @:= [he] she;
end for;
for he key she range engagedTo do
sheLikes := girlPrefers[she];
sheLikesBetter := sheLikes[.. pred(pos(sheLikes, he))];
heLikes := guyPrefers[he];
heLikesBetter := heLikes[.. pred(pos(heLikes, she))];
for guy range sheLikesBetter do
guysGirl := inverseEngaged[guy];
guyLikes := guyPrefers[guy];
if pos(guyLikes, guysGirl) > pos(guyLikes, she) and stable then
writeln(she <& " likes " <& guy <& " better than " <& he <& " and " <&
guy <& " likes " <& she <& " better than their current partner");
stable := FALSE;
end if;
end for;
for girl range heLikesBetter do
girlsGuy := engagedTo[girl];
girlLikes := girlPrefers[girl];
if pos(girlLikes, girlsGuy) > pos(girlLikes, he) and stable then
writeln(he <& " likes " <& girl <& " better than " <& she <& " and " <&
girl <& " likes " <& he <& " better than their current partner");
stable := FALSE;
end if;
end for;
end for;
end func;
var preferences: guyPrefers is preferences.value; var preferences: girlPrefers is preferences.value; guyPrefers @:= ["abe"] [] ("abi", "eve", "cath", "ivy", "jan", "dee", "fay", "bea", "hope", "gay"); guyPrefers @:= ["bob"] [] ("cath", "hope", "abi", "dee", "eve", "fay", "bea", "jan", "ivy", "gay"); guyPrefers @:= ["col"] [] ("hope", "eve", "abi", "dee", "bea", "fay", "ivy", "gay", "cath", "jan"); guyPrefers @:= ["dan"] [] ("ivy", "fay", "dee", "gay", "hope", "eve", "jan", "bea", "cath", "abi"); guyPrefers @:= ["ed"] [] ("jan", "dee", "bea", "cath", "fay", "eve", "abi", "ivy", "hope", "gay"); guyPrefers @:= ["fred"] [] ("bea", "abi", "dee", "gay", "eve", "ivy", "cath", "jan", "hope", "fay"); guyPrefers @:= ["gav"] [] ("gay", "eve", "ivy", "bea", "cath", "abi", "dee", "hope", "jan", "fay"); guyPrefers @:= ["hal"] [] ("abi", "eve", "hope", "fay", "ivy", "cath", "jan", "bea", "gay", "dee"); guyPrefers @:= ["ian"] [] ("hope", "cath", "dee", "gay", "bea", "abi", "fay", "ivy", "jan", "eve"); guyPrefers @:= ["jon"] [] ("abi", "fay", "jan", "gay", "eve", "bea", "dee", "cath", "ivy", "hope"); girlPrefers @:= ["abi"] [] ("bob", "fred", "jon", "gav", "ian", "abe", "dan", "ed", "col", "hal"); girlPrefers @:= ["bea"] [] ("bob", "abe", "col", "fred", "gav", "dan", "ian", "ed", "jon", "hal"); girlPrefers @:= ["cath"] [] ("fred", "bob", "ed", "gav", "hal", "col", "ian", "abe", "dan", "jon"); girlPrefers @:= ["dee"] [] ("fred", "jon", "col", "abe", "ian", "hal", "gav", "dan", "bob", "ed"); girlPrefers @:= ["eve"] [] ("jon", "hal", "fred", "dan", "abe", "gav", "col", "ed", "ian", "bob"); girlPrefers @:= ["fay"] [] ("bob", "abe", "ed", "ian", "jon", "dan", "fred", "gav", "col", "hal"); girlPrefers @:= ["gay"] [] ("jon", "gav", "hal", "fred", "bob", "abe", "col", "ed", "dan", "ian"); girlPrefers @:= ["hope"] [] ("gav", "jon", "bob", "abe", "ian", "dan", "hal", "ed", "col", "fred"); girlPrefers @:= ["ivy"] [] ("ian", "col", "hal", "gav", "fred", "bob", "abe", "ed", "jon", "dan"); girlPrefers @:= ["jan"] [] ("ed", "hal", "gav", "abe", "bob", "jon", "col", "ian", "fred", "dan");
const proc: main is func
local
var engaged: engagedTo is engaged.value;
var string: girl is "";
begin
writeln("Matchmaking:");
engagedTo := matchmaker(guyPrefers, girlPrefers);
writeln;
writeln("Engagements:");
for girl range sort(keys(engagedTo)) do
writeln(" " <& girl <& " and " <& engagedTo[girl]);
end for;
writeln;
writeln("Marriages are " <& [] ("unstable", "stable") [succ(ord(check(engagedTo, guyPrefers, girlPrefers)))]);
writeln;
writeln("Perturb:");
engagedTo @:= ["abi"] "fred";
engagedTo @:= ["bea"] "jon";
writeln("engage abi with fred and bea with jon");
writeln;
writeln("Marriages are " <& [] ("unstable", "stable") [succ(ord(check(engagedTo, guyPrefers, girlPrefers)))]);
end func;</lang>
Output:
Matchmaking: abi and abe cath and bob hope and col ivy and dan jan and ed bea and fred gay and gav eve and hal hope dumped col for ian abi dumped abe for jon dee and col ivy dumped dan for abe fay and dan Engagements: abi and jon bea and fred cath and bob dee and col eve and hal fay and dan gay and gav hope and ian ivy and abe jan and ed Marriages are stable Perturb: engage abi with fred and bea with jon bea likes fred better than jon and fred likes bea better than their current partner Marriages are unstable
SPARK / Ada
This solution works for Ada, too, since SPARK code is correct Ada code.
The data set package: <lang ada>package Preferences is
type Guy_X is (no_guy, abe, bob, col, dan, ed, fred, gav, hal, ian, jon); subtype Guy is Guy_X range Guy_X'Succ(Guy_X'First) .. Guy_X'Last;
type Girl_X is (no_girl, abi, bea, cath, dee, eve, fay, gay, hope, ivy, jan); subtype Girl is Girl_X range Girl_X'Succ(Girl_X'First) .. Girl_X'Last;
type Extended_Rank is range 0 .. 10; subtype Rank is Extended_Rank range 1 .. Extended_Rank'Last;
type His_Rank is array (Rank) of Girl; type He_Prefers is array (Guy) of His_Rank;
Guys_Like : constant He_Prefers := He_Prefers'(
abe => His_Rank'(abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay),
bob => His_Rank'(cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay),
col => His_Rank'(hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan),
dan => His_Rank'(ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi),
ed => His_Rank'(jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay),
fred => His_Rank'(bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay),
gav => His_Rank'(gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay),
hal => His_Rank'(abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee),
ian => His_Rank'(hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve),
jon => His_Rank'(abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope));
type Her_Rank is array(Rank) of Guy; type She_Prefers is array (Girl) of Her_Rank;
Girls_Like : constant She_Prefers := She_Prefers'(
abi => Her_Rank'(bob, fred, jon, gav, ian, abe, dan, ed, col, hal),
bea => Her_Rank'(bob, abe, col, fred, gav, dan, ian, ed, jon, hal),
cath => Her_Rank'(fred, bob, ed, gav, hal, col, ian, abe, dan, jon),
dee => Her_Rank'(fred, jon, col, abe, ian, hal, gav, dan, bob, ed),
eve => Her_Rank'(jon, hal, fred, dan, abe, gav, col, ed, ian, bob),
fay => Her_Rank'(bob, abe, ed, ian, jon, dan, fred, gav, col, hal),
gay => Her_Rank'(jon, gav, hal, fred, bob, abe, col, ed, dan, ian),
hope => Her_Rank'(gav, jon, bob, abe, ian, dan, hal, ed, col, fred),
ivy => Her_Rank'(ian, col, hal, gav, fred, bob, abe, ed, jon, dan),
jan => Her_Rank'(ed, hal, gav, abe, bob, jon, col, ian, fred, dan));
end Preferences; </lang> The package for creating the engagements and checking stability. This package can be analysed by the SPARK tools and proved to be free of any run-time error. <lang ada>with Preferences; --# inherit Preferences; package Propose is
type Engagements is array (Preferences.Girl) of Preferences.Guy_X;
procedure Engage (Pairs : out Engagements); --# derives Pairs from ;
procedure Check_Stable (Pairs : in Engagements;
OK : out Boolean;
Other_Girl : out Preferences.Girl_X;
Other_Guy : out Preferences.Guy_X);
--# derives OK,
--# Other_Girl,
--# Other_Guy from Pairs;
end Propose; </lang> <lang ada>with Preferences; use type Preferences.Extended_Rank; use type Preferences.Girl; use type Preferences.Guy; package body Propose is
-- renaming subtypes: subtype Guy is Preferences.Guy; subtype Girl is Preferences.Girl;
function Her_Rank_Of_Him (Her : Girl;
Him : Guy) return Preferences.Rank
is
R : Preferences.Rank;
begin
R := Preferences.Rank'First;
while Preferences.Girls_Like(Her)(R) /= Him
and R /= Preferences.Rank'Last
loop
R := Preferences.Rank'Succ(R);
end loop;
return R;
end Her_Rank_Of_Him;
function His_Rank_Of_Her (Him : Guy;
Her : Girl) return Preferences.Rank
is
R : Preferences.Rank;
begin
R := Preferences.Rank'First;
while Preferences.Guys_Like(Him)(R) /= Her
and R /= Preferences.Rank'Last
loop
R := Preferences.Rank'Succ(R);
end loop;
return R;
end His_Rank_Of_Her;
procedure Engage (Pairs : out Engagements)
is
type Free_Guy is array (Guy) of Boolean;
type Free_Girl is array (Girl) of Boolean;
type Last_Proposals is array (Guy) of Preferences.Extended_Rank;
-- Initialize all M in M_Free and W in W_Free to free.
M_Free : Free_Guy := Free_Guy'(others => True);
W_Free : Free_Girl := Free_Girl'(others => True);
Last_Proposal : Last_Proposals :=
Last_Proposals'(others => Preferences.Extended_Rank'First);
All_Paired : Boolean := False;
W : Girl;
M1 : Preferences.Guy_X;
begin
-- Initially set all engagements to null.
Pairs := Engagements'(others => Preferences.No_Guy);
-- while there is a free man M who still has a woman W to propose to
while not All_Paired loop
All_Paired := True;
for M in Guy loop
if M_Free(M) and Last_Proposal(M) < Preferences.Rank'Last then
All_Paired := False;
-- W = M's highest ranked such woman who he has not
-- proposed to yet
Last_Proposal(M) := Preferences.Rank'Succ(Last_Proposal(M));
W := Preferences.Guys_Like(M)(Last_Proposal(M));
-- if W is free
if W_Free(W) then
-- (M, W) become engaged
M_Free(M) := False;
W_Free(W) := False;
Pairs(W) := M;
else
-- else some pair (M1, W) already exists
M1 := Pairs(W);
if M1 > Preferences.no_guy and then
-- if W prefers M to M1
Her_Rank_Of_Him (Her => W, Him => M)
< Her_Rank_Of_Him (Her => W, Him => M1)
then
-- (M, W) become engaged
M_Free(M) := False;
Pairs(W) := M;
-- M1 becomes free
M_Free(M1) := True;
else
-- (M1, W) remain engaged
null;
end if;
end if;
end if;
end loop;
end loop;
end Engage;
procedure Check_Stable (Pairs : in Engagements;
OK : out Boolean;
Other_Girl : out Preferences.Girl_X;
Other_Guy : out Preferences.Guy_X)
is
M : Preferences.Guy_X;
W_Rank : Preferences.Rank;
begin
OK := True;
Other_Girl := Preferences.No_Girl;
Other_Guy := Preferences.No_Guy;
-- Loop over all girls.
for W in Girl loop
if Pairs(W) > Preferences.no_guy then
W_Rank := Her_Rank_Of_Him (W, Pairs(W));
-- Loop over all guys she prefers to her current guy.
for WR in Preferences.Rank range 1 .. W_Rank - 1 loop
M := Preferences.Girls_Like(W)(WR);
if M > Preferences.no_guy then
-- Loop over all girls for this guy in preference order.
for MR in Preferences.Rank
--# assert M > Preferences.no_guy;
loop
-- Exit if his current girl found before this girl.
exit when M = Pairs(Preferences.Guys_Like(M)(MR));
-- Unstable if this girl found before his current girl.
if Preferences.Guys_Like(M)(MR) = W then
OK := False;
Other_Girl := W;
Other_Guy := M;
end if;
end loop;
end if;
exit when not OK;
end loop;
end if;
exit when not OK;
end loop;
end Check_Stable;
end Propose; </lang> The test program tests all pairwise exchanges. This is Ada, it is not SPARK.
(Text IO is quite tedious in SPARK - it's not what the language was designed for.) <lang ada>------------------------------------ -- Test program. -- -- This is Ada, it is not SPARK.
with Ada.Text_IO; with Preferences; with Propose; procedure Matchmaker is
-- renaming subtypes: subtype Guy is Preferences.Guy; subtype Girl is Preferences.Girl;
Marriages : Propose.Engagements; Stable : Boolean; Him : Preferences.Guy_X; Her : Preferences.Girl_X; Stable_Marriages : Propose.Engagements;
procedure Report_Stable
is
begin
if Stable then
Ada.Text_IO.Put_Line ("Pairs are Stable");
else
Ada.Text_IO.Put ("Pairs are Unstable: ");
Ada.Text_IO.Put_Line
(Guy'Image(Him) & " and " & Girl'Image(Her) & " prefer each other.");
end if;
end Report_Stable;
begin
Propose.Engage(Pairs => Marriages);
for W in Girl loop
Ada.Text_IO.Put_Line (Girl'Image(W) &
" marries " &
Guy'Image(Marriages(W)));
end loop;
Propose.Check_Stable (Pairs => Marriages,
OK => Stable,
Other_Girl => Her,
Other_Guy => Him);
Report_Stable;
Stable_Marriages := Marriages;
for W1 in Girl range Girl'First .. Girl'Pred(Girl'Last) loop
for W2 in Girl range Girl'Succ(W1) .. Girl'Last loop
Ada.Text_IO.New_Line;
Ada.Text_IO.Put_Line ("Exchange " & Guy'Image(Marriages(W1)) &
" with " & Guy'Image(Marriages(W2)));
Him := Marriages(W1);
Marriages(W1) := Marriages(W2);
Marriages(W2) := Him;
Propose.Check_Stable (Pairs => Marriages,
OK => Stable,
Other_Girl => Her,
Other_Guy => Him);
Report_Stable;
Marriages := Stable_Marriages;
end loop;
end loop;
end MatchMaker; </lang> The begining of the output from the test. All pairwise exchanges create unstable pairings.
ABI marries JON BEA marries FRED CATH marries BOB DEE marries COL EVE marries HAL FAY marries DAN GAY marries GAV HOPE marries IAN IVY marries ABE JAN marries ED Pairs are Stable Exchange JON with FRED Pairs are Unstable: FRED and BEA prefer each other. Exchange JON with BOB Pairs are Unstable: BOB and CATH prefer each other. Exchange JON with COL Pairs are Unstable: JON and ABI prefer each other.
Swift
<lang Swift>class Person {
let name:String
var candidateIndex = 0
var fiance:Person?
var candidates = [Person]()
init(name:String) {
self.name = name
}
func rank(p:Person) -> Int {
for (i, candidate) in enumerate(self.candidates) {
if candidate === p {
return i
}
}
return self.candidates.count + 1
}
func prefers(p:Person) -> Bool {
if let fiance = self.fiance {
return self.rank(p) < self.rank(fiance)
}
return false
}
func nextCandidate() -> Person? {
if self.candidateIndex >= self.candidates.count {
return nil
}
return self.candidates[candidateIndex++]
}
func engageTo(p:Person) {
p.fiance?.fiance = nil
p.fiance = self
self.fiance?.fiance = nil
self.fiance = p
}
func swapWith(p:Person) {
let thisFiance = self.fiance
let pFiance = p.fiance
println("\(self.name) swapped partners with \(p.name)")
if pFiance != nil && thisFiance != nil {
self.engageTo(pFiance!)
p.engageTo(thisFiance!)
}
}
}
func isStable(guys:[Person], gals:[Person]) -> Bool {
for guy in guys {
for gal in gals {
if guy.prefers(gal) && gal.prefers(guy) {
return false
}
}
}
return true
}
func engageEveryone(guys:[Person]) {
var done = false
while !done {
done = true
for guy in guys {
if guy.fiance == nil {
done = false
if let gal = guy.nextCandidate() {
if gal.fiance == nil || gal.prefers(guy) {
guy.engageTo(gal)
}
}
}
}
}
}
func doMarriage() {
let abe = Person(name: "Abe")
let bob = Person(name: "Bob")
let col = Person(name: "Col")
let dan = Person(name: "Dan")
let ed = Person(name: "Ed")
let fred = Person(name: "Fred")
let gav = Person(name: "Gav")
let hal = Person(name: "Hal")
let ian = Person(name: "Ian")
let jon = Person(name: "Jon")
let abi = Person(name: "Abi")
let bea = Person(name: "Bea")
let cath = Person(name: "Cath")
let dee = Person(name: "Dee")
let eve = Person(name: "Eve")
let fay = Person(name: "Fay")
let gay = Person(name: "Gay")
let hope = Person(name: "Hope")
let ivy = Person(name: "Ivy")
let jan = Person(name: "Jan")
abe.candidates = [abi, eve, cath, ivy, jan, dee, fay, bea, hope, gay]
bob.candidates = [cath, hope, abi, dee, eve, fay, bea, jan, ivy, gay]
col.candidates = [hope, eve, abi, dee, bea, fay, ivy, gay, cath, jan]
dan.candidates = [ivy, fay, dee, gay, hope, eve, jan, bea, cath, abi]
ed.candidates = [jan, dee, bea, cath, fay, eve, abi, ivy, hope, gay]
fred.candidates = [bea, abi, dee, gay, eve, ivy, cath, jan, hope, fay]
gav.candidates = [gay, eve, ivy, bea, cath, abi, dee, hope, jan, fay]
hal.candidates = [abi, eve, hope, fay, ivy, cath, jan, bea, gay, dee]
ian.candidates = [hope, cath, dee, gay, bea, abi, fay, ivy, jan, eve]
jon.candidates = [abi, fay, jan, gay, eve, bea, dee, cath, ivy, hope]
abi.candidates = [bob, fred, jon, gav, ian, abe, dan, ed, col, hal]
bea.candidates = [bob, abe, col, fred, gav, dan, ian, ed, jon, hal]
cath.candidates = [fred, bob, ed, gav, hal, col, ian, abe, dan, jon]
dee.candidates = [fred, jon, col, abe, ian, hal, gav, dan, bob, ed]
eve.candidates = [jon, hal, fred, dan, abe, gav, col, ed, ian, bob]
fay.candidates = [bob, abe, ed, ian, jon, dan, fred, gav, col, hal]
gay.candidates = [jon, gav, hal, fred, bob, abe, col, ed, dan, ian]
hope.candidates = [gav, jon, bob, abe, ian, dan, hal, ed, col, fred]
ivy.candidates = [ian, col, hal, gav, fred, bob, abe, ed, jon, dan]
jan.candidates = [ed, hal, gav, abe, bob, jon, col, ian, fred, dan]
let guys = [abe, bob, col, dan, ed, fred, gav, hal, ian, jon]
let gals = [abi, bea, cath, dee, eve, fay, gay, hope, ivy, jan]
engageEveryone(guys)
for guy in guys {
println("\(guy.name) is engaged to \(guy.fiance!.name)")
}
println("Stable = \(isStable(guys, gals))")
jon.swapWith(fred)
println("Stable = \(isStable(guys, gals))")
}
doMarriage()</lang>
- Output:
Abe is engaged to Ivy Bob is engaged to Cath Col is engaged to Dee Dan is engaged to Fay Ed is engaged to Jan Fred is engaged to Bea Gav is engaged to Gay Hal is engaged to Eve Ian is engaged to Hope Jon is engaged to Abi Stable = true Jon swapped partners with Fred Stable = false
Tcl
<lang tcl>package require Tcl 8.5
- Functions as aliases to standard commands
interp alias {} tcl::mathfunc::pos {} ::lsearch -exact interp alias {} tcl::mathfunc::nonempty {} ::llength
- The stability check
proc check engaged {
global preferences set inverse [lreverse $engaged] set errmsg "%s and %s like each other better than their present partners,\
%s and %s respectively"
dict for {she he} $engaged {
set shelikes [dict get $preferences $she] set shelikesbetter [lrange $shelikes 0 [expr {pos($shelikes,$he)}]] set helikes [dict get $preferences $he] set helikesbetter [lrange $helikes 0 [expr {pos($helikes,$she)}]] foreach guy $shelikesbetter { set guysgirl [dict get $inverse $guy] set guylikes [dict get $preferences $guy] if {pos($guylikes,$guysgirl) > pos($guylikes,$she)} { puts [format $errmsg $she $guy $he $guysgirl] return 0 } } foreach gal $helikesbetter { set galsguy [dict get $engaged $gal] set gallikes [dict get $preferences $gal] if {pos($gallikes,$galsguy) > pos($gallikes,$he)} { puts [format $errmsg $he $gal $she $galsguy] return 0 } }
} return 1
}
- The match-making algorithm
proc matchmaker {} {
global guys gals preferences
set guysfree $guys
set engaged {}
array set p $preferences
while {nonempty($guysfree)} {
set guysfree [lassign $guysfree guy] set p($guy) [set guyslist [lassign $p($guy) gal]] if {![dict exists $engaged $gal]} { # She's free dict set engaged $gal $guy puts " $guy and $gal" continue } # The bounder proposes to an engaged lass! set fiance [dict get $engaged $gal] if {pos($p($gal), $fiance) > pos($p($gal), $guy)} { # She prefers the new guy dict set engaged $gal $guy puts " $gal dumped $fiance for $guy" set guy $fiance } if {nonempty($p($guy))} { lappend guysfree $guy }
} return $engaged
}
- Problem dataset; preferences unified since all names distinct
set guys {abe bob col dan ed fred gav hal ian jon} set gals {abi bea cath dee eve fay gay hope ivy jan} set preferences {
abe {abi eve cath ivy jan dee fay bea hope gay}
bob {cath hope abi dee eve fay bea jan ivy gay}
col {hope eve abi dee bea fay ivy gay cath jan}
dan {ivy fay dee gay hope eve jan bea cath abi}
ed {jan dee bea cath fay eve abi ivy hope gay}
fred {bea abi dee gay eve ivy cath jan hope fay}
gav {gay eve ivy bea cath abi dee hope jan fay}
hal {abi eve hope fay ivy cath jan bea gay dee}
ian {hope cath dee gay bea abi fay ivy jan eve}
jon {abi fay jan gay eve bea dee cath ivy hope}
abi {bob fred jon gav ian abe dan ed col hal}
bea {bob abe col fred gav dan ian ed jon hal}
cath {fred bob ed gav hal col ian abe dan jon}
dee {fred jon col abe ian hal gav dan bob ed}
eve {jon hal fred dan abe gav col ed ian bob}
fay {bob abe ed ian jon dan fred gav col hal}
gay {jon gav hal fred bob abe col ed dan ian}
hope {gav jon bob abe ian dan hal ed col fred}
ivy {ian col hal gav fred bob abe ed jon dan}
jan {ed hal gav abe bob jon col ian fred dan}
}
- The demonstration code
puts "Engagements:" set engaged [matchmaker]
puts "\nCouples:" set pfx "" foreach gal $gals {
puts -nonewline "$pfx $gal is engaged to [dict get $engaged $gal]" set pfx ",\n"
} puts "\n" puts "Engagement stability check [lindex {FAILED PASSED} [check $engaged]]"
puts "\n\nSwapping two fiances to introduce an error" set tmp [dict get $engaged [lindex $gals 0]] dict set engaged [lindex $gals 0] [dict get $engaged [lindex $gals 1]] dict set engaged [lindex $gals 1] $tmp foreach gal [lrange $gals 0 1] {
puts " $gal is now engaged to [dict get $engaged $gal]"
} puts "" puts "Engagement stability check [lindex {FAILED PASSED} [check $engaged]]"</lang>
- Output:
Engagements: abe and abi bob and cath col and hope dan and ivy ed and jan fred and bea gav and gay hope dumped col for ian abi dumped abe for jon hal and eve col and dee ivy dumped dan for abe dan and fay Couples: abi is engaged to jon, bea is engaged to fred, cath is engaged to bob, dee is engaged to col, eve is engaged to hal, fay is engaged to dan, gay is engaged to gav, hope is engaged to ian, ivy is engaged to abe, jan is engaged to ed Engagement stability check PASSED Swapping two fiances to introduce an error abi is now engaged to fred bea is now engaged to jon fred and bea like each other better than their present partners, abi and jon respectively Engagement stability check FAILED
Ursala
<lang Ursala>men =
{
'abe': <'abi','eve','cath','ivy','jan','dee','fay','bea','hope','gay'>, 'bob': <'cath','hope','abi','dee','eve','fay','bea','jan','ivy','gay'>, 'col': <'hope','eve','abi','dee','bea','fay','ivy','gay','cath','jan'>, 'dan': <'ivy','fay','dee','gay','hope','eve','jan','bea','cath','abi'>, 'ed': <'jan','dee','bea','cath','fay','eve','abi','ivy','hope','gay'>, 'fred': <'bea','abi','dee','gay','eve','ivy','cath','jan','hope','fay'>, 'gav': <'gay','eve','ivy','bea','cath','abi','dee','hope','jan','fay'>, 'hal': <'abi','eve','hope','fay','ivy','cath','jan','bea','gay','dee'>, 'ian': <'hope','cath','dee','gay','bea','abi','fay','ivy','jan','eve'>, 'jon': <'abi','fay','jan','gay','eve','bea','dee','cath','ivy','hope'>}
women =
{
'abi': <'bob','fred','jon','gav','ian','abe','dan','ed','col','hal'>, 'bea': <'bob','abe','col','fred','gav','dan','ian','ed','jon','hal'>, 'cath': <'fred','bob','ed','gav','hal','col','ian','abe','dan','jon'>, 'dee': <'fred','jon','col','abe','ian','hal','gav','dan','bob','ed'>, 'eve': <'jon','hal','fred','dan','abe','gav','col','ed','ian','bob'>, 'fay': <'bob','abe','ed','ian','jon','dan','fred','gav','col','hal'>, 'gay': <'jon','gav','hal','fred','bob','abe','col','ed','dan','ian'>, 'hope': <'gav','jon','bob','abe','ian','dan','hal','ed','col','fred'>, 'ivy': <'ian','col','hal','gav','fred','bob','abe','ed','jon','dan'>, 'jan': <'ed','hal','gav','abe','bob','jon','col','ian','fred','dan'>}
match = # finds a stable list of engagements from data as given above
-+
^=rrmhPnXS ^/~&l ^/~&rl ^|DlrHSs/~& ^TlK2hlPrSLPAS\~&r -+
~&lK2hlPrSXS,
*=rnmihBPK12D ~&mmhPnXNCB^rnPrmPllSPcA\~&r ~&lrrPwZK17@rnPlX+-,
^|rrPlrlPXX/~& ^/~&nNAS ^/~&l+ ^|H\~&+ -:+ * ^|/~& -<+ \/-=+ ~&DSL@tK33+-
preferred = # finds non-couples that would prefer each other to their betrothed
~&lSLPrSLrlXS2c^|DlrHS\~& ~~irlXX+ ^D/~&l+ ^|H\~&+ -:+ *T ^|/~& //~=;+ -~l;+ \/~&H
- cast %sWLm
main = # stable, perturbed, and preferred alternatives to the perturbed
<
'stable': match/men women, 'perturbed': ~&lSrSxPp match/men women, 'preferred': preferred/(men,women) ~&lSrSxPp match/men women></lang>
The matches are perturbed by reversing the order of the women.
- Output:
<
'stable': <
('jon','abi'),
('fred','bea'),
('bob','cath'),
('col','dee'),
('hal','eve'),
('dan','fay'),
('gav','gay'),
('ian','hope'),
('abe','ivy'),
('ed','jan')>,
'perturbed': <
('jon','jan'),
('fred','ivy'),
('bob','hope'),
('col','gay'),
('hal','fay'),
('dan','eve'),
('gav','dee'),
('ian','cath'),
('abe','bea'),
('ed','abi')>,
'preferred': <
('jon','abi'),
('jon','fay'),
('fred','abi'),
('fred','dee'),
('fred','gay'),
('fred','eve'),
('bob','cath'),
('col','dee'),
('col','fay'),
('col','ivy'),
('hal','eve'),
('dan','fay'),
('gav','gay'),
('gav','ivy'),
('gav','cath'),
('gav','abi'),
('abe','abi'),
('abe','jan'),
('abe','dee'),
('abe','fay'),
('ed','jan'),
('ed','cath'),
('ed','fay')>>
XSLT 2.0
Assume that the input is in XML form as listed here. The following XSLT 2.0 style-sheet...
<lang><xsl:stylesheet version="2.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform" xmlns:fn="http://www.w3.org/2005/xpath-functions" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:m="http://rosettacode.org/wiki/Stable_marriage_problem" xmlns:t="http://rosettacode.org/wiki/Stable_marriage_problem/temp" exclude-result-prefixes="xsl xs fn t m">
<xsl:output indent="yes" encoding="UTF-8" omit-xml-declaration="yes" /> <xsl:strip-space elements="*" />
<xsl:template match="*">
<xsl:copy> <xsl:apply-templates select="@*,node()" /> </xsl:copy>
</xsl:template>
<xsl:template match="@*|comment()|processing-instruction()">
<xsl:copy />
</xsl:template>
<xsl:template match="m:interest" mode="match-making">
<m:engagement>
<m:dude name="{../@name}" /><m:maid name="{.}" />
</m:engagement>
</xsl:template>
<xsl:template match="m:dude" mode="match-making">
<xsl:param name="eliminations" select="()" />
<m:dude name="{@name}">
<xsl:copy-of select="for $b in @name return m:interest[not(. = $eliminations[m:dude/@name=$b]/m:maid/@name)]" />
</m:dude>
</xsl:template>
<xsl:template match="*" mode="perturbation">
<xsl:copy> <xsl:apply-templates select="@*,node()" mode="perturbation"/> </xsl:copy>
</xsl:template>
<xsl:template match="@*" mode="perturbation">
<xsl:copy />
</xsl:template>
<xsl:template match="m:engagement[position() lt 3]/m:maid/@name" mode="perturbation">
<xsl:copy-of select="for $c in count(../../preceding-sibling::m:engagement)
return ../../../m:engagement[2 - $c]/m:maid/@name" />
</xsl:template>
<xsl:template match="m:stable-marriage-problem">
<xsl:variable name="population" select="m:dude|m:maid" />
<xsl:variable name="solution">
<xsl:call-template name="solve-it">
<xsl:with-param name="dudes" select="m:dude" />
<xsl:with-param name="maids" select="m:maid" tunnel="yes" />
</xsl:call-template>
</xsl:variable>
<xsl:variable name="perturbed">
<xsl:apply-templates select="$solution/*" mode="perturbation" />
</xsl:variable>
<m:stable-marriage-problem-result>
<m:solution is-stable="{t:is-stable( $population, $solution/*)}">
<xsl:copy-of select="$solution/*" />
</m:solution>
<m:message>Perturbing the matches! Swapping <xsl:value-of select="$solution/*[1]/m:maid/@name" /> for <xsl:value-of select="$solution/*[2]/m:maid/@name" /></m:message> <m:message><xsl:choose> <xsl:when test="t:is-stable( $population, $perturbed/*)"> <xsl:text>The perturbed configuration is stable.</xsl:text> </xsl:when> <xsl:otherwise>The perturbed configuration is unstable.</xsl:otherwise> </xsl:choose></m:message>
</m:stable-marriage-problem-result>
</xsl:template>
<xsl:template name="solve-it">
<xsl:param name="dudes" as="element()*" /> <xsl:param name="maids" as="element()*" tunnel="yes" /> <xsl:param name="engagements" as="element()*" select="()" /> <xsl:variable name="fresh-proposals"> <xsl:apply-templates select="$dudes[not(@name = $engagements/m:dude/@name)]/m:interest[1]" mode="match-making" /> </xsl:variable> <xsl:variable name="proposals" select="$engagements | $fresh-proposals/m:engagement" /> <xsl:variable name="acceptable" select="$proposals[ for $g in m:maid/@name, $b in m:dude/@name, $this-interest in $maids[@name=$g]/m:interest[.=$b]
return every $interest in for $other-b in $proposals[m:maid[@name=$g]]/m:dude/@name[. ne $b] return $maids[@name=$g]/m:interest[.=$other-b] satisfies $interest >> $this-interest
]" />
<xsl:variable name="new-dudes">
<xsl:apply-templates select="$dudes" mode="match-making">
<xsl:with-param name="eliminations" select="$fresh-proposals/m:engagement" />
</xsl:apply-templates>
</xsl:variable>
<xsl:choose>
<xsl:when test="$dudes[not(for $b in @name return $acceptable[m:dude/@name=$b])]">
<xsl:call-template name="solve-it">
<xsl:with-param name="dudes" select="$new-dudes/m:dude" />
<xsl:with-param name="engagements" select="$acceptable" />
</xsl:call-template>
</xsl:when>
<xsl:otherwise>
<xsl:copy-of select="$acceptable" />
</xsl:otherwise>
</xsl:choose>
</xsl:template>
<xsl:function name="t:is-stable" as="xs:boolean">
<xsl:param name="population" as="element()*" /> <xsl:param name="engagements" as="element()*" /> <xsl:sequence select=" every $e in $engagements,
$b in string($e/m:dude/@name), $g in string($e/m:maid/@name), $desired-g in $population/self::m:dude[@name=$b]/m:interest[$g=following-sibling::m:interest], $desired-maid in $population/self::m:maid[@name=$desired-g] satisfies
not(
$desired-maid/m:interest[.=$b] << $desired-maid/m:interest[.=$engagements[m:maid[@name=$desired-g]]/m:dude/@name])
" />
</xsl:function>
</xsl:stylesheet></lang>
...when applied to the said input document will yield...
<lang><t>
<m:stable-marriage-problem-result xmlns:m="http://rosettacode.org/wiki/Stable_marriage_problem"> <m:solution is-stable="true"> <m:engagement> <m:dude name="bob"/> <m:maid name="cath"/> </m:engagement> <m:engagement> <m:dude name="ed"/> <m:maid name="jan"/> </m:engagement> <m:engagement> <m:dude name="fred"/> <m:maid name="bea"/> </m:engagement> <m:engagement> <m:dude name="gav"/> <m:maid name="gay"/> </m:engagement> <m:engagement> <m:dude name="ian"/> <m:maid name="hope"/> </m:engagement> <m:engagement> <m:dude name="jon"/> <m:maid name="abi"/> </m:engagement> <m:engagement> <m:dude name="hal"/> <m:maid name="eve"/> </m:engagement> <m:engagement> <m:dude name="abe"/> <m:maid name="ivy"/> </m:engagement> <m:engagement> <m:dude name="col"/> <m:maid name="dee"/> </m:engagement> <m:engagement> <m:dude name="dan"/> <m:maid name="fay"/> </m:engagement> </m:solution> <m:message>Perturbing the matches! Swapping cath for jan</m:message> <m:message>The perturbed configuration is unstable.</m:message> </m:stable-marriage-problem-result>
</t></lang>