Last letter-first letter
A certain children's game involves starting with a word in a particular category. Each participant in turn says a word, but that word must begin with the final letter of the previous word. Once a word has been given, it cannot be repeated. If an opponent cannot give a word in the category, they fall out of the game.
You are encouraged to solve this task according to the task description, using any language you may know.
For example, with "animals" as the category,
Child 1: dog Child 2: goldfish Child 1: hippopotamus Child 2: snake ...
- Task
Take the following selection of 70 English Pokemon names (extracted from Wikipedia's list of Pokemon) and generate the/a sequence with the highest possible number of Pokemon names where the subsequent name starts with the final letter of the preceding name.
No Pokemon name is to be repeated.
audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask
Extra brownie points for dealing with the full list of 646 names.
Ada
<lang Ada>with Ada.Containers.Indefinite_Vectors, Ada.Text_IO;
procedure Lalefile is
package Word_Vec is new Ada.Containers.Indefinite_Vectors
(Index_Type => Positive,
Element_Type => String);
use type Word_Vec.Vector, Ada.Containers.Count_Type;
type Words_Type is array (Character) of Word_Vec.Vector;
procedure Read(Words: out Words_Type) is
F: Ada.Text_IO.File_Type;
begin
Ada.Text_IO.Open(File => F,
Name => "pokemon70.txt",
Mode => Ada.Text_IO.In_File);
loop
declare
Word: String := Ada.Text_IO.Get_Line(F);
begin
exit when Word = "";
Words(Word(Word'First)).Append(Word);
end;
end loop;
exception
when Ada.Text_IO.End_Error => null;
end Read;
procedure Write (List: Word_Vec.Vector; Prefix: String := " ") is
Copy: Word_Vec.Vector := List;
begin
loop
exit when Copy.Is_Empty;
Ada.Text_IO.Put_Line(Prefix & Copy.First_Element);
Copy.Delete_First;
end loop;
end Write;
function Run(Start: Character; Words: Words_Type) return Word_Vec.Vector is
Result: Word_Vec.Vector := Word_Vec.Empty_Vector;
begin
for I in Words(Start).First_Index .. Words(Start).Last_Index loop
declare
Word: String := Words(Start).Element(I);
Dupl: Words_Type := Words;
Alternative : Word_Vec.Vector;
begin
Dupl(Start).Delete(I);
Alternative := Word & Run(Word(Word'Last), Dupl);
if Alternative.Length > Result.Length then
Result := Alternative;
end if;
end;
end loop;
return Result;
end Run;
W: Words_Type; A_Vector: Word_Vec.Vector; Best: Word_Vec.Vector := Word_Vec.Empty_Vector;
begin
Read(W);
Ada.Text_IO.Put("Processing ");
for Ch in Character range 'a' .. 'z' loop
Ada.Text_IO.Put(Ch & ", ");
A_Vector := Run(Ch, W);
if A_Vector.Length > Best.Length then
Best := A_Vector;
end if;
end loop;
Ada.Text_IO.New_Line;
Ada.Text_IO.Put_Line("Length of longest Path:" &
Integer'Image(Integer(Best.Length)));
Ada.Text_IO.Put_Line("One such path:");
Write(Best);
end Lalefile;</lang>
Output:
Processing a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, Length of longest Path: 23 One such path: machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino
BaCon
Naive implementation showing the algorithm. <lang freebasic>all$ = "audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon " \ "cresselia croagunk darmanitan deino emboar emolga exeggcute gabite " \ "girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan " \ "kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine " \ "nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 " \ "porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking " \ "sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko " \ "tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask"
SUB check(list$, rest$)
LOCAL x
FOR x = 1 TO AMOUNT(rest$)
IF RIGHT$(list$, 1) = LEFT$(TOKEN$(rest$, x), 1) THEN check(APPEND$(list$, 0, TOKEN$(rest$, x)), DEL$(rest$, x))
NEXT
IF AMOUNT(list$) > total THEN
total = AMOUNT(list$)
result$ = list$
END IF
END SUB
FOR z = 1 TO AMOUNT(all$)
CALL check(TOKEN$(all$, z), DEL$(all$,z))
NEXT
PRINT total, ": ", result$
PRINT NL$, "Speed: ", TIMER, " msecs."</lang>
- Output:
23: machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino Speed: 662734 msecs.
Optimized implementation. The idea is to quantify the equations. <lang freebasic>all$ = "audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon " \ "cresselia croagunk darmanitan deino emboar emolga exeggcute gabite " \ "girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan " \ "kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine " \ "nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 " \ "porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking " \ "sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko " \ "tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask"
SPLIT all$ TO name$ SIZE MaxSize
DECLARE start, end, used, result ARRAY MaxSize
FOR y = 0 TO MaxSize-1
start[y] = ASC(LEFT$(name$[y], 1)) end[y] = ASC(RIGHT$(name$[y], 1)) used[y] = -1
NEXT
FOR i = 0 TO MaxSize-1
used[i] = 0 CALL check(used, i, 1) used[i] = -1
NEXT
PRINT maxtotal, ": "; FOR a = 0 TO maxtotal-1
FOR y = 0 TO MaxSize-1
IF result[y] = a THEN PRINT name$[y]," ";
NEXT
NEXT
PRINT NL$, "Speed: ", TIMER, " msecs."
SUB check(ya[], ultim, nr)
LOCAL x
FOR x = 0 TO MaxSize-1
IF end[ultim] = start[x] AND ya[x] = -1 THEN
ya[x] = nr
CALL check(ya, x, nr+1)
ya[x] = -1
END IF
IF nr > maxtotal THEN
maxtotal = nr
OPTION MEMTYPE long
COPY ya TO result SIZE MaxSize
END IF
NEXT
END SUB </lang>
- Output:
23: machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino Speed: 818 msecs.
BASIC256
<lang basic256>dim names$(1) names$ = { "audino", "bagon", "baltoy", "banette", "bidoof", "braviary", "bronzor", "carracosta", "charmeleon", "cresselia", "croagunk", "darmanitan", "deino", "emboar", "emolga", "exeggcute", "gabite", "girafarig", "gulpin", "haxorus", "heatmor", "heatran", "ivysaur", "jellicent", "jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba", "loudred", "lumineon", "lunatone", "machamp", "magnezone", "mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu", "pinsir", "poliwrath", "poochyena", "porygon2", "porygonz", "registeel", "relicanth", "remoraid", "rufflet", "sableye", "scolipede", "scrafty", "seaking", "sealeo", "silcoon", "simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga", "trapinch", "treecko", "tyrogue", "vigoroth", "vulpix", "wailord", "wartortle", "whismur", "wingull", "yamask" }
global names$, lnames, index, maxlen, first, last maxlen = 0
lnames = names$[?]-1 dim index(names$[?]) dim first(names$[?]) dim last(names$[?]) for t = 0 to lnames index[t] = t last[t] = asc(right(names$[t],1)) first[t] = asc(left(names$[t],1)) next t
- try each name as the first name on the list
for t = 0 to lnames
call swapindex(0,t) call downlevel(1) call swapindex(0,t)
next t
end
subroutine downlevel(lev)
#print n$[?] + " " + lev
if lev <= lnames then
for t = lev to lnames
if last[index[lev-1]] = first[index[t]] then
call swapindex(lev,t)
if lev >= maxlen then
maxlen = lev
call showsolution(lev)
end if
call downlevel(lev+1)
call swapindex(lev,t)
end if
next t
end if
end subroutine
subroutine showsolution(l)
print l+1;
for t = 0 to l
print " " + names$[index[t]];
next t
print
end subroutine
subroutine swapindex(a, b)
# swap element a and bin in the array index (used to swap names$) t = index[a] index[a] = index[b] index[b] = t
end subroutine </lang>
Output:
2 bagon nosepass 3 bagon nosepass sableye 4 bagon nosepass sableye emboar 5 bagon nosepass sableye emboar registeel ... 23 machamp pinsir rufflet trapinch heatmor remoraid darmanitan nosepass starly yamask kricketune emboar relicanth haxorus simisear registeel landorus seaking girafarig gabite exeggcute emolga audino 23 machamp pinsir rufflet trapinch heatmor remoraid darmanitan nosepass starly yamask kricketune exeggcute emboar registeel landorus simisear relicanth haxorus seaking girafarig gabite emolga audino 23 machamp pinsir rufflet trapinch heatmor remoraid darmanitan nosepass starly yamask kricketune exeggcute emboar relicanth haxorus simisear registeel landorus seaking girafarig gabite emolga audino
BBC BASIC
<lang bbcbasic> DIM names$(69)
names$() = "audino", "bagon", "baltoy", "banette", \
\ "bidoof", "braviary", "bronzor", "carracosta", "charmeleon", \
\ "cresselia", "croagunk", "darmanitan", "deino", "emboar", \
\ "emolga", "exeggcute", "gabite", "girafarig", "gulpin", \
\ "haxorus", "heatmor", "heatran", "ivysaur", "jellicent", \
\ "jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba", \
\ "loudred", "lumineon", "lunatone", "machamp", "magnezone", \
\ "mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu", \
\ "pinsir", "poliwrath", "poochyena", "porygon2", "porygonz", \
\ "registeel", "relicanth", "remoraid", "rufflet", "sableye", \
\ "scolipede", "scrafty", "seaking", "sealeo", "silcoon", \
\ "simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga", \
\ "trapinch", "treecko", "tyrogue", "vigoroth", "vulpix", \
\ "wailord", "wartortle", "whismur", "wingull", "yamask"
maxPathLength% = 0
maxPathLengthCount% = 0
maxPathExample$ = ""
FOR i% = 0 TO DIM(names$(),1)
SWAP names$(0), names$(i%)
PROClastfirst(names$(), 1)
SWAP names$(0), names$(i%)
NEXT
PRINT "Maximum length = " ; maxPathLength%
PRINT "Number of solutions with that length = " ; maxPathLengthCount%
PRINT "One such solution: " ' maxPathExample$
END
DEF PROClastfirst(names$(), offset%)
LOCAL i%, l%
IF offset% > maxPathLength% THEN
maxPathLength% = offset%
maxPathLengthCount% = 1
ELSE IF offset% = maxPathLength% THEN;
maxPathLengthCount% += 1
maxPathExample$ = ""
FOR i% = 0 TO offset%-1
maxPathExample$ += names$(i%) + CHR$13 + CHR$10
NEXT
ENDIF
l% = ASCRIGHT$(names$(offset% - 1))
FOR i% = offset% TO DIM(names$(),1)
IF ASCnames$(i%) = l% THEN
SWAP names$(i%), names$(offset%)
PROClastfirst(names$(), offset%+1)
SWAP names$(i%), names$(offset%)
ENDIF
NEXT
ENDPROC</lang>
Output:
Maximum length = 23 Number of solutions with that length = 1248 One such solution: machamp pinsir rufflet trapinch heatmor remoraid darmanitan nosepass starly yamask kricketune exeggcute emboar relicanth haxorus simisear registeel landorus seaking girafarig gabite emolga audino
Bracmat
Naive
<lang bracmat>( audino bagon baltoy banette bidoof braviary bronzor
carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask : ?names
& 0:?max & :?sequence & ( lalefile
= done todo A M Z Length first
. !arg:(!done.)&!done:?sequence
| !arg:(.?todo)
& ( !todo
: ?A
%@?M
(?Z&lalefile$(!M.!A !Z)&~)
|
)
| !arg:(@(%:? @?first) ?:?done.?todo)
& :?M
& ( !todo
: ?A
@(%:!first ?:?M)
( ?Z
& lalefile$(!M !done.!A !Z)
& ~
)
| !M:
& !done:? [?Length
& !Length:>!max:?max
& !done:?sequence
|
)
)
& lalefile$(.!names) & out$("Length:" !max "Sequence:" !sequence) );</lang> Output (read from bottom to top):
Length: 23 Sequence: audino emolga exeggcute gabite girafarig seaking haxorus trapinch rufflet heatmor relicanth simisear nosepass darmanitan loudred registeel emboar kricketune yamask scrafty landorus petilil machamp
Optimized
Optimizations:
The whl loop transforms the flat list of names to, conceptually, a search tree with nodes at three levels. The lowest level contains the names. The top level contains the word's first letter and the second level contains its last letter. Words starting with a specific letter are all children of one single top node, speeding up search for candidates. Under a second level node all words have the same letter at the start and the same letter at the end. When looking for candidates it always suffices to take the first word and ignore the rest. This optimization eliminates all solutions that merely are the result of swapping pairs of words with the same begin and end. Notice that the tree is built using the 'smart' binary operators *, ^, + and \L (logarithm). Bracmat uses the commutative, distributive and associative laws to transform expressions containing these operators to canonical forms that fit the requiremens of the search tree. For example, the words in the list sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue end up in this tree:
s
^ ( (.e)\L(sableye*scolipede)
+ (.g)\Lseaking
+ (.k)\Lspoink
+ (.n)\Lsilcoon
+ (.o)\Lsealeo
+ (.r)\Lsimisear
+ (.x)\Lsnorlax
+ (.y)\L(scrafty*snivy*starly)
)
* t
^ ( (.a)\Ltirtouga
+ (.e)\Ltyrogue
+ (.h)\Ltrapinch
+ (.o)\Ltreecko
)
Another, less important, optimization is the way in which the last letter of a name is found, using the position pattern [ rather than the pattern that matches at most one letter, @.
The optimized version is about 4.5 times faster than the naive version.
<lang bracmat>( audino bagon baltoy banette bidoof braviary bronzor
carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask : ?names
& 1:?newnames & whl
' ( !names:@(%?name:%@?first ? @?last) ?names & !first^(.!last)\L!name*!newnames:?newnames )
& !newnames:?names & 0:?max & :?sequence & ( lalefile
= done todo A M Z Length first
, Ms a z last candidates
. !arg:(!done.)&!done:?sequence
| !arg:(.?todo)
& ( !todo
: ?A
* %?first^?candidates
* ( ?Z
& !candidates
: ?a
+ ?last\L(%?M*?Ms)
+ ( ?z
& lalefile$(!M.!A*!first^(!a+!last\L!Ms+!z)*!Z)
& ~
)
)
|
)
| !arg:(@(%:? [-2 ?first) ?:?done.?todo)
& :?M
& ( !todo:?A*!first^%?candidates*?Z
& !candidates
: ?a
+ ?last\L(%?M*?Ms)
+ ( ?z
& lalefile
$ (!M !done.!A*!first^(!a+!last\L!Ms+!z)*!Z)
& ~
)
| !M:
& !done:? [?Length
& !Length:>!max:?max
& !done:?sequence
|
)
)
& lalefile$(.!names) & out$("Length:" !max "Sequence:" !sequence) );</lang> Output (read from bottom to top):
Length: 23 Sequence: audino emolga kricketune yamask scrafty haxorus trapinch rufflet simisear landorus registeel heatmor relicanth emboar exeggcute gabite girafarig seaking nosepass darmanitan loudred petilil machamp
C
From the D version. <lang c>#include <stdlib.h>
- include <string.h>
- include <stdio.h>
- include <inttypes.h>
typedef struct {
uint16_t index; char last_char, first_char;
} Ref;
Ref* longest_path_refs; size_t longest_path_refs_len;
Ref* refs; size_t refs_len;
size_t n_solutions;
const char** longest_path; size_t longest_path_len;
/// tally statistics
void search(size_t curr_len) {
if (curr_len == longest_path_refs_len) {
n_solutions++;
} else if (curr_len > longest_path_refs_len) {
n_solutions = 1;
longest_path_refs_len = curr_len;
memcpy(longest_path_refs, refs, curr_len * sizeof(Ref));
}
// recursive search
intptr_t last_char = refs[curr_len - 1].last_char;
for (size_t i = curr_len; i < refs_len; i++)
if (refs[i].first_char == last_char) {
Ref aux = refs[curr_len];
refs[curr_len] = refs[i];
refs[i] = aux;
search(curr_len + 1);
refs[i] = refs[curr_len];
refs[curr_len] = aux;
}
}
void find_longest_chain(const char* items[],
size_t items_len) {
refs_len = items_len;
refs = calloc(refs_len, sizeof(Ref));
// enough space for all items longest_path_refs_len = 0; longest_path_refs = calloc(refs_len, sizeof(Ref));
for (size_t i = 0; i < items_len; i++) {
size_t itemsi_len = strlen(items[i]);
if (itemsi_len <= 1)
exit(1);
refs[i].index = (uint16_t)i;
refs[i].last_char = items[i][itemsi_len - 1];
refs[i].first_char = items[i][0];
}
// try each item as possible start
for (size_t i = 0; i < items_len; i++) {
Ref aux = refs[0];
refs[0] = refs[i];
refs[i] = aux;
search(1);
refs[i] = refs[0];
refs[0] = aux;
}
longest_path_len = longest_path_refs_len;
longest_path = calloc(longest_path_len, sizeof(const char*));
for (size_t i = 0; i < longest_path_len; i++)
longest_path[i] = items[longest_path_refs[i].index];
free(longest_path_refs); free(refs);
}
int main() {
const char* pokemon[] = {"audino", "bagon", "baltoy", "banette",
"bidoof", "braviary", "bronzor", "carracosta", "charmeleon",
"cresselia", "croagunk", "darmanitan", "deino", "emboar",
"emolga", "exeggcute", "gabite", "girafarig", "gulpin",
"haxorus", "heatmor", "heatran", "ivysaur", "jellicent",
"jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba",
"loudred", "lumineon", "lunatone", "machamp", "magnezone",
"mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu",
"pinsir", "poliwrath", "poochyena", "porygon2", "porygonz",
"registeel", "relicanth", "remoraid", "rufflet", "sableye",
"scolipede", "scrafty", "seaking", "sealeo", "silcoon",
"simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga",
"trapinch", "treecko", "tyrogue", "vigoroth", "vulpix",
"wailord", "wartortle", "whismur", "wingull", "yamask"};
size_t pokemon_len = sizeof(pokemon) / sizeof(pokemon[0]);
find_longest_chain(pokemon, pokemon_len);
printf("Maximum path length: %u\n", longest_path_len);
printf("Paths of that length: %u\n", n_solutions);
printf("Example path of that length:\n");
for (size_t i = 0; i < longest_path_len; i += 7) {
printf(" ");
for (size_t j = i; j < (i+7) && j < longest_path_len; j++)
printf("%s ", longest_path[j]);
printf("\n");
}
free(longest_path);
return 0;
}</lang> Output:
Maximum path length: 23 Paths of that length: 1248 Example path of that length: machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino
Runtime: about 0.49 seconds, gcc compiler.
Approximate
For dealing with full list (646 names), here's an approximate method. Names are restricted to begin and end with a lower case letter, so for example in my input file "porygon2" is written as "porygon-two". It finds some chains with 300-odd length for 646 names, and found a chain with 23 for the 70 names (by luck, that is), and since it's basically a one-pass method, running time is next to none. C99 code. <lang c>#include <stdio.h>
- include <stdlib.h>
- include <string.h>
- include <ctype.h>
- define forall(i, n) for (int i = 0; i < n; i++)
typedef struct edge { char s, e, *str; struct edge *lnk; } edge; typedef struct { edge* e[26]; int nin, nout, in[26], out[26];} node; typedef struct { edge *e, *tail; int len, has[26]; } chain;
node nodes[26]; edge *names, **tmp; int n_names;
/* add edge to graph */ void store_edge(edge *g) { if (!g) return; int i = g->e, j = g->s; node *n = nodes + j;
g->lnk = n->e[i];
n->e[i] = g, n->out[i]++, n->nout++; n = nodes + i, n->in[j]++, n->nin++; }
/* unlink an edge between nodes i and j, and return the edge */ edge* remove_edge(int i, int j) { node *n = nodes + i; edge *g = n->e[j]; if (g) { n->e[j] = g->lnk; g->lnk = 0; n->out[j]--, n->nout--;
n = nodes + j; n->in[i]--; n->nin--; } return g; }
void read_names() { FILE *fp = fopen("poke646", "rt"); int i, len; char *buf; edge *p;
if (!fp) abort();
fseek(fp, 0, SEEK_END); len = ftell(fp); buf = malloc(len + 1); fseek(fp, 0, SEEK_SET); fread(buf, 1, len, fp); fclose(fp);
buf[len] = 0; for (n_names = i = 0; i < len; i++) if (isspace(buf[i])) buf[i] = 0, n_names++;
if (buf[len-1]) n_names++;
memset(nodes, 0, sizeof(node) * 26); tmp = calloc(n_names, sizeof(edge*));
p = names = malloc(sizeof(edge) * n_names); for (i = 0; i < n_names; i++, p++) { if (i) p->str = names[i-1].str + len + 1; else p->str = buf;
len = strlen(p->str); p->s = p->str[0] - 'a'; p->e = p->str[len-1] - 'a'; if (p->s < 0 || p->s >= 26 || p->e < 0 || p->e >= 26) { printf("bad name %s: first/last char must be letter\n", p->str); abort(); } } printf("read %d names\n", n_names); }
void show_chain(chain *c) { printf("%d:", c->len); for (edge * e = c->e; e || !putchar('\n'); e = e->lnk) printf(" %s", e->str); }
/* Which next node has most enter or exit edges. */ int widest(int n, int out) { if (nodes[n].out[n]) return n;
int mm = -1, mi = -1; forall(i, 26) { if (out) { if (nodes[n].out[i] && nodes[i].nout > mm) mi = i, mm = nodes[i].nout; } else { if (nodes[i].out[n] && nodes[i].nin > mm) mi = i, mm = nodes[i].nin; } }
return mi; }
void insert(chain *c, edge *e) { e->lnk = c->e; if (!c->tail) c->tail = e; c->e = e; c->len++; }
void append(chain *c, edge *e) { if (c->tail) c->tail->lnk = e; else c->e = e; c->tail = e; c->len++; }
edge * shift(chain *c) { edge *e = c->e; if (e) { c->e = e->lnk; if (!--c->len) c->tail = 0; } return e; }
chain* make_chain(int s) { chain *c = calloc(1, sizeof(chain));
/* extend backwards */ for (int i, j = s; (i = widest(j, 0)) >= 0; j = i) insert(c, remove_edge(i, j));
/* extend forwards */ for (int i, j = s; (i = widest(j, 1)) >= 0; j = i) append(c, remove_edge(j, i));
for (int step = 0;; step++) { edge *e = c->e;
for (int i = 0; i < step; i++) if (!(e = e->lnk)) break; if (!e) return c;
int n = 0; for (int i, j = e->s; (i = widest(j, 0)) >= 0; j = i) { if (!(e = remove_edge(i, j))) break; tmp[n++] = e; }
if (n > step) { forall(i, step) store_edge(shift(c)); forall(i, n) insert(c, tmp[i]); step = -1; } else while (--n >= 0) store_edge(tmp[n]); } return c; }
int main(void) { int best = 0; read_names();
forall(i, 26) { /* rebuild the graph */ memset(nodes, 0, sizeof(nodes)); forall(j, n_names) store_edge(names + j);
/* make a chain from node i */ chain *c = make_chain(i); if (c->len > best) { show_chain(c); best = c->len; } free(c); }
printf("longest found: %d\n", best); return 0; }</lang>output<lang>read 646 names 307: voltorb breloom magikarp palpito... 308: voltorb bayleef forretress swinub b... 310: voltorb bayleef forretress sw... 312: voltorb breloom mandibuzz zek... 320: voltorb beldum mandibuzz zekrom m... 322: voltorb beldum mandibuzz zekrom murk... 323: voltorb breloom mandibuzz zekr... longest found: 323</lang>
Clojure
<lang clojure>(ns rosetta-code.last-letter-first-letter
(:require clojure.string))
(defn by-first-letter
"Returns a map from letters to a set of words that start with that letter"
[words]
(into {} (map (fn k v
[k (set v)]))
(group-by first words)))
(defn longest-path-from
"Find a longest path starting at word, using only words-by-first-letter for successive words.
Returns a pair of [length list-of-words] to describe the path."
[word words-by-first-letter]
(let [words-without-word (update words-by-first-letter (first word)
disj word)
next-words (words-without-word (last word))]
(if (empty? next-words)
[1 [word]]
(let [sub-paths (map #(longest-path-from % words-without-word) next-words)
[length words-of-path] (apply max-key first sub-paths)]
[(inc length) (cons word words-of-path)]))))
(defn longest-word-chain
"Find a longest path among the words in word-list, by performing a longest path search
starting at each word in the list."
[word-list]
(let [words-by-letter (by-first-letter word-list)]
(apply max-key first
(pmap #(longest-path-from % words-by-letter)
word-list))))
(defn word-list-from-file [file-name]
(let [contents (slurp file-name)
words (clojure.string/split contents #"[ \n]")]
(filter #(not (empty? %)) words)))
(time (longest-word-chain (word-list-from-file "pokemon.txt")))</lang> Evaluating the last line: <lang clojure>"Elapsed time: 2867.337816 msecs" [23
("machamp"
"pinsir"
"relicanth"
"heatmor"
"registeel"
"landorus"
"seaking"
"girafarig"
"gabite"
"exeggcute"
"emboar"
"rufflet"
"trapinch"
"haxorus"
"simisear"
"remoraid"
"darmanitan"
"nosepass"
"scrafty"
"yamask"
"kricketune"
"emolga"
"audino")]</lang>
It initially ran in about 5 seconds, then I changed map to pmap (parallel map) in longest-word-chain.
This gave a nice speedup for a dual core laptop; the speedup for parallel searches was over 3x on a server.
C#
<lang csharp>using System; using System.Collections.Generic; using System.Linq; using System.Text;
namespace ConsoleApplication1 {
class Program
{
static void Main(string[] args)
{
string pokemon_names = @"audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon
cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask";
string[] pokemon = pokemon_names.Split(new char[]{' ','\n'});
List<string> chain = new List<string>(pokemon.Length);
for (int i = 0; i < pokemon.Length; i++)
{
swap(ref pokemon[0], ref pokemon[i]);
Search( pokemon, chain, 1 );
swap(ref pokemon[0], ref pokemon[i]);
}
foreach (string s in chain)
Console.WriteLine(s);
Console.ReadKey();
}
static void Search(string[] pokemon, List<string> longest_chain, int len )
{
if (len > longest_chain.Count)
{
longest_chain.Clear();
for (int i = 0; i < len; i++)
longest_chain.Add(pokemon[i]);
}
char lastchar = pokemon[len - 1][pokemon[len-1].Length - 1];
for (int i = len; i < pokemon.Length; i++)
{
if (pokemon[i][0] == lastchar)
{
swap(ref pokemon[i], ref pokemon[len]);
Search(pokemon, longest_chain, len + 1);
swap(ref pokemon[i], ref pokemon[len]);
}
}
}
static void swap(ref string s1, ref string s2)
{
string tmp = s1;
s1 = s2;
s2 = tmp;
}
}
}</lang>
machamp petilil landorus sableye emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus scrafty yamask kricketune exeggcute emolga audino
Common Lisp
Pretty brute force here. Takes a couple of seconds to run. <lang lisp>;;; return all the words that start with an initial letter
(defun filter-with-init (words init)
(remove-if-not (lambda (word) (eql init (aref word 0))) words))
- produce a hash table whose key is the initial letter of a word and whose value is
- a list of the words that start with that initial letter
(defun group-by-first-letter (words)
(let ((map_letters (make-hash-table))
(inits (remove-duplicates (mapcar (lambda (word) (aref word 0)) words))))
(dolist (init inits map_letters)
(setf (gethash init map_letters) (filter-with-init words init)))
))
- Get the last letter in a word or array
(defun last-element (array) (aref array (- (length array) 1)))
- Produce a hash table whose key is a word and whose value is a list of the
- words that can follow that word
(defun get-followers (words)
(let ((map-word-to-followers (make-hash-table :test 'equal))
(init_hash (group-by-first-letter words)))
(dolist (word words map-word-to-followers)
(setf
(gethash word map-word-to-followers)
(gethash (last-element word) init_hash)))))
- Retrieve all the keys from a hash table
(defun keys (hashtbl)
(let ((allkeys ())) (maphash #'(lambda (key val) (setf allkeys (cons key allkeys))) hashtbl) allkeys))
- Find the words which can follow a word and haven't been used yet. The parameters are
- word - word being tested
- followers - the hash table returned from get-followers
- available - hash table with word as key and boolean indicating whether that word
- has been used previously as value
(defun get-available-followers (word followers available)
(if (null word)
(keys followers)
(remove-if-not #'(lambda (word) (gethash word available)) (gethash word followers))))
- Find the best in a list using an arbitrary test
(defun best (lst test)
(let ((top (car lst)))
(do
((rest (cdr lst) (cdr rest)))
((null rest) top)
(if (funcall test (car rest) top) (setf top (car rest))))))
- Find the best path in a list
(defun best-list-path (paths)
(best paths #'(lambda (path1 path2) (> (length path1) (length path2)))))
- Find the best path given all the supporting information we need
(defun best-path-from-available (word followers available depth path available-followers)
(let ((results
(mapcar #'(lambda (new-word)
(dfs-recurse new-word followers available (+ 1 depth) (cons word path)))
available-followers)))
(best-list-path results)))
- Recurse to find the best available path - the meat of the algorithm
(defun dfs-recurse (word followers available depth path)
(let ((ret))
; Mark the word as unavailable
(setf (gethash word available) nil)
; Find the longest path starting with word
(let ((available-followers (get-available-followers word followers available)))
(setf ret
(if (null available-followers)
(cons word path)
(best-path-from-available word followers available depth path available-followers))))
; Mark the word as available again
(setf (gethash word available) t)
; Return our longest path
ret))
- Create the availability table
(defun make-available-table (words)
(let
((available (make-hash-table)))
(dolist (word words available) (setf (gethash word available) t))))
- Find the best path for a set of words
(defun best-path (words)
(let
((followers (get-followers words))
(available (make-available-table words)))
(cdr (reverse (dfs-recurse nil followers available 0 nil)))))
- set up the words as a set of strings
(setf *words* (mapcar #'symbol-name '(audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask)))
(setf *path* (best-path *words*))</lang> Output:<lang>("MACHAMP" "PETILIL" "LANDORUS" "SCRAFTY" "YAMASK" "KRICKETUNE" "EMBOAR" "REGISTEEL"
"LOUDRED" "DARMANITAN" "NOSEPASS" "SIMISEAR" "RELICANTH" "HEATMOR" "RUFFLET" "TRAPINCH" "HAXORUS" "SEAKING" "GIRAFARIG" "GABITE" "EXEGGCUTE" "EMOLGA" "AUDINO")</lang>
D
Simple Version
Modified from the Go version: <lang d>import std.stdio, std.algorithm, std.string;
void trySwap(string[] items, ref string item, in size_t len, ref string[] longest) pure nothrow @safe {
swap(items[len], item); search(items, len + 1, longest); swap(items[len], item);
}
void search(string[] items, in size_t len, ref string[] longest) pure nothrow @safe {
if (len > longest.length)
longest = items[0 .. len].dup;
immutable lastChar = items[len - 1][$ - 1];
foreach (ref item; items[len .. $])
if (item[0] == lastChar)
trySwap(items, item, len, longest);
}
void main() @safe {
auto pokemon = "audino bagon baltoy banette bidoof braviary
bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask".split;
string[] solution;
foreach (ref name; pokemon)
trySwap(pokemon, name, 0, solution);
writefln("%-(%s\n%)", solution);
}</lang> Output:
machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino
The run-time is about 0.9 seconds with the dmd compiler and about 0.55 seconds with the ldc2 compiler.
Improved Version
With two small changes the code gets faster. Here the names are represented as in C (so swapping them means just swapping a pointer, instead of swapping a pointer+length as before), and during the computation their last char is swapped with their second char (so there's no need to keep the string lengths around or use strlen). <lang d>import std.stdio, std.algorithm, std.string, std.array, std.conv;
void search(immutable(char)*[] items, in int len,
ref immutable(char)*[] longest) pure {
if (len > longest.length)
longest = items[0 .. len].dup;
immutable lastChar = items[len - 1][1];
foreach (ref item; items[len .. $])
if (item[0] == lastChar) {
swap(items[len], item);
search(items, len + 1, longest);
swap(items[len], item);
}
}
void main() {
static immutable(char)* prep(in string s) pure {
assert(s.length > 1);
auto sd = s.dup;
swap(sd[1], sd[$ - 1]);
return sd.toStringz;
}
static string unprep(immutable(char)* sd) pure {
auto ms = sd.to!(char[]);
swap(ms[1], ms[$ - 1]);
return ms;
}
auto pokemon = "audino bagon baltoy banette bidoof braviary
bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask".split.map!prep.array;
immutable(char)*[] solution;
foreach (ref name; pokemon) {
swap(pokemon[0], name);
search(pokemon, 1, solution);
swap(pokemon[0], name);
}
writefln("%-(%s\n%)", solution.map!unprep);
}</lang>
This leads to tight enough code for the foreach loop in the search function:
<lang asm>LBB0_4:
movl (%esi), %eax movb 19(%esp), %cl cmpb %cl, (%eax)
jne LBB0_6
movl (%edi,%ebx,4), %ecx movl %eax, (%edi,%ebx,4) movl %ecx, (%esi) movl %edi, 8(%esp) movl 48(%esp), %eax movl %eax, 4(%esp) movl 12(%esp), %eax movl %eax, (%esp) movl 20(%esp), %eax calll __D25last_letter_first_letter26searchFNaAPyaxiKAPyaZv subl $12, %esp movl (%edi,%ebx,4), %eax movl (%esi), %ecx movl %ecx, (%edi,%ebx,4) movl %eax, (%esi)
LBB0_6:
addl $4, %esi decl %ebp jne LBB0_4</lang>
The run-time is about 0.65 seconds with LDC2 compiler. The output is similar.
Faster Version
<lang d>import std.stdio, std.algorithm, std.string, std.range, std.typecons;
Tuple!(uint, string[]) findLongestChain(in string[] words) pure nothrow {
static struct Pair { string word; bool unused; }
uint nSolutions;
void search(Pair[][] sequences, in size_t minHead,
in string currWord, string[] currentPath,
size_t currentPathLen,
ref string[] longestPath) nothrow {
currentPath[currentPathLen] = currWord;
currentPathLen++;
if (currentPathLen == longestPath.length) {
nSolutions++;
} else if (currentPathLen > longestPath.length) {
nSolutions = 1;
longestPath = currentPath[0 .. currentPathLen].dup;
}
// Recursive search.
immutable size_t lastCharIndex = currWord[$ - 1] - minHead;
if (lastCharIndex < sequences.length)
foreach (ref pair; sequences[lastCharIndex])
if (pair.unused) {
pair.unused = false;
search(sequences, minHead, pair.word, currentPath,
currentPathLen, longestPath);
pair.unused = true;
}
}
if (words.empty)
typeof(return)(0, null);
immutable heads = words.map!q{ a[0] }.array;
immutable size_t minHead = reduce!min(heads[0],
heads[1.. $].representation);
immutable size_t maxHead = reduce!max(heads[0],
heads[1.. $].representation);
auto sequences = new Pair[][](maxHead - minHead + 1, 0);
foreach (const word; words)
sequences[word[0] - minHead] ~= Pair(word, true);
auto currentPath = new string[words.length]; string[] longestPath;
// Try each item as possible start.
foreach (seq; sequences)
foreach (ref pair; seq) {
pair.unused = false;
search(sequences, minHead, pair.word,
currentPath, 0, longestPath);
pair.unused = true;
}
return typeof(return)(nSolutions, longestPath);
}
void main() {
auto pokemon = "audino bagon baltoy banette bidoof braviary
bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask".toLower.split;
// Remove duplicates. pokemon.length -= pokemon.sort().uniq.copy(pokemon).length;
const sol = pokemon.findLongestChain;
writeln("Maximum path length: ", sol[1].length);
writeln("Paths of that length: ", sol[0]);
writeln("Example path of that length:");
writefln("%( %-(%s %)\n%)", sol[1].chunks(7));
}</lang>
- Output:
Maximum path length: 23 Paths of that length: 1248 Example path of that length: machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino
Runtime: about 0.20 seconds with dmd compiler, about 0.15 seconds with ldc2 compiler.
Alternative Version
<lang d>import std.stdio, std.algorithm, std.array, std.typecons,
std.container, std.range;
auto findChain(in string[] seq) pure nothrow /*@safe*/ {
const adj = seq
.map!(item => tuple(item, seq
.filter!(x => x[0] == item[$ - 1])
.array))
.assocArray;
SList!string res;
foreach (immutable item; adj.byKey) {
void inner(in string it, SList!string lst) nothrow {
lst.insertFront(it);
if (lst[].walkLength > res[].walkLength)
res = lst;
foreach (immutable x; adj[it])
if (!lst[].canFind(x))
inner(x, lst);
}
inner(item, SList!string()); }
return res.array.retro;
}
void main() /*@safe*/ {
"audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask".split.findChain.writeln;
}</lang>
- Output:
["machamp", "petilil", "landorus", "scrafty", "yamask", "kricketune", "emboar", "registeel", "loudred", "darmanitan", "nosepass", "simisear", "relicanth", "heatmor", "rufflet", "trapinch", "haxorus", "seaking", "girafarig", "gabite", "exeggcute", "emolga", "audino"]
Run-time is about 3.1 seconds with ldc2 compiler.
Delphi
Visual implementation, this unit is a VCL Form with a Memo, a Button, a Checkbox, a DataGrid, a DBMemo, a DataSource and a ClientDataSet with tree fields (length integer,count integer,list memo): <lang delphi>unit Unit1;
interface
uses
Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms, Dialogs, StdCtrls, DBCtrls, DB, DBClient, Grids, DBGrids, ExtCtrls;
type
TLastLFirstL = class(TForm)
Panel1: TPanel;
Button1: TButton;
Memo1: TMemo;
DataSource1: TDataSource;
ClientDataSet1: TClientDataSet;
ClientDataSet1Longitud: TIntegerField;
ClientDataSet1Cantidad: TIntegerField;
ClientDataSet1Lista: TMemoField;
Panel2: TPanel;
DBMemo1: TDBMemo;
DBGrid1: TDBGrid;
Splitter1: TSplitter;
CheckBox1: TCheckBox;
procedure FormCreate(Sender: TObject);
procedure Button1Click(Sender: TObject);
procedure FormDestroy(Sender: TObject);
private
{ Private declarations }
FPokemons:TStrings; //internal list of words, taken from memo
FIndex:TStrings; //index of words, based on starting letter
FCurrList:TStrings; //current list of words being made
FMax:integer; //max length of list found so far
FCount:array of array[boolean]of integer; //counting of lists length ocurrences
protected
procedure BuildIndex; //build FIndex based on FPokemons contents
procedure ClearIndex; //empty FIndex
procedure PokeChain(starting:Char;mylevel:integer); //recursive procedure that builds words lists
procedure BuildChains; //starts the lists building, by calling PokeChain for every FPokemons
procedure AddCurrList; //called each time a list is "finished" (no more words to add to it)
public
{ Public declarations }
end;
var
LastLFirstL: TLastLFirstL;
implementation
{$R *.dfm}
{ TForm1 }
{ if the actual list is the longest found so far it is added to the dataset, otherwise its ocurrence is just counted} procedure TLastLFirstL.AddCurrList; var
i,cc: integer; foundit:boolean;
begin
with ClientDataSet1 do begin
cc := FCurrList.Count;
if cc <= FMax then begin //count it
foundit := false;
for i := 0 to High(FCount) do begin
foundit := FCount[i][false] = cc;
if foundit then begin
FCount[i][true] := FCount[i][true] + 1;
break;
end;
end;
if not foundit then begin
//length that we never add to the dataset
i := High(FCount);
SetLength(FCount,i+2);
Inc(i);
FCount[i][false] := cc;
FCount[i][true] := 1;
end;
exit;
end;
//new longest list is FCurrList, add it to the dataset
FMax := cc;
SetLength(FCount,High(Fcount)+2); //make room for ocurrence count
FCount[High(FCount)][false] := cc;
FCount[High(FCount)][true] := 1;
//actual dataset adding
Append;
Fields[0].AsInteger := cc;
Fields[1].AsInteger := 0;
Fields[2].AsString := FCurrList.Text; //first one is example one
Post;
end;
end;
{} procedure TLastLFirstL.BuildChains; var
stSeen:array of array[boolean] of char; poke:string; i:integer; tc:int64; filteqs:boolean; k: Integer;
begin
//do some cleaning before starting
while not ClientDataSet1.IsEmpty do
ClientDataSet1.Delete;
Finalize(FCount);
FMax := 0;
filteqs := CheckBox1.Checked;
//measure time
tc := gettickcount;
//each word is given the opportunity of starting a list
if filteqs then begin
//ignore words with same start and end as others already seen
filteqs := False;
for i := 0 to FPokemons.Count - 1 do begin
poke := FPokemons[i];
for k := 0 to High(stSeen) do begin
filteqs := (stSeen[k][false] = poke[1]) and (stSeen[k][true] = poke[length(poke)]);
if filteqs then
break;
end;
if filteqs then //already seen equivalent
continue;
FPokemons.Objects[i] := Pointer(1);
FCurrList.Clear; //new list of words
FCurrList.Add(poke);
PokeChain(poke[length(poke)],2); //continue the list
//register as seen, for future equivalents
k := High(stSeen);
SetLength(stSeen,k+2);
Inc(k);
stSeen[k][false] := poke[1];
stSeen[k][true] := poke[length(poke)];
FPokemons.Objects[i] := nil;
end;
Finalize(stSeen);
end else begin
for i := 0 to FPokemons.Count - 1 do begin
poke := FPokemons[i];
FPokemons.Objects[i] := Pointer(1);
FCurrList.Clear; //new list of words
FCurrList.Add(poke);
PokeChain(poke[length(poke)],2); //continue the list
FPokemons.Objects[i] := nil;
end;
end;
tc := gettickcount - tc; //don't consider dataset counting as part of the process
//set actual counting of ocurrences on the dataset
for i := 0 to High(FCount) do with ClientDataSet1 do begin
if Locate('Longitud',FCount[i][false],[]) then
Edit
else begin
Append;
Fields[0].AsInteger := FCount[i][false];
Fields[2].AsString := 'No example preserved';
end;
Fields[1].AsInteger := FCount[i][true];
Post;
end;
ClientDataSet1.IndexFieldNames := 'Longitud';
//show time taken
Panel1.Caption := IntToStr(tc div 1000) + '.' + IntToStr(tc - (tc div 1000) * 1000) + ' segs.';
end;
{ builds an index based on the first letter of every word in consideration, because all we care about is the first and the last letter of every word. The index is a TStrings where each element is the starting letter and the corresponding object is a TList with all the indices of the words that starts with that letter. } procedure TLastLFirstL.BuildIndex; var
i,ii: Integer; poke:string; st,ed:char; List:TList; k: Integer; found:boolean;
begin
ClearIndex; //just in case is not the first execution
if not Assigned(FIndex) then // just in case IS the first execution
FIndex := TStringList.Create;
for i := 0 to FPokemons.Count - 1 do begin
poke := FPokemons[i];
st := poke[1];
ed := poke[Length(poke)];
ii := FIndex.IndexOf(st);
if ii<0 then //first time we see this starting letter
ii := FIndex.AddObject(st,TList.Create);
List := TList(FIndex.Objects[ii]);
found := false;
if CheckBox1.Checked then begin //ignore equivalent words (same start, same end)
//all the List are words with the same start, so lets check the end
for k := 0 to List.Count - 1 do begin
poke := FPokemons[integer(List[k])];
found := poke[Length(poke)] = ed;
if found then
break;
end;
end;
if not found then // not checking equivalents, or firts time this end is seen
List.Add(Pointer(i));
end;
end;
{ do your thing! } procedure TLastLFirstL.Button1Click(Sender: TObject); begin
Panel1.Caption := 'Calculating..'; FPokemons.Assign(Memo1.Lines); //words in the game BuildIndex; BuildChains;
end;
{ frees all the TList used by the index, clears the index } procedure TLastLFirstL.ClearIndex; var
i:integer;
begin
if not Assigned(FIndex) then exit; for i := 0 to FIndex.Count - 1 do begin TList(FIndex.Objects[i]).Free; end; FIndex.Clear;
end;
procedure TLastLFirstL.FormCreate(Sender: TObject); begin
FPokemons := TStringList.Create; FCurrList := TStringList.Create;
end;
procedure TLastLFirstL.FormDestroy(Sender: TObject); begin
FCurrList.Free; FPokemons.Free; ClearIndex; //IMPORTANT! FIndex.Free;
end;
{where the magic happens. Recursive procedure that adds a word to the current list of words. Receives the starting letter of the word to add, and the "position" of the word in the chain. The position is used to ensure a word is not used twice for the list. } procedure TLastLFirstL.PokeChain(starting: Char;mylevel:integer); var
i,ii,plevel:integer; List:TList; didit:boolean;
begin
application.processMessages; //don't let the interface die..
didit := False; //if we can't add another word, then we have reached the maximun length for the list
ii := FIndex.IndexOf(starting);
if ii >= 0 then begin //there are words with this starting letter
List := TList(FIndex.Objects[ii]);
for i := 0 to List.Count - 1 do begin
ii := integer(List[i]);
plevel := integer(FPokemons.Objects[ii]); // if the integer stored in the Object property is lower than mylevel, then this word is already in the list
if (plevel > mylevel) or (plevel = 0) then begin // you can use the word
//a try finally would be a good thing here, but...
FCurrList.Add(FPokemons[ii]); //add the word to the list
FPokemons.Objects[ii] := Pointer(mylevel); //signal is already in the list
PokeChain(FPokemons[ii][length(FPokemons[ii])],mylevel+1); //add more words to the list
FcurrList.Delete(FCurrList.Count-1); //already did my best, lets try with another word
FPokemons.Objects[ii] := nil; //unsignal it, so it can be used "later"
didit := True; //we did add one word to the list
end;
end;
end;
if not didit then //there is no way of making the list longer, process it
AddCurrList;
end;
end.</lang> Runtime varies depending if you run the "optimized" version or not. Ranges from 6 to 18 seconds.
NOTE: "optimized" version is actually a different algorithm, but in most cases returns the same results.
Elixir
<lang elixir>defmodule LastLetter_FirstLetter do
def search(names) do
first = Enum.group_by(names, &String.first/1)
sequences = Enum.reduce(names, [], fn name,acc -> add_name(first, acc, [name]) end)
max = Enum.max_by(sequences, &length/1) |> length
max_seqs = Enum.filter(sequences, fn seq -> length(seq) == max end)
IO.puts "there are #{length(sequences)} possible sequences"
IO.puts "the longest is #{max} names long"
IO.puts "there are #{length(max_seqs)} such sequences. one is:"
hd(max_seqs) |> Enum.with_index |>
Enum.each(fn {name, idx} ->
:io.fwrite " ~2w ~s~n", [idx+1, name]
end)
end
defp add_name(first, sequences, seq) do
last_letter = String.last(hd(seq))
potentials = Map.get(first, last_letter, []) -- seq
if potentials == [] do
[Enum.reverse(seq) | sequences]
else
Enum.reduce(potentials, sequences, fn name, acc -> add_name(first, acc, [name | seq]) end)
end
end
end
names = ~w(
audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask
)
LastLetter_FirstLetter.search(names)</lang>
- Output:
there are 2076396 possible sequences the longest is 23 names long there are 1248 such sequences. one is: 1 machamp 2 petilil 3 landorus 4 scrafty 5 yamask 6 kricketune 7 emboar 8 registeel 9 loudred 10 darmanitan 11 nosepass 12 simisear 13 relicanth 14 heatmor 15 rufflet 16 trapinch 17 haxorus 18 seaking 19 girafarig 20 gabite 21 exeggcute 22 emolga 23 audino
Erlang
This is a parallel version. It takes 2.1 seconds. The (commented out) serial version takes 7.1 seconds. Both times measured on my (low end) Mac Mini. I thought parallel code would help in getting the brownie points. But even a small increase to 100 Pokemons makes the code run for more than the few spare hours I have in the evening. <lang Erlang> -module( last_letter_first_letter ).
-export( [solve/1, task/0] ).
solve( Names ) ->
Dict = lists:foldl( fun dict_append/2, dict:new(), Names ), Chains = construct_chains_in_parallel( Dict ),
% Chains = [construct_chain_from_key(Dict, X) || X <- dict:fetch_keys(Dict)],
lists:foldl( fun construct_chain_longest/2, [], Chains ).
task() -> solve( binary:split(names(), <<" ">>, [global]) ).
construct_chains_in_parallel( Dict ) ->
My_pid = erlang:self(),
Pids = [erlang:spawn( fun() -> My_pid ! {erlang:self(), construct_chain_from_key(Dict, X)} end) || X <- dict:fetch_keys(Dict)],
[receive {X, Chain} -> Chain end || X <- Pids].
construct_chain_from_key( Dict, First_letter ) -> Names = construct_chain_names( dict:find(First_letter, Dict) ), construct_chain_from_names( Names, Dict, [] ).
construct_chain_from_names( [], _Dict, Best_chain ) -> Best_chain; construct_chain_from_names( [{Name, Last_letter} | T], Dict, Best_chain ) ->
New_dict = dict_delete( Name, Dict ),
New_chain = [Name | construct_chain_from_key( New_dict, Last_letter )],
construct_chain_from_names( T, Dict, construct_chain_longest(Best_chain, New_chain) ).
construct_chain_longest( Chain1, Chain2 ) when length(Chain1) > length(Chain2) -> Chain1; construct_chain_longest( _Chain1, Chain2 ) -> Chain2.
construct_chain_names( {ok, {Name, Last_letter}} ) -> [{Name, Last_letter}]; construct_chain_names( {ok, Values} ) -> Values; construct_chain_names( error ) -> [].
dict_append( Name, Acc ) -> {First_letter, {Name, Last_letter}} = dict_item( Name ), dict:append( First_letter, {Name, Last_letter}, Acc ).
dict_item( <<First_letter, _T/binary>>=Name ) -> Until_last_letter = erlang:byte_size( Name ) - 1, <<_H:Until_last_letter/binary, Last_letter>> = Name, {First_letter, {Name, Last_letter}}.
dict_delete( <<First_letter, _T/binary>>=Name, Dict ) -> Name_last_letters = dict:fetch(First_letter, Dict), dict:store( First_letter, lists:keydelete(Name, 1, Name_last_letters), Dict ).
names() -> <<"audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask">>. </lang>
- Output:
11> last_letter_first_letter:task(). [<<"machamp">>,<<"pinsir">>,<<"rufflet">>,<<"trapinch">>, <<"heatmor">>,<<"remoraid">>,<<"darmanitan">>, <<"nosepass">>,<<"starly">>,<<"yamask">>,<<"kricketune">>, <<"exeggcute">>,<<"emboar">>,<<"relicanth">>,<<"haxorus">>, <<"simisear">>,<<"registeel">>,<<"landorus">>,<<"seaking">>, <<"girafarig">>,<<"gabite">>,<<"emolga">>,<<"audino">>]
Go
Depth first, starting with each possible name. <lang go>package main
import (
"fmt" "strings"
)
var pokemon = `audino bagon baltoy...67 names omitted...`
func main() {
// split text into slice representing directed graph
var d []string
for _, l := range strings.Split(pokemon, "\n") {
d = append(d, strings.Fields(l)...)
}
fmt.Println("searching", len(d), "names...")
// try each name as possible start
for i := range d {
d[0], d[i] = d[i], d[0]
search(d, 1, len(d[0]))
d[0], d[i] = d[i], d[0]
}
fmt.Println("maximum path length:", len(ex))
fmt.Println("paths of that length:", nMax)
fmt.Print("example path of that length:")
for i, n := range ex {
if i%6 == 0 {
fmt.Print("\n ")
}
fmt.Print(n, " ")
}
fmt.Println()
}
var ex []string var nMax int
func search(d []string, i, ncPath int) {
// tally statistics
if i == len(ex) {
nMax++
} else if i > len(ex) {
nMax = 1
ex = append(ex[:0], d[:i]...)
}
// recursive search
lastName := d[i-1]
lastChar := lastName[len(lastName)-1]
for j := i; j < len(d); j++ {
if d[j][0] == lastChar {
d[i], d[j] = d[j], d[i]
search(d, i+1, ncPath+1+len(d[i]))
d[i], d[j] = d[j], d[i]
}
}
}</lang> Output:
searching 70 names... maximum path length: 23 paths of that length: 1248 example path of that length: machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino
Haskell
Note: This takes ~80 seconds to complete on my machine. <lang Haskell>import Data.List import qualified Data.ByteString.Char8 as B
allPokemon :: [B.ByteString] allPokemon = map B.pack $ words
"audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon \ \cresselia croagunk darmanitan deino emboar emolga exeggcute gabite \ \girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan \ \kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine \ \nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 \ \porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking \ \sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko \ \tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask"
growChains :: B.ByteString -> [B.ByteString] growChains pcs
| nextChainSet == [] = head pcs
| otherwise = growChains nextChainSet
where nextChainSet = pcs >>= findLinks
findLinks pc = map (\x -> pc ++ [x]) $ filter (isLink $ last pc) (allPokemon \\ pc)
isLink pl pr = B.last pl == B.head pr
main = mapM_ B.putStrLn $ growChains $ map (\x -> [x]) allPokemon</lang> Output:
machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino
A simpler version (no ByteString), about 2.4 times slower (GHC -O3), same output: <lang Haskell>import Data.List
allPokemon = words
"audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon \ \cresselia croagunk darmanitan deino emboar emolga exeggcute gabite \ \girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan \ \kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine \ \nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 \ \porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking \ \sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko \ \tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask"
growChains :: String -> [String] growChains pcs
| nextChainSet == [] = head pcs
| otherwise = growChains nextChainSet
where nextChainSet = pcs >>= findLinks
findLinks pc = map (\x -> pc ++ [x]) $ filter (isLink $ last pc) (allPokemon \\ pc)
isLink pl pr = last pl == head pr
main = mapM_ putStrLn $ growChains $ map (\x -> [x]) allPokemon</lang>
Icon and Unicon
Works in both languages (brute force):
<lang unicon>global words
procedure main()
words := table()
every word := genwords(&input) do {
/words[word[1]] := []
put(words[word[1]], word)
}
bP := []
every p := getPath(!!words,[]) do if *\p > *bP then bP := copy(p)
write("Longest: ",*bP)
every writes((!bP||" ")|"\n")
end
procedure getPath(word, p)
if word == !p then return p if /words[word[-1]] then suspend p <- p ||| [word] else suspend getPath(!words[word[-1]], p <- p ||| [word])
end
procedure genwords(f)
while l := !f do
l ? while tab(upto(&letters)) do suspend tab(many(&letters))\1
end</lang>
Sample run on sample data:
->llfl <llfl.in Longest: 23 machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino ->
J
Here, we use a brute force breadth-first search. Unless we know ahead of time how long "longest" is, we must try all possibilities to ensure that an unchecked possibility is not longer than a possibility which we have found.
<lang j>pokenames=: ;:0 :0-.LF
audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask
)
seqs=: 3 :0
links=. <@I. _1 =/&({&>&y) 0
next=. ,.i.#links
while.#next do.
r=. next
assert. 1e9>*/8,$r
next=. (#~ (-: ~.)"1) >;<@(] <@,"1 0 links {::~ {:)"1 r
end.
r
)</lang>
The line assert. 1e9>*/8,$r was added to avoid a very bad behavior from microsoft windows which appeared on different arguments, when intermediate results became too large (the machine would have to be rebooted when intermediate results became an order of magnitude larger than the available physical memory). By ensuring that the program would end before consuming that much virtual memory, this behavior from the operating system can be avoided. Note that 9!:21 and/or 9!:33 could also be used to prevent OS instability triggered by requesting too many resources.
With this procedure we are able to conduct the entire search for this list of names:
<lang j>$R=: seqs pokenames 1248 23</lang>
With this data set, we have 1248 sequences of names which have the longest possible length, and those sequences are 23 names long. Here's one of them:
<lang j> >pokenames {~{.R machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino </lang>
Java
<lang java>// derived from C final class LastLetterFirstLetter {
static int maxPathLength = 0; static int maxPathLengthCount = 0; static final StringBuffer maxPathExample = new StringBuffer(500);
static final String[] names = {"audino", "bagon", "baltoy", "banette",
"bidoof", "braviary", "bronzor", "carracosta", "charmeleon",
"cresselia", "croagunk", "darmanitan", "deino", "emboar",
"emolga", "exeggcute", "gabite", "girafarig", "gulpin",
"haxorus", "heatmor", "heatran", "ivysaur", "jellicent",
"jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba",
"loudred", "lumineon", "lunatone", "machamp", "magnezone",
"mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu",
"pinsir", "poliwrath", "poochyena", "porygon2", "porygonz",
"registeel", "relicanth", "remoraid", "rufflet", "sableye",
"scolipede", "scrafty", "seaking", "sealeo", "silcoon",
"simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga",
"trapinch", "treecko", "tyrogue", "vigoroth", "vulpix",
"wailord", "wartortle", "whismur", "wingull", "yamask"};
static void recursive(String[] part, int offset) {
if (offset > maxPathLength) {
maxPathLength = offset;
maxPathLengthCount = 1;
} else if (offset == maxPathLength) {
maxPathLengthCount++;
maxPathExample.setLength(0);
for (int i = 0; i < offset; i++) {
maxPathExample.append((i % 5 == 0 ? "\n " : " "));
maxPathExample.append(part[i]);
}
}
final char lastChar = part[offset - 1].charAt(part[offset - 1].length()-1);
for (int i = offset; i < part.length; i++) {
if (part[i].charAt(0) == lastChar) {
String tmp = names[offset];
names[offset] = names[i];
names[i] = tmp;
recursive(names, offset+1);
names[i] = names[offset];
names[offset] = tmp;
}
}
}
public static void main(String[] args) {
for (int i = 0; i < names.length; i++) {
String tmp = names[0];
names[0] = names[i];
names[i] = tmp;
recursive(names, 1);
names[i] = names[0];
names[0] = tmp;
}
System.out.println("maximum path length : " + maxPathLength);
System.out.println("paths of that length : " + maxPathLengthCount);
System.out.println("example path of that length:" + maxPathExample);
}
} </lang>
Output:
maximum path length : 23 paths of that length : 1248 example path of that length: machamp pinsir rufflet trapinch heatmor remoraid darmanitan nosepass starly yamask kricketune exeggcute emboar relicanth haxorus simisear registeel landorus seaking girafarig gabite emolga audino
jq
Short and sweet, with a nod to efficiency in the form of a dictionary for lookup of still-available words.
jq's "debug" filter is used to illustrate how progress can be monitored. It writes to stderr. If your jq does not include "debug", simply remove or comment-out the entire line.
Utility functions: <lang jq># convert a list of unique words to a dictionary def dictionary:
reduce .[] as $word ({}; .[$word[0:1]] += [$word]) ;
- remove "word" from the input dictionary assuming the key is already there:
def remove(word):
.[word[0:1]] -= [word];</lang>
The last-letter/first-letter game: <lang ja># left-right admissibility def admissible:
.[0][-1:] == .[1][0:1];
- input: [word, dictionary_of_available_words_excluding_word]
- output: a (possibly empty) stream of admissible values: [next_word, updated_dictionary],
- where next_word can follow the given word.
def next:
.[0] as $word
| if $word == null then empty
else .[1] as $dictionary
| $word[-1:] as $last
| (($dictionary[$last] // []) | .[]) as $next
| [ $next, ($dictionary | remove($next)) ]
end ;
- Produce an array representing a thread starting at "word":
- Input: [word, dictionary_of_available_words]
def thread:
if .[1] == [] then [ .[0] ] else (next // null) as $next | [.[0]] + (if $next then ($next | thread) else [] end) end ;
- Input: list of words
- Output: [ maximal_length, maximal_thread]
def maximal:
def maximum(start):
. as $dictionary
| reduce ( [start, ($dictionary | remove(start))] | thread ) as $thread
([0, null];
($thread|length) as $l
| if $l > .[0] then [$l, $thread] else . end );
dictionary as $dictionary
| reduce .[] as $name
( [0,null];
($dictionary | maximum($name)) as $ans
# If your jq does not include "debug", simply remove or comment-out the following line: | ([$name, $ans[0]] | debug) as $debug
| if $ans[0] > .[0] then $ans else . end );</lang>
Example: <lang jq>def names:
["audino", "bagon", "baltoy", "banette",
"bidoof", "braviary", "bronzor", "carracosta", "charmeleon",
"cresselia", "croagunk", "darmanitan", "deino", "emboar",
"emolga", "exeggcute", "gabite", "girafarig", "gulpin",
"haxorus", "heatmor", "heatran", "ivysaur", "jellicent",
"jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba",
"loudred", "lumineon", "lunatone", "machamp", "magnezone",
"mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu",
"pinsir", "poliwrath", "poochyena", "porygon2", "porygonz",
"registeel", "relicanth", "remoraid", "rufflet", "sableye",
"scolipede", "scrafty", "seaking", "sealeo", "silcoon",
"simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga",
"trapinch", "treecko", "tyrogue", "vigoroth", "vulpix",
"wailord", "wartortle", "whismur", "wingull", "yamask" ] ;
names | maximal</lang>
- Output:
(scrollable)
The "DEBUG" lines are included to illustrate how progress can be monitored. They show the maximal length for the indicated initial word.
<lang sh>$ jq -n -f Last_letter-first_letter.jq ["DEBUG:",["audino",1]] ["DEBUG:",["bagon",20]] ["DEBUG:",["baltoy",21]] ["DEBUG:",["banette",20]] ["DEBUG:",["bidoof",1]] ["DEBUG:",["braviary",21]] ["DEBUG:",["bronzor",22]] ["DEBUG:",["carracosta",2]] ["DEBUG:",["charmeleon",20]] ["DEBUG:",["cresselia",2]] ["DEBUG:",["croagunk",21]] ["DEBUG:",["darmanitan",20]] ["DEBUG:",["deino",1]] ["DEBUG:",["emboar",19]] ["DEBUG:",["emolga",2]] ["DEBUG:",["exeggcute",19]] ["DEBUG:",["gabite",20]] ["DEBUG:",["girafarig",20]] ["DEBUG:",["gulpin",20]] ["DEBUG:",["haxorus",20]] ["DEBUG:",["heatmor",20]] ["DEBUG:",["heatran",20]] ["DEBUG:",["ivysaur",22]] ["DEBUG:",["jellicent",21]] ["DEBUG:",["jumpluff",1]] ["DEBUG:",["kangaskhan",20]] ["DEBUG:",["kricketune",20]] ["DEBUG:",["landorus",21]] ["DEBUG:",["ledyba",2]] ["DEBUG:",["loudred",21]] ["DEBUG:",["lumineon",20]] ["DEBUG:",["lunatone",20]] ["DEBUG:",["machamp",23]] ["DEBUG:",["magnezone",20]] ["DEBUG:",["mamoswine",20]] ["DEBUG:",["nosepass",19]] ["DEBUG:",["petilil",22]] ["DEBUG:",["pidgeotto",1]] ["DEBUG:",["pikachu",1]] ["DEBUG:",["pinsir",22]] ["DEBUG:",["poliwrath",21]] ["DEBUG:",["poochyena",2]] ["DEBUG:",["porygon2",1]] ["DEBUG:",["porygonz",1]] ["DEBUG:",["registeel",21]] ["DEBUG:",["relicanth",21]] ["DEBUG:",["remoraid",21]] ["DEBUG:",["rufflet",21]] ["DEBUG:",["sableye",20]] ["DEBUG:",["scolipede",20]] ["DEBUG:",["scrafty",21]] ["DEBUG:",["seaking",21]] ["DEBUG:",["sealeo",1]] ["DEBUG:",["silcoon",20]] ["DEBUG:",["simisear",21]] ["DEBUG:",["snivy",21]] ["DEBUG:",["snorlax",1]] ["DEBUG:",["spoink",21]] ["DEBUG:",["starly",21]] ["DEBUG:",["tirtouga",2]] ["DEBUG:",["trapinch",20]] ["DEBUG:",["treecko",1]] ["DEBUG:",["tyrogue",20]] ["DEBUG:",["vigoroth",21]] ["DEBUG:",["vulpix",1]] ["DEBUG:",["wailord",21]] ["DEBUG:",["wartortle",20]] ["DEBUG:",["whismur",22]] ["DEBUG:",["wingull",22]] ["DEBUG:",["yamask",20]] [
23, [ "machamp", "petilil", "landorus", "scrafty", "yamask", "kricketune", "emboar", "registeel", "loudred", "darmanitan", "nosepass", "simisear", "relicanth", "heatmor", "rufflet", "trapinch", "haxorus", "seaking", "girafarig", "gabite", "exeggcute", "emolga", "audino" ]]</lang>
Julia
<lang julia>using IterTools.groupby
orderwords(words::Vector) = Dict(w[1][1] => Set(w) for w in groupby(first, words)) longest(a, b) = ifelse(length(a) > length(b), a, b) function linkfirst(byfirst::Dict, sofar::Vector)
@assert(!isempty(sofar))
chmatch = sofar[end][end]
if ! haskey(byfirst, chmatch) return sofar end
options = setdiff(byfirst[chmatch], sofar)
if isempty(options)
return sofar
else
alternatives = ( linkfirst(byfirst, vcat(sofar, word)) for word in options )
mx = reduce(longest, alternatives)
return mx
end
end function llfl(words)
byfirst = orderwords(words) alternatives = ( linkfirst(byfirst, [word]) for word in words ) return reduce(longest, alternatives)
end
pokemon = String.(unique(split("""
audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask """)))
l = llfl(pokemon) println("Example of longest seq.:\n", join(l, ", ")) println("Max length: ", length(l)</lang>
- Output:
Example of longest seq.: machamp, pinsir, relicanth, heatmor, registeel, landorus, starly, yamask, kricketune, emboar, rufflet, trapinch, haxorus, simisear, remoraid, darmanitan, nosepass, seaking, girafarig, gabite, exeggcute, emolga, audino Max length: 23
Kotlin
<lang scala>// version 1.1.2
var maxPathLength = 0 var maxPathLengthCount = 0 val maxPathExample = StringBuilder(500)
val names = arrayOf(
"audino", "bagon", "baltoy", "banette", "bidoof", "braviary", "bronzor", "carracosta", "charmeleon", "cresselia", "croagunk", "darmanitan", "deino", "emboar", "emolga", "exeggcute", "gabite", "girafarig", "gulpin", "haxorus", "heatmor", "heatran", "ivysaur", "jellicent", "jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba", "loudred", "lumineon", "lunatone", "machamp", "magnezone", "mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu", "pinsir", "poliwrath", "poochyena", "porygon2", "porygonz", "registeel", "relicanth", "remoraid", "rufflet", "sableye", "scolipede", "scrafty", "seaking", "sealeo", "silcoon", "simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga", "trapinch", "treecko", "tyrogue", "vigoroth", "vulpix", "wailord", "wartortle", "whismur", "wingull", "yamask"
)
fun search(part: Array<String>, offset: Int) {
if (offset > maxPathLength) {
maxPathLength = offset
maxPathLengthCount = 1
}
else if (offset == maxPathLength) {
maxPathLengthCount++
maxPathExample.setLength(0)
for (i in 0 until offset) {
maxPathExample.append(if (i % 5 == 0) "\n " else " ")
maxPathExample.append(part[i])
}
}
val lastChar = part[offset - 1].last()
for (i in offset until part.size) {
if (part[i][0] == lastChar) {
val tmp = names[offset]
names[offset] = names[i]
names[i] = tmp
search(names, offset + 1)
names[i] = names[offset]
names[offset] = tmp
}
}
}
fun main(args: Array<String>) {
for (i in 0 until names.size) {
val tmp = names[0]
names[0] = names[i]
names[i] = tmp
search(names, 1)
names[i] = names[0]
names[0] = tmp
}
println("Maximum path length : $maxPathLength")
println("Paths of that length : $maxPathLengthCount")
println("Example path of that length : $maxPathExample")
}</lang>
- Output:
Maximum path length : 23 Paths of that length : 1248 Example path of that length : machamp pinsir rufflet trapinch heatmor remoraid darmanitan nosepass starly yamask kricketune exeggcute emboar relicanth haxorus simisear registeel landorus seaking girafarig gabite emolga audino
Mathematica
<lang Mathematica>longestChain[list_] :=
NestWhileList[
Append @@@
Select[DeleteDuplicatesBy[
Tuples[{#, list}], {#1, 1, #2} &], ! MemberQ @@ # &&
StringTake[#1, -1, -1] == StringTake[#2, 1] &] &,
List /@ list, # != {} &]-2, 1;
Print[longestChain[{"audino", "bagon", "baltoy", "banette", "bidoof",
"braviary", "bronzor", "carracosta", "charmeleon", "cresselia", "croagunk", "darmanitan", "deino", "emboar", "emolga", "exeggcute", "gabite", "girafarig", "gulpin", "haxorus", "heatmor", "heatran", "ivysaur", "jellicent", "jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba", "loudred", "lumineon", "lunatone", "machamp", "magnezone", "mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu", "pinsir", "poliwrath", "poochyena", "porygon2", "porygonz", "registeel", "relicanth", "remoraid", "rufflet", "sableye", "scolipede", "scrafty", "seaking", "sealeo", "silcoon", "simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga", "trapinch", "treecko", "tyrogue", "vigoroth", "vulpix", "wailord", "wartortle", "whismur", "wingull", "yamask"}]];</lang>
Uses the tactic of only checking chains with the same starting and ending values.
- Output:
{baltoy, yamask, kangaskhan, nosepass, sableye, emboar, registeel, landorus, scolipede, emolga, audino}
ooRexx
<lang ooRexx> -- create the searcher and run it searcher = .chainsearcher~new
- class chainsearcher
- method init
expose max searchsize currentlongest
pokemon_names = "audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon" -
"cresselia croagunk darmanitan deino emboar emolga exeggcute gabite" -
"girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan" -
"kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine" -
"nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2" -
"porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking" -
"sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko" -
"tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask"
pokemon = pokemon_names~makearray(" ")
searchsize = pokemon~items
currentlongest = 0
say "searching" searchsize "names..."
longestchain = .array~new
-- run the sequence using each possible starting pokemon
loop i = 1 to pokemon~items
-- swap the ith name to the front of our list
self~swap(pokemon, 1, i)
-- run the chain from here
self~searchChain(pokemon, longestchain, 2)
-- swap the name back so we have the list in original form
self~swap(pokemon, 1, i)
end
say "maximum path length:" longestchain~items
say "paths of that length:" max
say "example path of that length:"
loop name over longestchain
say " "name
end
- method swap
use arg list, a, b tmp = list[a] list[a] = list[b] list[b] = tmp
-- recursive search routine for adding to the chain
- method searchChain
expose max searchsize currentlongest use arg pokemon, longestchain, currentchain
-- get the last character
lastchar = pokemon[currentchain - 1]~right(1)
-- now we search through all of the permutations of remaining
-- matches to see if we can find a longer chain
loop i = currentchain to searchsize
-- for every candidate name from here, recursively extend the chain.
if pokemon[i]~left(1) == lastchar then do
if currentchain == currentLongest then max += 1
-- have we now gone deeper than the current longest chain?
else if currentchain > currentLongest then do
-- chuck this result and refill with current set
longestchain~empty
longestchain~appendall(pokemon~section(1, currentchain - 1))
longestchain~append(pokemon[i])
max = 1
currentLongest = currentchain
end
-- perform the swap again
self~swap(pokemon, currentchain, i)
-- run the chain from here
self~searchChain(pokemon, longestchain, currentchain + 1)
-- swap the name back so we have the list in original form
self~swap(pokemon, currentchain, i)
end
end
</lang>
searching 70 names...
maximum path length: 23
paths of that length: 1248
example path of that length:
machamp
petilil
landorus
scrafty
yamask
kricketune
emboar
registeel
loudred
darmanitan
nosepass
simisear
relicanth
heatmor
rufflet
trapinch
haxorus
seaking
girafarig
gabite
exeggcute
emolga
audino
OpenEdge/Progress
The following gets the job done, but the time taken (40 minutes) is somewhat worrying when compared to other language solutions. So I am not going after the brownie points just yet...
<lang progress>DEFINE VARIABLE cpokemon AS CHARACTER INITIAL "audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon ~ cresselia croagunk darmanitan deino emboar emolga exeggcute gabite ~ girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan ~ kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine ~ nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 ~ porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking ~ sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko ~ tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask".
DEFINE TEMP-TABLE tt NO-UNDO
FIELD cname AS CHARACTER FIELD cfirst AS CHARACTER FIELD clast AS CHARACTER FIELD lused AS LOGICAL FIELD ilength AS INTEGER FIELD imax AS INTEGER FIELD cchain AS CHARACTER
INDEX ttname cname INDEX ttfirst cfirst lused INDEX ttlast clast lused .
DEFINE VARIABLE ii AS INTEGER NO-UNDO.
DO ii = 1 TO NUM-ENTRIES( cpokemon, " " ):
CREATE tt.
ASSIGN
tt.cname = ENTRY( ii, cpokemon, " " )
tt.cfirst = SUBSTRING( tt.cname, 1, 1 )
tt.clast = SUBSTRING( tt.cname, LENGTH( tt.cname ), 1 )
.
END.
FUNCTION getChain RETURNS INTEGER (
i_cname AS CHARACTER, i_clast AS CHARACTER, i_ilength AS INTEGER, i_cchain AS CHARACTER
):
DEFINE BUFFER tt FOR tt.
DEFINE VARIABLE lend_of_chain AS LOGICAL NO-UNDO INITIAL TRUE.
FOR EACH tt
WHERE tt.cfirst = i_clast
AND tt.lused = FALSE
OR i_clast = ""
:
lend_of_chain = FALSE.
tt.lused = TRUE.
getChain( tt.cname, tt.clast, i_ilength + 1, i_cchain + tt.cname + " " ).
tt.lused = FALSE.
END.
IF lend_of_chain THEN DO:
FIND tt WHERE tt.cname = ENTRY( 1, i_cchain, " " ).
IF i_ilength = tt.ilength THEN
tt.imax = tt.imax + 1.
ELSE IF i_ilength > tt.ilength THEN
ASSIGN
tt.ilength = i_ilength
tt.cchain = i_cchain
tt.imax = 1
.
END.
END FUNCTION. /* getChain */
DEFINE VARIABLE itime AS INTEGER NO-UNDO EXTENT 2. DEFINE VARIABLE lcontinue AS LOGICAL NO-UNDO.
itime[1] = ETIME. getChain( "", "", 0, "" ). itime[2] = ETIME.
FOR EACH tt BY tt.ilength DESCENDING:
MESSAGE
"Maximum path length:" tt.ilength SKIP
"Paths of that length:" tt.imax SKIP(1)
"Example path of that length:" tt.cchain SKIP(1)
"Time taken:" STRING( INTEGER( ( itime[2] - itime[1] ) / 1000 ), "HH:MM:SS" )
VIEW-AS ALERT-BOX BUTTONS YES-NO TITLE tt.cname UPDATE lcontinue.
IF lcontinue = FALSE THEN
STOP.
END.</lang>
Output:
--------------------------- machamp --------------------------- Maximum path length: 23 Paths of that length: 1248 Example path of that length: machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino Time taken: 00:40:09 --------------------------- Yes No ---------------------------
PicoLisp
<lang PicoLisp>(de pokemonChain (File)
(let Names (make (in File (while (read) (link @))))
(for Name Names
(let C (last (chop Name))
(set Name
(filter '((Nm) (pre? C Nm)) Names) ) ) )
(let Res NIL
(for Name Names
(let Lst NIL
(recur (Name Lst)
(if (or (memq Name Lst) (not (val (push 'Lst Name))))
(when (> (length Lst) (length Res))
(setq Res Lst) )
(mapc recurse (val Name) (circ Lst)) ) ) ) )
(flip Res) ) ) )</lang>
Test:
: (pokemonChain "pokemon.list") -> (machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino) : (length @) -> 23
Perl
This is rather 'one liner' code, not to be used in production.
The idea is to try all possible variants recursively.
- First, it creates the map-like structure: first letter → array of (name + last letter).
- During the cycle it uses @w as stack;
- @m keeps the longest sequence which is copied from @w;
- to prevent the words from appearing twice, they are (temporarily) deleted from the structure keeping the value in a stack variable.
<lang perl>use strict; my(%f,@m);
/^(.).*(.)$/,$f{$1}{$_}=$2 for qw( audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask );
sub poke {
our @w;
my $h = $f{$_[0]};
for my $word (keys %$h) {
my $v = $h->{$word}; delete $h->{$word}; push @w, $word; @m = @w if @w > @m; poke($v); pop @w; $h->{$word} = $v;
}
}
poke($_) for keys %f; print @m.": @m\n";</lang>
- Output:
23: machamp petilil landorus seaking girafarig gabite emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus scrafty yamask kricketune exeggcute emolga audino
Perl 6
A breadth-first search that uses disk files to avoid memory exhaustion. Each candidate sequence is encoded at one character per name, so to avoid reuse of names we merely have to make sure there are no repeat characters in our encoded string. (The encoding starts at ASCII space for the first name, so newline is not among the encoded characters.) <lang perl6>my @names = <
audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask
>;
my @last = @names.map: {.substr(*-1,1).ord } my @succs = [] xx 128; for @names.kv -> $i, $name {
my $ix = $name.ord; # $name.substr(0,1).ord push @succs[$ix], $i;
}
my $OUT = open "llfl.new", :w orelse .die; $OUT.print: chr($_ + 32),"\n" for 0 ..^ @names; close $OUT; my $new = +@names; my $len = 1;
while $new {
say "Length { $len++ }: $new candidates";
shell 'mv llfl.new llfl.known';
my $IN = open "llfl.known" orelse .die;
my $OUT = open "llfl.new", :w orelse .die;
$new = 0;
loop {
my $cand = $IN.get // last; for @succs[@last[$cand.ord - 32]][] -> $i { my $ic = chr($i + 32); next if $cand ~~ /$ic/; $OUT.print: $ic,$cand,"\n"; $new++; }
} $IN.close; $OUT.close;
}
my $IN = open "llfl.known" orelse .die; my $eg = $IN.lines.pick; say "Length of longest: ", $eg.chars; say join ' ', $eg.ords.reverse.map: { @names[$_ - 32] }</lang>
- Output:
Length 1: 70 candidates Length 2: 172 candidates Length 3: 494 candidates Length 4: 1288 candidates Length 5: 3235 candidates Length 6: 7731 candidates Length 7: 17628 candidates Length 8: 37629 candidates Length 9: 75122 candidates Length 10: 139091 candidates Length 11: 236679 candidates Length 12: 367405 candidates Length 13: 516210 candidates Length 14: 650916 candidates Length 15: 733915 candidates Length 16: 727566 candidates Length 17: 621835 candidates Length 18: 446666 candidates Length 19: 260862 candidates Length 20: 119908 candidates Length 21: 40296 candidates Length 22: 10112 candidates Length 23: 1248 candidates Length of longest: 23 machamp petilil loudred darmanitan nosepass simisear rufflet trapinch heatmor registeel landorus starly yamask kricketune exeggcute emboar relicanth haxorus seaking girafarig gabite emolga audino
Phix
Using simple start-with-same-letter word chains to minimise the number of elements we have to consider: <lang Phix>constant words = {"audino","bagon","baltoy","banette","bidoof","braviary","bronzor","carracosta","charmeleon","cresselia","croagunk",
"darmanitan","deino","emboar","emolga","exeggcute","gabite","girafarig","gulpin","haxorus","heatmor","heatran",
"ivysaur","jellicent","jumpluff","kangaskhan","kricketune","landorus","ledyba","loudred","lumineon","lunatone",
"machamp","magnezone","mamoswine","nosepass","petilil","pidgeotto","pikachu","pinsir","poliwrath","poochyena",
"porygon2","porygonz","registeel","relicanth","remoraid","rufflet","sableye","scolipede","scrafty","seaking",
"sealeo","silcoon","simisear","snivy","snorlax","spoink","starly","tirtouga","trapinch","treecko","tyrogue",
"vigoroth","vulpix","wailord","wartortle","whismur","wingull","yamask"}
function word_chains() sequence first = repeat(0,256), -- start of chains for a given letter
-- first['a']=1, first['b']=2, first['c']=8, etc.
snext = repeat(0,length(words)) -- chains of words starting with the same letter
-- a: snext[1]=0, b: snext[2..7]={3,4,5,6,7,0}, etc.
for i=1 to length(words) do
integer ch = words[i][1]
if first[ch]=0 then
first[ch] = i
end if
for j=i+1 to length(words) do
if words[j][1]=ch then
snext[i] = j
exit
end if
end for
end for
return {first,snext}
end function
constant {first,snext} = word_chains()
-- maintain words already taken as a linked list: integer tstart sequence taken = repeat(0,length(words)) -- 0=no, -1=end of chain, +ve=next
-- and keep a copy of the best for later integer bstart sequence best integer maxn = 0 integer count
procedure try(integer ch, integer last, integer n)
integer next = first[ch]
while next!=0 do
if taken[next]=0 then
taken[last] = next
taken[next] = -1
try(words[next][$],next,n+1)
taken[last] = -1
taken[next] = 0
end if
next = snext[next]
end while
if n>maxn then
bstart = tstart
best = taken
maxn = n
count = 1
elsif n=maxn then
count += 1
end if
end procedure
atom t0=time()
for i=1 to length(words) do
tstart = i taken[i] = -1 try(words[i][$],i,1) taken[i] = 0
end for
printf(1,"Runtime: %2.3f seconds. Max length:%d, found %d of such, one of which is:\n",{time()-t0,maxn,count}) while 1 do
printf(1,"%s ",words[bstart]) bstart = best[bstart] if bstart=-1 then exit end if
end while</lang>
- Output:
Runtime: 0.656 seconds. Max length:23, found 1248 of such, one of which is: machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino
My claim for the extra brownie points, using the list from the Racket entry:
Runtime: 0.000 seconds. Max length:2, found 9 of such, one of which is: Porygon-Z Zubat
Which is quite correct: 9 names begin with 'Z', and plenty with 'T' but none with 't' ;-)
Adding a couple of upper(), it found a 302 in a couple of minutes but was still on permutations starting
with word[1] when I got bored and killed it, quickly calculating at the very least another 4.5 days and
quite probably not finishing within my lifetime...
Prolog
Works with SWI-Prolog and module lambda.pl written by Ulrich Neumerkel found there http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl <lang Prolog>:- use_module(library(lambda)).
- - dynamic res/3.
last_first(Len, Nb, L) :- retractall(res(_,_,_)), assert(res(0, 0, [])), % compute all the lists of connected words last_first, res(Len, Nb, L1), % to have only the words maplist(\X^Y^(X = [Y, _, _]), L1, L).
% create the lists of connected words (initiate the first word) last_first :- init(L), forall(select(Word, L, L1), \+lance_p([Word | L1])).
% compute all the lists beginning with a word % memorize the longest lance_p(L) :- p(LF, L), retract(res(Len, Nb, Lst)), length(LF, Len1), ( Len1 > Len -> assert(res(Len1, 1, LF)) ; Len1 = Len -> Nb1 is Nb + 1, assert(res(Len, Nb1, Lst)) ; assert(res(Len, Nb, Lst))), fail.
% describe the property of the list of connected words p([A | T], [A | L]) :- select(B, L, L1), p0(A,B), T = [B | T1], p([B | T1], [B | L1]).
% a list with one element is valid p([_], _).
% are words conected ?
p0([_, _, W], [_, W, _]).
% each word is associated with its first and last letters % audino --> [audino, a, o] init(L) :-
L0 = [ audino, bagon, baltoy, banette, bidoof, braviary, bronzor, carracosta, charmeleon, cresselia, croagunk, darmanitan, deino, emboar, emolga, exeggcute, gabite, girafarig, gulpin, haxorus, heatmor, heatran, ivysaur, jellicent, jumpluff, kangaskhan, kricketune, landorus, ledyba, loudred, lumineon, lunatone, machamp, magnezone, mamoswine, nosepass, petilil, pidgeotto, pikachu, pinsir, poliwrath, poochyena, porygon2, porygonz, registeel, relicanth, remoraid, rufflet, sableye, scolipede, scrafty, seaking, sealeo, silcoon, simisear, snivy, snorlax, spoink, starly, tirtouga, trapinch, treecko, tyrogue, vigoroth, vulpix, wailord, wartortle, whismur, wingull, yamask], maplist(init_, L0, L).
% audino --> [audino, a, o] init_(W, [W, F, L]) :- first_letter(W, F), last_letter(W, L).
first_letter(A, F) :-
atom_chars(A, [F | _]).
last_letter(A, L) :- atom_chars(A, LC), reverse(LC, [L | _]). </lang> Output :
?- time(last_first(Len, Nb, L)). % 592,161,339 inferences, 125.690 CPU in 128.264 seconds (98% CPU, 4711284 Lips) Len = 23, Nb = 1248, L = [machamp,petilil,landorus,scrafty,yamask,kricketune,emboar,registeel,loudred,darmanitan,nosepass,simisear,relicanth,heatmor,rufflet,trapinch,haxorus,seaking,girafarig,gabite,exeggcute,emolga,audino].
Python
<lang python>from collections import defaultdict
def order_words(words):
byfirst = defaultdict(set)
for word in words:
byfirst[word[0]].add( word )
#byfirst = dict(byfirst)
return byfirst
def linkfirst(byfirst, sofar):
\ For all words matching last char of last word in sofar as FIRST char and not in sofar, return longest chain as sofar + chain
assert sofar
chmatch = sofar[-1][-1]
options = byfirst[chmatch] - set(sofar)
#print(' linkfirst options: %r %r' % (chmatch, options))
if not options:
return sofar
else:
alternatives = ( linkfirst(byfirst, list(sofar) + [word])
for word in options )
mx = max( alternatives, key=len )
#input('linkfirst: %r' % mx)
return mx
def llfl(words):
byfirst = order_words(words) return max( (linkfirst(byfirst, [word]) for word in words), key=len )
if __name__ == '__main__':
pokemon = audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon
cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask
pokemon = pokemon.strip().lower().split()
pokemon = sorted(set(pokemon))
l = llfl(pokemon)
for i in range(0, len(l), 8): print(' '.join(l[i:i+8]))
print(len(l))</lang>
- Sample output
audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent 23
Alternative version
Adapted from the D version. This uses Psyco. <lang python>import psyco
nsolutions = 0
def search(sequences, ord_minc, curr_word, current_path,
current_path_len, longest_path): global nsolutions
current_path[current_path_len] = curr_word current_path_len += 1
if current_path_len == len(longest_path):
nsolutions += 1
elif current_path_len > len(longest_path):
nsolutions = 1
longest_path[:] = current_path[:current_path_len]
# recursive search
last_char_index = ord(curr_word[-1]) - ord_minc
if last_char_index >= 0 and last_char_index < len(sequences):
for pair in sequences[last_char_index]:
if not pair[1]:
pair[1] = True
search(sequences, ord_minc, pair[0], current_path,
current_path_len, longest_path)
pair[1] = False
def find_longest_chain(words):
ord_minc = ord(min(word[0] for word in words))
ord_maxc = ord(max(word[0] for word in words))
sequences = [[] for _ in xrange(ord_maxc - ord_minc + 1)]
for word in words:
sequences[ord(word[0]) - ord_minc].append([word, False])
current_path = [None] * len(words) longest_path = []
# try each item as possible start
for seq in sequences:
for pair in seq:
pair[1] = True
search(sequences, ord_minc, pair[0],
current_path, 0, longest_path)
pair[1] = False
return longest_path
def main():
global nsolutions
pokemon = """audino bagon baltoy banette bidoof braviary
bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask""".lower().split()
# remove duplicates pokemon = sorted(set(pokemon))
sol = find_longest_chain(pokemon)
print "Maximum path length:", len(sol)
print "Paths of that length:", nsolutions
print "Example path of that length:"
for i in xrange(0, len(sol), 7):
print " ", " ".join(sol[i : i+7])
psyco.full() main()</lang> Output:
Maximum path length: 23 Paths of that length: 1248 Example path of that length: machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino
Run time: about 0.44 seconds with Psyco and Python 2.6.6.
Racket
This is a naive solution, which works fast enough as is (takes about 5 seconds on an old machine): <lang racket>#lang racket
(define names "
audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask")
(struct word (first last string) #:prefab) (define words
(for/list ([str (string-split names)])
(word (string->symbol (substring str 0 1))
(string->symbol (substring str (sub1 (string-length str))))
str)))
(define (find-longest last words)
(for/fold ([best '()])
([w (in-list words)]
#:when (or (not last) (eq? last (word-first w))))
(define long (cons w (find-longest (word-last w) (remq w words))))
(if (> (length long) (length best)) long best)))
(define longest (find-longest #f words)) (printf "Longest chain found has ~a words:\n ~a\n"
(length longest) (string-join (map word-string longest) " -> "))
</lang>
- Output:
Longest chain found has 23 words: machamp -> petilil -> landorus -> scrafty -> yamask -> kricketune -> emboar -> registeel -> loudred -> darmanitan -> nosepass -> simisear -> relicanth -> heatmor -> rufflet -> trapinch -> haxorus -> seaking -> girafarig -> gabite -> exeggcute -> emolga -> audino
This is a (probably over-)complex version which tries to construct longest chains using three different combination/relinking functions. Not that the definiton of `word` is slightly different here. <lang racket>#lang racket (require "pokemon-names.rkt")
- Some fundamentals... finding the first (henceforth referred to as "a") and last ("z")
- letters of a word can be computationally intensive... look at symbol->word, and you'll
- see that when we have to deal with a name like
- "Mime Jr.", the last alphabetic letter
- is not the last character. And the first and last characters (at least) have to be
- case-normalised so they can be compared with char=? (it's not particulary helpful to
- map them down to integer character codes; we'll want to see them for debugging).
(define-struct word (sym char-a char-z) #:prefab)
- names are input as symbols both for ease of comparsion, and because it's easier to type
(define (symbol->word sym)
(let* ((str (symbol->string sym))
(chrs (string->list str))
(fst (for/first ((c chrs) #:when (char-alphabetic? c)) (char-downcase c)))
(lst (for/last ((c chrs) #:when (char-alphabetic? c)) (char-downcase c))))
(make-word sym fst lst)))
- We're sometimes not interested in debugging a chain of; just in knowing how long it is
- and what its extreme characters are. This does the trick.
(define (summarise-chain c)
(format "(~a.~a.~a)" (word-char-a (first c)) (sub1 (length c)) (word-char-z (last c))))
- Test the above (run `raco test last_letter-first_letter-common.rkt`)
(define-syntax-rule (hash-set-or-remove hsh key val remove-pred?)
(let ((v val))
(if (remove-pred? v)
(hash-remove hsh key)
(hash-set hsh key v))))
(define-syntax-rule (find-a-in-chain-pool chains a dont-match-sym)
(for/first ((c chains)
(i (in-naturals)) ;; usually need an index for regenerating chains pool
;; a word can only exist in one chain, so this compares chains' identities
#:unless (eq? (word-sym (first c)) dont-match-sym)
#:when (char=? (word-char-a (first c)) a))
(cons i c)))
(define-syntax-rule (copy-list-ignoring-indices lst i1 i2)
(for/list ((idx (in-naturals))
(e (in-list lst))
#:unless (= idx i1)
#:unless (= idx i2))
e))
- Simple ... find a chain that can be put on the end of c... append it, and
- reiterate
(define (append-ab..bz-chains chain chain-idx chains)
(let* ((a1.chain-a (find-a-in-chain-pool chains (word-char-z (last chain)) (word-sym (first chain)))))
(and a1.chain-a
(let ((a1.chain-idx (first a1.chain-a))
(a1.chain-chain (rest a1.chain-a)))
(cons (append chain a1.chain-chain)
(copy-list-ignoring-indices chains chain-idx a1.chain-idx))))))
- If chain has an a..a loop in it, then we see if we can take that loop, and
- place it in a longer chain at a point where a is used.
- `chain` is the shorter chain containing the loop
(define (merge-chain-into-chain-accepting-a..a-in-chain chain chain-idx chains)
;; for a..a loops in chain, returns a hash from the looped char, to the longest
;; found loop
(define (find-a..a-loops chain)
(let ((chain-length (length chain)))
(for*/fold
((hsh (hash)))
((sub-range-start (in-range chain-length))
(aa (in-value (word-char-a (list-ref chain sub-range-start))))
(sub-range-end (in-range sub-range-start chain-length))
#:when (eq? aa (word-char-z (list-ref chain sub-range-end)))
(range-length (in-value (add1 (- sub-range-end sub-range-start)))))
(hash-update
hsh aa
(lambda (longest-range)
(if (and longest-range (> (third longest-range) range-length))
longest-range
(list sub-range-start sub-range-end range-length)))
#f))))
(let* ((chain-first-name (word-sym (first chain)))
(chain-length (length chain))
(a..a-list (sort (hash->list (find-a..a-loops chain)) > #:key third)))
(for*/first (((chain2 chain2-idx) (in-parallel (in-list chains) (in-naturals)))
#:unless (eq? chain-first-name (word-sym (car chain2)))
(chain2-length (in-value (length chain2)))
#:when (>= chain2-length chain-length) ; only move the largest a..a-subchain into a larger chain
(a..a (in-list a..a-list))
((insertion-point-word insertion-point-idx) (in-parallel (in-list chain2) (in-naturals)))
#:when (eq? (car a..a) (word-char-a insertion-point-word)))
(let* ((new-chain (append (take chain (second a..a)) (drop chain (add1 (third a..a)))))
(a..a-chain (take (drop chain (second a..a)) (fourth a..a)))
(new-chain2 (append (take chain2 insertion-point-idx) a..a-chain (drop chain2 insertion-point-idx))))
(let ((new-chains (copy-list-ignoring-indices chains chain-idx chain2-idx)))
(if (null? new-chain) (cons new-chain2 new-chains)
(cons new-chain (cons new-chain2 new-chains))))))))
- this is a bit more combinatorially intensive... for all c2, substitute a
- subrange in c2 that is longer than an equivalent subrange in c
(define (merge-subranges-of-chains-into-chain chain chain-idx chains)
(let ((chain-first-name (word-sym (first chain)))
(chain-length (length chain))
(chain-first-a (word-char-a (first chain)))
(chain-last-z (word-char-z (last chain))))
(for*/first ; try to replace a subrange in c2 with c
(((chain2 chain2-idx) (in-parallel (in-list chains) (in-naturals)))
(chain2-length (in-value (length chain2)))
#:unless (eq? chain-first-name (word-sym (car chain2)))
(c2-sub-range-start (in-range chain2-length))
(c2-sub-range-end (in-range c2-sub-range-start
(min chain2-length (+ c2-sub-range-start chain-length))))
#:unless (and (= c2-sub-range-start 0) (= c2-sub-range-end (sub1 chain2-length)))
#:when (or (zero? c2-sub-range-start)
(eq? (word-char-a (list-ref chain2 c2-sub-range-start))
chain-first-a))
#:when (or (= (sub1 chain2-length) c2-sub-range-end)
(eq? (word-char-z (list-ref chain2 c2-sub-range-end))
chain-last-z))
(c2-sub-range-len (in-value (add1 (- c2-sub-range-end c2-sub-range-start))))
#:when (> chain-length c2-sub-range-len)
(c2-sub-range (in-value (take (drop chain2 c2-sub-range-start) c2-sub-range-len)))
(new-c2 (in-value (append (take chain2 c2-sub-range-start)
chain
(drop chain2 (add1 c2-sub-range-end))))))
(cons c2-sub-range ; put the subrange back into the chains pool
(cons new-c2 ; put the modified onto the chains pool
(copy-list-ignoring-indices chains chain-idx chain2-idx))))))
(define (longest-chain/constructive names #:known-max (known-max +inf.0))
(define names-list (map symbol->word names))
(define (link-chains chains)
(let
((new-chains
(for*/first
(((chain chain-idx) (in-parallel (in-list chains) (in-naturals)))
(new-chains
(in-value
(or
(append-ab..bz-chains chain chain-idx chains)
(merge-chain-into-chain-accepting-a..a-in-chain chain chain-idx chains)
(merge-subranges-of-chains-into-chain chain chain-idx chains))))
#:when new-chains)
new-chains)))
(if new-chains (link-chains new-chains) chains)))
(define (keep-trying
(run-count 0)
(linked-chains (link-chains (map list (shuffle names-list))))
(previous-best null)
(previous-best-length 0)
(this-run-best-length #f))
(let* ((longest-chain (argmax length linked-chains))
(longest-chain-len (length longest-chain))
(new-best? (< previous-best-length longest-chain-len))
(best-length (if new-best? longest-chain-len previous-best-length))
(best (if new-best? longest-chain previous-best)))
(when new-best? (newline)
(displayln (list (map word-sym longest-chain) longest-chain-len))
(flush-output))
(if (and new-best? (>= best-length known-max))
(displayln "terminating: known max reached or exceeded")
(begin
(when (zero? (modulo (add1 run-count) 250)) (eprintf ".") (flush-output (current-error-port)))
(if (= run-count 1000)
(keep-trying 0 (link-chains (map list (shuffle names-list))) best best-length 0)
(let ((sorted-linked-chains (sort linked-chains #:key length >)))
(keep-trying (if new-best? 0 (add1 run-count))
(link-chains
(cons (car sorted-linked-chains)
(map list (shuffle (apply append (cdr sorted-linked-chains))))))
best best-length
(and this-run-best-length
(if new-best? #f
(if (< this-run-best-length longest-chain-len)
(begin (eprintf ">~a" longest-chain-len)
(flush-output (current-error-port))
longest-chain-len)
this-run-best-length))))))))))
(keep-trying))
(time (longest-chain/constructive names-70 #:known-max 23)) (longest-chain/constructive names-646)</lang>
Run with racket -t last_letter-first_letter-randomised.rkt 2>&1, to redirect standard error to standard out.
- Output:
((machamp petilil landorus seaking girafarig gabite exeggcute emboar relicanth heatran nosepass simisear registeel loudred deino) 15) ((machamp petilil landorus seaking girafarig gabite exeggcute emboar relicanth haxorus snivy yamask kangaskhan nosepass simisear registeel lunatone emolga audino) 19) ((machamp petilil landorus seaking girafarig gabite exeggcute emboar rufflet trapinch heatmor relicanth haxorus snivy yamask kangaskhan nosepass simisear registeel lunatone emolga audino) 22) ....>10>17>19....>14>17>20>21....>15>18>21>22....>16>17>22....>15>17>18>21....>19>20....>16>18>20>22....>14>21 ((machamp petilil landorus seaking girafarig gabite emboar rufflet trapinch heatmor relicanth haxorus simisear registeel loudred darmanitan nosepass starly yamask kricketune exeggcute emolga audino) 23) terminating: known max reached or exceeded cpu time: 24077 real time: 24070 gc time: 36
As an aside... I've had this take 40 s; and I've had it run in 35 ms. It really is the luck of the draw!
((Jellicent Tangrowth Hippopotas Slowking Gyarados Spiritomb Breloom Mandibuzz Zweilous Shellos Stoutland Deoxys Swoobat Togekiss Seedot Toxicroak Krokorok Kabutops Seadra Anorith Heracross Slakoth Haxorus Shelmet Tauros Skiploom Manectric Castform Milotic Chingling Golem Mothim Meganium Metapod Ducklett Tornadus Swellow Whismur Rufflet Taillow Wormadam Medicham Mismagius Snubbull Latias Solosis Sandshrew Woobat Teddiursa Abomasnow Wingull Lapras Seel Lillipup Paras Sandslash Hoppip Prinplup Piplup Petilil Lickilicky Yanmega Abra Ariados Solrock Klink Kingler Relicanth Hariyama Altaria Azumarill Luvdisc Charmander Rotom Maractus Skuntank Kirlia Azelf Farfetch'd Delibird Dratini Illumise Exploud Diglett Torkoal Lampent Turtwig Girafarig Golbat Tepig Grumpig Granbull Larvesta Azurill Loudred Dialga Amoonguss Sigilyph Herdier Rampardos Seaking Golett Timburr Raichu Umbreon Noctowl Latios Sawk Kyurem Miltank Klinklang Gorebyss Slaking Gliscor Rhyhorn Nidorina Alakazam Machamp Pidgeot Trubbish Hitmontop Politoed Dewgong Gardevoir Regigigas Swampert Tympole Electrode Exeggcute Eelektrik Kingdra Accelgor Remoraid Dewott Tentacool Litwick Koffing Gigalith Hypno Octillery Yanma Arcanine Elekid Dusknoir Reshiram Mesprit Tropius Swalot Tranquill Luxray Yamask Kyogre Eevee Electivire Emolga Alomomola Ampharos Spinarak Kricketune Exeggutor Roselia Arbok Krookodile Escavalier Rayquaza Aron Ninetales Serperior Registeel Lileep Patrat Throh Hitmonlee Espeon Nidoqueen Ninjask Kakuna Axew Wigglytuff Frillish Houndour Regice Eelektross Swinub Budew Whiscash Hoothoot Torterra Aipom Mareep Poliwag Grimer Roggenrola Armaldo Omastar Rhyperior Ralts Scolipede Excadrill Luxio Oshawott Togetic Crawdaunt Torchic Cofagrigus Shroomish Houndoom Marill Larvitar Raticate Electrike Ekans Starmie Emboar Regirock Karrablast Tangela Aerodactyl Lairon Nidoran Natu Unfezant Trapinch Horsea Archen Nidoran Nosepass Staravia Ambipom Murkrow Weezing Gothita Absol Lotad Darmanitan Nincada Arceus Spheal Lilligant Tynamo Omanyte Elgyem Mew Watchog Golduck Kabuto Oddish Ho-Oh Heatran Nidoking Golurk Klang Garchomp Porygon-Z Zekrom Meowth Hippowdon Nuzleaf Feraligatr Rapidash Haunter Reuniclus Seviper Raikou Ursaring Glalie Entei Igglybuff Froslass Spearow Wailord Duskull Ludicolo Onix Xatu Unown Numel Landorus Seismitoad Deerling Grovyle Empoleon Nidorino) 283)
...
((Voltorb Beartic Croconaw Wynaut Tangrowth Hippopotas Smoochum Moltres Shuppet Thundurus Slowking Gyarados Spiritomb Breloom Mandibuzz Zweilous Shellos Stoutland Deoxys Swoobat Togekiss Seedot Toxicroak Krokorok Kabutops Snorunt Tirtouga Anorith Heracross Slakoth Haxorus Shelmet Tauros Skiploom Manectric Castform Milotic Chingling Golem Mothim Meganium Metapod Ducklett Tornadus Swellow Whismur Rufflet Taillow Wormadam Medicham Mismagius Snubbull Latias Solosis Sandshrew Woobat Teddiursa Abomasnow Wingull Lapras Seel Lillipup Paras Sandslash Hoppip Prinplup Piplup Probopass Stunfisk Krabby Yanmega Abra Ariados Solrock Klink Kingler Relicanth Hariyama Altaria Azumarill Luvdisc Chatot Tyranitar Rotom Maractus Skuntank Kirlia Azelf Farfetch'd Delibird Dratini Ivysaur Riolu Uxie Electabuzz Zapdos Sawsbuck Kyogre Exploud Diglett Torkoal Lampent Turtwig Girafarig Golbat Tepig Grumpig Granbull Larvesta Azurill Loudred Dialga Amoonguss Sigilyph Herdier Rampardos Seaking Golett Timburr Raichu Umbreon Noctowl Latios Sawk Kyurem Miltank Klinklang Gorebyss Slaking Gigalith Huntail Ledyba Aggron Nidorina Alakazam Machamp Pidgeot Trubbish Hitmontop Politoed Dewgong Gardevoir Regigigas Swampert Tentacruel Lickitung Glameow Whirlipede Electrode Exeggcute Eelektrik Kingdra Accelgor Remoraid Dewott Tentacool Litwick Koffing Gloom Marshtomp Psyduck Kadabra Articuno Octillery Yanma Arcanine Elekid Dusknoir Reshiram Mesprit Tropius Swalot Tranquill Luxray Yamask Kricketot Tyrogue Eevee Electivire Emolga Alomomola Ampharos Sentret Togepi Infernape Exeggutor Roselia Arbok Krookodile Escavalier Rayquaza Aron Ninetales Serperior Registeel Lileep Patrat Throh Honchkrow Wobbuffet Totodile Espeon Nidoqueen Ninjask Kakuna Axew Wigglytuff Frillish Houndour Regice Eelektross Swinub Budew Whiscash Hoothoot Torterra Aipom Mareep Poliwag Grimer Roggenrola Armaldo Omastar Rhyperior Ralts Surskit Tympole Excadrill Lugia Audino Oshawott Togetic Crawdaunt Torchic Cofagrigus Shroomish Houndoom Mudkip Ponyta Archeops Spinarak Kricketune Electrike Ekans Simisear Raticate Emboar Regirock Karrablast Tangela Aerodactyl Liepard Dusclops Spoink Kecleon Nidoran Natu Unfezant Trapinch Horsea Archen Nidoran Nosepass Snover Rattata Ambipom Murkrow Weezing Gothita Absol Lotad Durant Terrakion Nincada Arceus Spheal Lilligant Tynamo Omanyte Elgyem Mew Watchog Golduck Kabuto Oddish Ho-Oh Heatran Nidoking Golurk Klang Garchomp Porygon-Z Zekrom Magikarp Pawniard Deerling Gurdurr Rhydon Nuzleaf Foongus Shellder Rapidash Haunter Reuniclus Seviper Raikou Ursaring Garbodor Roserade Entei Igglybuff Froslass Spearow Wailord Duskull Ludicolo Onix Xatu Unown Numel Landorus Seismitoad Drifblim Machop Palpitoad Darkrai Illumise Empoleon Nidorino) 329)
Never terminates. The longest chain I have found (so far?) is 333 long:
((Voltorb Breloom Medicham Machop Piplup Palpitoad Deerling Golett Turtwig Glameow Wingull Lilligant Timburr Registeel Lotad Duskull Latias Serperior Reuniclus Spinarak Krokorok Klinklang Golem Mew Whiscash Huntail Lugia Accelgor Rattata Aerodactyl Luvdisc Chingling Grumpig Garchomp Prinplup Petilil Loudred Ducklett Tornadus Spearow Whimsicott Tangrowth Hoothoot Tentacruel Lampent Togekiss Skiploom Marshtomp Patrat Thundurus Solosis Sneasel Lillipup Poliwhirl Lapras Sandslash Honchkrow Wobbuffet Torkoal Latios Slaking Gligar Rampardos Shellos Sentret Tropius Sigilyph Herdier Remoraid Dusclops Stoutland Drilbur Reshiram Misdreavus Slowking Golduck Klink Koffing Gyarados Shuppet Tauros Swellow Wynaut Torchic Castform Maractus Spiritomb Bayleef Furret Tangela Altaria Aipom Murkrow Wigglytuff Forretress Spheal Lickitung Gigalith Heracross Snorunt Totodile Exeggcute Electrode Ekans Solrock Klang Girafarig Gorebyss Swalot Trapinch Ho-Oh Hitmontop Porygon-Z Zapdos Shroomish Houndour Relicanth Hoppip Poliwrath Houndoom Mareep Poliwag Golurk Kirlia Axew Wormadam Mandibuzz Zweilous Swinub Beldum Manectric Cherrim Moltres Staraptor Rayquaza Azurill Lairon Nidoqueen Noctowl Leavanny Yamask Kricketune Eevee Escavalier Rufflet Torterra Archen Ninjask Kakuna Absol Lunatone Excadrill Ludicolo Octillery Yanma Archeops Spoink Kabuto Onix Xatu Unown Nidoran Ninetales Sawsbuck Kyurem Magikarp Politoed Dewott Trubbish Hippopotas Seel Linoone Empoleon Nincada Amoonguss Swoobat Teddiursa Audino Oshawott Tepig Gloom Metagross Shelmet Tentacool Larvesta Ariados Skorupi Illumise Exploud Durant Tynamo Omastar Roggenrola Arbok Kricketot Taillow Weezing Grimer Rhyperior Rapidash Haxorus Skuntank Kingdra Alomomola Azelf Ferroseed Drifblim Marowak Kingler Roselia Azumarill Lanturn Natu Ursaring Golbat Toxicroak Kecleon Numel Landorus Samurott Togepi Infernape Electrike Electivire Electabuzz Zekrom Metang Galvantula Arceus Seedot Tirtouga Aron Nosepass Seismitoad Dialga Articuno Oddish Horsea Alakazam Meganium Marill Liepard Deoxys Smoochum Mudkip Probopass Stunfisk Krookodile Elekid Delibird Dratini Igglybuff Foongus Swampert Tyranitar Raikou Uxie Eelektross Slakoth Hariyama Abra Anorith Haunter Raichu Umbreon Nidorina Aggron Nuzleaf Floatzel Litwick Kyogre Exeggutor Raticate Emboar Regirock Kabutops Sandshrew Watchog Gurdurr Roserade Entei Ivysaur Regice Emolga Abomasnow Wailord Diglett Tyrogue Espeon Nidoran Nidoking Granbull Ledyba Arcanine Elgyem Mothim Mismagius Sawk Kadabra Ampharos Snubbull Larvitar Riolu Unfezant Togetic Charizard Dewgong Gothita Ambipom Machamp Paras Simisear Ralts Seaking Gliscor Rotom Milotic Cyndaquil Lileep Pawniard Dragonair Regigigas Surskit Tranquill Ledian Nidorino Omanyte Eelektrik Karrablast Throh Happiny Yanmega Armaldo) 333)
File: pokemon-names.rkt <lang racket>#lang racket (provide names-646 names-70) (define names-70
'(audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask))
- If this were true, then the 2 would be ignored, which seems a bit wrong; so wordigy the "2" -> "two"
(define Porygon2 (if #f 'Porygon2 'Porygon-two))
- note that Porygon2 is used with a comma in the list below
(define names-646
`(Bulbasaur Ivysaur Venusaur Charmander Charmeleon Charizard Squirtle Wartortle Blastoise Caterpie Metapod Butterfree Weedle Kakuna Beedrill Pidgey Pidgeotto Pidgeot Rattata Raticate Spearow Fearow Ekans Arbok Pikachu Raichu Sandshrew Sandslash Nidoran Nidorina Nidoqueen Nidoran Nidorino Nidoking Clefairy Clefable Vulpix Ninetales Jigglypuff Wigglytuff Zubat Golbat Oddish Gloom Vileplume Paras Parasect Venonat Venomoth Diglett Dugtrio Meowth Persian Psyduck Golduck Mankey Primeape Growlithe Arcanine Poliwag Poliwhirl Poliwrath Abra Kadabra Alakazam Machop Machoke Machamp Bellsprout Weepinbell Victreebel Tentacool Tentacruel Geodude Graveler Golem Ponyta Rapidash Slowpoke Slowbro Magnemite Magneton |Farfetch'd| Doduo Dodrio Seel Dewgong Grimer Muk Shellder Cloyster Gastly Haunter Gengar Onix Drowzee Hypno Krabby Kingler Voltorb Electrode Exeggcute Exeggutor Cubone Marowak Hitmonlee Hitmonchan Lickitung Koffing Weezing Rhyhorn Rhydon Chansey Tangela Kangaskhan Horsea Seadra Goldeen Seaking Staryu Starmie |Mr. Mime| Scyther Jynx Electabuzz Magmar Pinsir Tauros Magikarp Gyarados Lapras Ditto Eevee Vaporeon Jolteon Flareon Porygon Omanyte Omastar Kabuto Kabutops Aerodactyl Snorlax Articuno Zapdos Moltres Dratini Dragonair Dragonite Mewtwo Mew Chikorita Bayleef Meganium Cyndaquil Quilava Typhlosion Totodile Croconaw Feraligatr Sentret Furret Hoothoot Noctowl Ledyba Ledian Spinarak Ariados Crobat Chinchou Lanturn Pichu Cleffa Igglybuff Togepi Togetic Natu Xatu Mareep Flaaffy Ampharos Bellossom Marill Azumarill Sudowoodo Politoed Hoppip Skiploom Jumpluff Aipom Sunkern Sunflora Yanma Wooper Quagsire Espeon Umbreon Murkrow Slowking Misdreavus Unown Wobbuffet Girafarig Pineco Forretress Dunsparce Gligar Steelix Snubbull Granbull Qwilfish Scizor Shuckle Heracross Sneasel Teddiursa Ursaring Slugma Magcargo Swinub Piloswine Corsola Remoraid Octillery Delibird Mantine Skarmory Houndour Houndoom Kingdra Phanpy Donphan ,Porygon2 Stantler Smeargle Tyrogue Hitmontop Smoochum Elekid Magby Miltank Blissey Raikou Entei Suicune Larvitar Pupitar Tyranitar Lugia Ho-Oh Celebi Treecko Grovyle Sceptile Torchic Combusken Blaziken Mudkip Marshtomp Swampert Poochyena Mightyena Zigzagoon Linoone Wurmple Silcoon Beautifly Cascoon Dustox Lotad Lombre Ludicolo Seedot Nuzleaf Shiftry Taillow Swellow Wingull Pelipper Ralts Kirlia Gardevoir Surskit Masquerain Shroomish Breloom Slakoth Vigoroth Slaking Nincada Ninjask Shedinja Whismur Loudred Exploud Makuhita Hariyama Azurill Nosepass Skitty Delcatty Sableye Mawile Aron Lairon Aggron Meditite Medicham Electrike Manectric Plusle Minun Volbeat Illumise Roselia Gulpin Swalot Carvanha Sharpedo Wailmer Wailord Numel Camerupt Torkoal Spoink Grumpig Spinda Trapinch Vibrava Flygon Cacnea Cacturne Swablu Altaria Zangoose Seviper Lunatone Solrock Barboach Whiscash Corphish Crawdaunt Baltoy Claydol Lileep Cradily Anorith Armaldo Feebas Milotic Castform Kecleon Shuppet Banette Duskull Dusclops Tropius Chimecho Absol Wynaut Snorunt Glalie Spheal Sealeo Walrein Clamperl Huntail Gorebyss Relicanth Luvdisc Bagon Shelgon Salamence Beldum Metang Metagross Regirock Regice Registeel Latias Latios Kyogre Groudon Rayquaza Jirachi Deoxys Turtwig Grotle Torterra Chimchar Monferno Infernape Piplup Prinplup Empoleon Starly Staravia Staraptor Bidoof Bibarel Kricketot Kricketune Shinx Luxio Luxray Budew Roserade Cranidos Rampardos Shieldon Bastiodon Burmy Wormadam Mothim Combee Vespiquen Pachirisu Buizel Floatzel Cherubi Cherrim Shellos Gastrodon Ambipom Drifloon Drifblim Buneary Lopunny Mismagius Honchkrow Glameow Purugly Chingling Stunky Skuntank Bronzor Bronzong Bonsly |Mime Jr.| Happiny Chatot Spiritomb Gible Gabite Garchomp Munchlax Riolu Lucario Hippopotas Hippowdon Skorupi Drapion Croagunk Toxicroak Carnivine Finneon Lumineon Mantyke Snover Abomasnow Weavile Magnezone Lickilicky Rhyperior Tangrowth Electivire Magmortar Togekiss Yanmega Leafeon Glaceon Gliscor Mamoswine Porygon-Z Gallade Probopass Dusknoir Froslass Rotom Uxie Mesprit Azelf Dialga Palkia Heatran Regigigas Giratina Cresselia Phione Manaphy Darkrai Shaymin Arceus Victini Snivy Servine Serperior Tepig Pignite Emboar Oshawott Dewott Samurott Patrat Watchog Lillipup Herdier Stoutland Purrloin Liepard Pansage Simisage Pansear Simisear Panpour Simipour Munna Musharna Pidove Tranquill Unfezant Blitzle Zebstrika Roggenrola Boldore Gigalith Woobat Swoobat Drilbur Excadrill Audino Timburr Gurdurr Conkeldurr Tympole Palpitoad Seismitoad Throh Sawk Sewaddle Swadloon Leavanny Venipede Whirlipede Scolipede Cottonee Whimsicott Petilil Lilligant Basculin Sandile Krokorok Krookodile Darumaka Darmanitan Maractus Dwebble Crustle Scraggy Scrafty Sigilyph Yamask Cofagrigus Tirtouga Carracosta Archen Archeops Trubbish Garbodor Zorua Zoroark Minccino Cinccino Gothita Gothorita Gothitelle Solosis Duosion Reuniclus Ducklett Swanna Vanillite Vanillish Vanilluxe Deerling Sawsbuck Emolga Karrablast Escavalier Foongus Amoonguss Frillish Jellicent Alomomola Joltik Galvantula Ferroseed Ferrothorn Klink Klang Klinklang Tynamo Eelektrik Eelektross Elgyem Beheeyem Litwick Lampent Chandelure Axew Fraxure Haxorus Cubchoo Beartic Cryogonal Shelmet Accelgor Stunfisk Mienfoo Mienshao Druddigon Golett Golurk Pawniard Bisharp Bouffalant Rufflet Braviary Vullaby Mandibuzz Heatmor Durant Deino Zweilous Hydreigon Larvesta Volcarona Cobalion Terrakion Virizion Tornadus Thundurus Reshiram Zekrom Landorus Kyurem))</lang>
REXX
brute force version
(This program is modeled after the ooRexx version, with a bug fix.)
This REXX version allows a limit on the word scan (very useful for testing and debugging), and
also has various speed optimizations.
<lang rexx>/*REXX program finds the longest path of word's last─letter ───► first─letter. */
@='audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan',
'deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent', 'jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine', 'nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth', 'remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink', 'starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask'
- = words(@) @.=; ig= 0; !.= 0 /*nullify array and the longest path. */
parse arg limit .; if limit\== then #=limit /*allow user to specify a scan limit. */ call build@ /*build a stemmed array from the @ list*/
do v=# by -1 for # /*scrub the @ list for unusable words. */
parse var @.v F 2 -1 L /*obtain first and last letter of word.*/
if !.1.F>1 | !.9.L>1 then iterate /*is this a dead word?*/
say 'ignoring dead word:' @.v; ig= ig+1; @= delword(@, v, 1)
end /*v*/ /*delete dead word from @ ──┘ */
$$$= /*nullify the possible longest path. */ if ig\==0 then do; call build@; say; say 'ignoring' ig "dead word"s(ig).; say
end
MP= 0; MPL= 0 /*the initial Maximum Path Length. */
do j=1 for # /* ─ ─ ─ */
parse value @.1 @.j with @.j @.1; call scan $$$, 2
parse value @.1 @.j with @.j @.1
end /*j*/
g= words($$$) say 'Of' # "words," MP 'path's(MP) "have the maximum path length of" g'.' say; say 'One example path of that length is: ' word($$$, 1)
do m=2 to g; say left(, 36) word($$$, m); end /*m*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ s: if arg(1)==1 then return arg(3); return word( arg(2) 's', 1) /*a pluralizer.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ build@: do i=1 for #; @.i=word(@, i) /*build a stemmed array from the list. */
F= left(@.i, 1); !.1.F= !.1.F + 1 /*F: 1st char; !.1.F=count of 1st char*/
L=right(@.i, 1); !.9.L= !.9.L + 1 /*L: last " !.9.L= " " last " */
end /*i*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/ scan: procedure expose @. # !. $$$ MP MPL; parse arg $$$,!; p=! - 1
parse var @.p -1 LC /*obtain last character of previous @. */
if !.1.LC==0 then return /*is this a dead─end word? */
/* [↓] PARSE obtains first char of @.i*/
do i=! to #; parse var @.i p 2 /*scan for the longest word path. */
if p==LC then do /*is the first─character ≡ last─char? */
if !==MPL then MP= MP+1 /*bump the Maximum Paths Counter. */
else if !>MPL then do; $$$=@.1 /*rebuild. */
do n=2 for !-2; $$$=$$$ @.n
end /*n*/
$$$=$$$ @.i /*add last.*/
MP=1; MPL=! /*new path.*/
end
parse value @.! @.i with @.i @.!; call scan $$$, !+1
parse value @.! @.i with @.i @.!
end
end /*i*/; return /*exhausted this particular scan. */</lang>
- output when using the default input:
Of 70 words, 1248 paths have the maximum path length of 23.
One example path of that length is: machamp
petilil
landorus
scrafty
yamask
kricketune
emboar
registeel
loudred
darmanitan
nosepass
simisear
relicanth
heatmor
rufflet
trapinch
haxorus
seaking
girafarig
gabite
exeggcute
emolga
audino
optimized version
This optimized version has two major improvements:
- removes dead words (words that cannot be used in a path)
- stops scanning when a dead-end word is encountered.
With the full list of words being used, there are no dead words (but there are when a limit is used to shorten the list).
In the scan subroutine, a check is made to see if the word being used is a dead-end word, and if so, the rest of
the recursive scan is aborted and the the next word is scanned.
The optimized version is around 25% faster than the brute-force version.
<lang rexx>/*REXX program finds the longest path of word's last─letter ───► first─letter. */
@='audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan',
'deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent', 'jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine', 'nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth', 'remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink', 'starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask'
- = words(@); @.=; @s=; ig=0; og=0; !.=0 /*nullify array and the longest path. */
parse arg limit .; if limit\== then #=limit /*allow user to specify a scan limit. */ call build@ /*build a stemmed array from the @ list*/
do v=# by -1 for # /*scrub the @ list for unusable words. */
parse var @.v F 2 -1 L /*obtain first and last letter of word.*/
if !.1.F>1 | !.9.L>1 then iterate /*is this a dead word?*/
say 'ignoring dead word:' @.v; ig=ig+1; @=delword(@, v, 1)
end /*v*/ /*delete dead word from @ ──┘ */
- = words(@) /*recalculate the number of words in @.*/
do v=# by -1 for # /*scrub the @ list for stoppable words.*/
parse var @.v F 2 -1 L /*obtain first and last letter of word.*/
if !.1.L>0 then iterate /*is this a stop word? */
say 'removing stop word:' @.v; og=og+1; @=delword(@, v, 1); @s=@s @.v
end /*v*/ /*delete dead word from @ ──┘ */
if og\==0 then do; call build@; say; say 'ignoring' og "stop word"s(og).
say 'stop words: ' @s; say
end
$$$= /*nullify the possible longest path. */ MP= 0; MPL= 0 /*the initial Maximum Path Length. */
do j=1 for # /* ─ ─ ─ */
parse value @.1 @.j with @.j @.1; call scan $$$, 2
parse value @.1 @.j with @.j @.1
end /*j*/
g= words($$$) say 'Of' # "words," MP 'path's(MP) "have the maximum path length of" g'.' say; say 'One example path of that length is: ' word($$$, 1)
do m=2 to g; say left(, 36) word($$$, m); end /*m*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ s: if arg(1)==1 then return arg(3); return word( arg(2) 's', 1) /*a pluralizer.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ build@: do i=1 for #; @.i= word(@, i) /*build a stemmed array from the list. */
F= left(@.i, 1); !.1.F= !.1.F + 1 /*F: 1st char; !.1.F=count of 1st char*/
L=right(@.i, 1); !.9.L= !.9.L + 1 /*L: last " !.9.L= " " last " */
end /*i*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/ scan: procedure expose @. # !. $$$ MP MPL; parse arg $$$,!; p= ! - 1
parse var @.p -1 LC /*obtain last character of previous @. */
if !.1.LC==0 then return /*is this a dead─end word? */
/* [↓] PARSE obtains first char of @.i*/
do i=! to #; parse var @.i p 2 /*scan for the longest word path. */
if p==LC then do /*is the first─character ≡ last─char? */
if !==MPL then MP= MP+1 /*bump the Maximum Paths Counter. */
else if !>MPL then do; $$$= @.1 /*rebuild. */
do n=2 for !-2; $$$=$$$ @.n
end /*n*/
$$$= $$$ @.i /*add last.*/
MP=1; MPL=! /*new path.*/
end
parse value @.! @.i with @.i @.!; call scan $$$, !+1
parse value @.! @.i with @.i @.!
end
end /*i*/; return /*exhausted this particular scan. */</lang>
- output is the same as the brute force version.
Ring
<lang ring>
- Project : Last letter-first letter
ready = [] names = ["audino", "bagon", "baltoy", "banette",
"bidoof", "braviary", "bronzor", "carracosta", "charmeleon",
"cresselia", "croagunk", "darmanitan", "deino", "emboar",
"emolga", "exeggcute", "gabite", "girafarig", "gulpin",
"haxorus", "heatmor", "heatran", "ivysaur", "jellicent",
"jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba",
"loudred", "lumineon", "lunatone", "machamp", "magnezone",
"mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu",
"pinsir", "poliwrath", "poochyena", "porygon2", "porygonz",
"registeel", "relicanth", "remoraid", "rufflet", "sableye",
"scolipede", "scrafty", "seaking", "sealeo", "silcoon",
"simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga",
"trapinch", "treecko", "tyrogue", "vigoroth", "vulpix",
"wailord", "wartortle", "whismur", "wingull", "yamask"]
strbegin = "gabite" strdir = "first" nr = 1 add(ready,strbegin) see strbegin + nl while true
if strdir = "first"
strc = right(strbegin, 1)
flag = 1
nr = nr + 1
if nr <= len(names)
if left(names[nr],1) = strc
for n = 1 to len(ready)
if names[nr] = ready[n]
flag = 0
ok
next
if flag = 1
add(ready,names[nr])
see names[nr] + nl
strbegin = names[nr]
nr = 0
strdir = "last"
loop
ok
ok
ok
else
strc = right(strbegin, 1)
flag = 1
nr = nr + 1
if nr <= len(names)
if left(names[nr],1) = strc
for n = 1 to len(ready)
if names[nr] = ready[n]
flag = 0
ok
next
if flag = 1
add(ready,names[nr])
see names[nr] + nl
strbegin = names[nr]
nr = 0
strdir = "first"
loop
ok
ok
ok
ok
end </lang> Output:
gabite emboar registeel landorus sableye emolga audino
Ruby
<lang ruby>class LastL_FirstL
def initialize(names)
@names = names.dup
@first = names.group_by {|name| name[0]}
@sequences = []
end
def add_name(seq)
last_letter = seq[-1][-1]
potentials = @first.include?(last_letter) ? (@first[last_letter] - seq) : []
if potentials.empty?
@sequences << seq
else
potentials.each {|name| add_name(seq + [name])}
end
end
def search
@names.each {|name| add_name [name]}
max = @sequences.max_by {|seq| seq.length}.length
max_seqs = @sequences.select {|seq| seq.length == max}
puts "there are #{@sequences.length} possible sequences"
puts "the longest is #{max} names long"
puts "there are #{max_seqs.length} such sequences. one is:"
max_seqs.last.each_with_index {|name, idx| puts " %2d %s" % [idx+1, name]}
end
end
names = %w{
audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask
}
lf = LastL_FirstL.new(names) lf.search</lang> outputs
there are 2076396 possible sequences the longest is 23 names long there are 1248 such sequences. one is: 1 machamp 2 pinsir 3 rufflet 4 trapinch 5 heatmor 6 remoraid 7 darmanitan 8 nosepass 9 starly 10 yamask 11 kricketune 12 exeggcute 13 emboar 14 relicanth 15 haxorus 16 simisear 17 registeel 18 landorus 19 seaking 20 girafarig 21 gabite 22 emolga 23 audino
Scala
Naive
<lang Scala>object LastLetterFirstLetterNaive extends App {
def solve(names: Set[String]) = {
def extend(solutions: List[List[String]]): List[List[String]] = {
val more = solutions.flatMap{solution =>
val lastLetter = solution.head takeRight 1
(names -- solution).filter(_.take(1) equalsIgnoreCase lastLetter).map(_ :: solution)
}
if (more.isEmpty) solutions else extend(more)
}
extend(names.toList.map(List(_))).map(_.reverse) }
val names70 = Set("audino", "bagon", "baltoy", "banette", "bidoof", "braviary", "bronzor", "carracosta", "charmeleon", "cresselia", "croagunk", "darmanitan", "deino", "emboar", "emolga", "exeggcute", "gabite", "girafarig", "gulpin", "haxorus", "heatmor", "heatran", "ivysaur", "jellicent", "jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba", "loudred", "lumineon", "lunatone", "machamp", "magnezone", "mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu", "pinsir", "poliwrath", "poochyena", "porygon2", "porygonz", "registeel", "relicanth", "remoraid", "rufflet", "sableye", "scolipede", "scrafty", "seaking", "sealeo", "silcoon", "simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga", "trapinch", "treecko", "tyrogue", "vigoroth", "vulpix", "wailord", "wartortle", "whismur", "wingull", "yamask")
val solutions = solve(names70)
println(s"Maximum path length: ${solutions.head.length}")
println(s"Paths of that length: ${solutions.size}")
println("Example path of that length:")
println(solutions.head.sliding(7,7).map(_.mkString(" ")).map(" "+_).mkString("\n"))
}</lang> Output:
Maximum path length: 23 Paths of that length: 1248 Example path of that length: machamp petilil loudred darmanitan nosepass snivy yamask kricketune emboar rufflet trapinch heatmor relicanth haxorus simisear registeel landorus seaking girafarig gabite exeggcute emolga audino
With Lookup Table (Faster)
<lang Scala>object LastLetterFirstLetterLookup extends App {
def solve(names: Set[String]) = {
val transitions = {
val startsWith = names.groupBy(_.take(1).toLowerCase).withDefaultValue(Set.empty)
names.map{name => name -> startsWith(name.takeRight(1).toLowerCase)}.toMap
}
def extend(solutions: List[List[String]]): List[List[String]] =
solutions.flatMap{solution =>
(transitions(solution.head) -- solution).map(_ :: solution)
} match {
case Nil => solutions
case more => extend(more)
}
extend(names.toList.map(List(_))).map(_.reverse) }
val names70 = Set("audino", "bagon", "baltoy", "banette", "bidoof", "braviary", "bronzor", "carracosta", "charmeleon", "cresselia", "croagunk", "darmanitan", "deino", "emboar", "emolga", "exeggcute", "gabite", "girafarig", "gulpin", "haxorus", "heatmor", "heatran", "ivysaur", "jellicent", "jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba", "loudred", "lumineon", "lunatone", "machamp", "magnezone", "mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu", "pinsir", "poliwrath", "poochyena", "porygon2", "porygonz", "registeel", "relicanth", "remoraid", "rufflet", "sableye", "scolipede", "scrafty", "seaking", "sealeo", "silcoon", "simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga", "trapinch", "treecko", "tyrogue", "vigoroth", "vulpix", "wailord", "wartortle", "whismur", "wingull", "yamask")
val solutions = solve(names70)
println(s"Maximum path length: ${solutions.head.length}")
println(s"Paths of that length: ${solutions.size}")
println("Example path of that length:")
println(solutions.head.sliding(7,7).map(_.mkString(" ")).map(" "+_).mkString("\n"))
}</lang>
Parallelised With Lookup Table (Faster)
<lang Scala>object LastLetterFirstLetterLookupParallel extends App {
def solve(names: Set[String]) = {
val transitions = {
val startsWith = names.groupBy(_.take(1).toLowerCase).withDefaultValue(Set.empty)
names.map{name => name -> startsWith(name.takeRight(1).toLowerCase)}.toMap
}
import scala.collection.parallel.immutable.ParSeq
def extend(solutions: ParSeq[List[String]]): ParSeq[List[String]] =
solutions.flatMap{solution =>
(transitions(solution.head) -- solution).map(_ :: solution)
} match {
case seq if seq.isEmpty => solutions
case more => extend(more)
}
extend(names.toList.map(List(_)).par).map(_.reverse) }
val names70 = Set("audino", "bagon", "baltoy", "banette", "bidoof", "braviary", "bronzor", "carracosta", "charmeleon", "cresselia", "croagunk", "darmanitan", "deino", "emboar", "emolga", "exeggcute", "gabite", "girafarig", "gulpin", "haxorus", "heatmor", "heatran", "ivysaur", "jellicent", "jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba", "loudred", "lumineon", "lunatone", "machamp", "magnezone", "mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu", "pinsir", "poliwrath", "poochyena", "porygon2", "porygonz", "registeel", "relicanth", "remoraid", "rufflet", "sableye", "scolipede", "scrafty", "seaking", "sealeo", "silcoon", "simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga", "trapinch", "treecko", "tyrogue", "vigoroth", "vulpix", "wailord", "wartortle", "whismur", "wingull", "yamask")
val solutions = solve(names70)
println(s"Maximum path length: ${solutions.head.length}")
println(s"Paths of that length: ${solutions.size}")
println("Example path of that length:")
println(solutions.head.sliding(7,7).map(_.mkString(" ")).map(" "+_).mkString("\n"))
}</lang>
Seed7
<lang seed7>$ include "seed7_05.s7i";
var integer: maxPathLength is 0; var integer: maxPathLengthCount is 0; var string: maxPathExample is "";
var array string: names is [] (
"audino", "bagon", "baltoy", "banette", "bidoof", "braviary", "bronzor", "carracosta", "charmeleon", "cresselia", "croagunk", "darmanitan", "deino", "emboar", "emolga", "exeggcute", "gabite", "girafarig", "gulpin", "haxorus", "heatmor", "heatran", "ivysaur", "jellicent", "jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba", "loudred", "lumineon", "lunatone", "machamp", "magnezone", "mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu", "pinsir", "poliwrath", "poochyena", "porygon2", "porygonz", "registeel", "relicanth", "remoraid", "rufflet", "sableye", "scolipede", "scrafty", "seaking", "sealeo", "silcoon", "simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga", "trapinch", "treecko", "tyrogue", "vigoroth", "vulpix", "wailord", "wartortle", "whismur", "wingull", "yamask");
const proc: recursive (in array string: part, in integer: offset) is func
local
var integer: index is 0;
var char: lastChar is ' ';
var string: tmp is "";
begin
if pred(offset) > maxPathLength then
maxPathLength := pred(offset);
maxPathLengthCount := 1;
elsif pred(offset) = maxPathLength then
incr(maxPathLengthCount);
maxPathExample := "";
for index range 1 to pred(offset) do
if pred(index) rem 5 = 0 then
maxPathExample &:= "\n ";
else
maxPathExample &:= " ";
end if;
maxPathExample &:= part[index];
end for;
end if;
lastChar := part[pred(offset)][length(part[pred(offset)])];
for index range offset to length(part) do
if part[index][1] = lastChar then
tmp := names[offset];
names[offset] := names[index];
names[index] := tmp;
recursive(names, succ(offset));
names[index] := names[offset];
names[offset] := tmp;
end if;
end for;
end func;
const proc: main is func
local
var integer: index is 0;
var string: tmp is "";
begin
for index range 1 to length(names) do
tmp := names[1];
names[1] := names[index];
names[index] := tmp;
recursive(names, 2);
names[index] := names[1];
names[1] := tmp;
end for;
writeln("maximum path length: " <& maxPathLength lpad 4);
writeln("paths of that length: " <& maxPathLengthCount lpad 4);
writeln("example path of that length:" <& maxPathExample);
end func;</lang>
Output:
maximum path length: 23 paths of that length: 1248 example path of that length: machamp pinsir rufflet trapinch heatmor remoraid darmanitan nosepass starly yamask kricketune exeggcute emboar relicanth haxorus simisear registeel landorus seaking girafarig gabite emolga audino
Sidef
<lang ruby>class LLFL(Array words) {
has f = Hash()
method init {
words.each {|w|
var m = w.match(/^(.).*(.)$/)
f{m[0]}{w} = m[1]
}
}
method longest_chain {
var stack = []
var longest = []
func poke(c) {
var h = f{c}
h.each_k { |word|
var v = h.delete(word)
stack.push(word)
longest[] = stack[] if (stack.len > longest.len)
__FUNC__(v) if f.exists(v)
stack.pop
h{word} = v
}
}
f.each_k { poke(_) }
return longest
}
}
var words = %w(
audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask
)
var obj = LLFL(words) var longest = obj.longest_chain()
say "#{longest.len}: #{longest.join(' ')}"</lang>
- Output:
23: machamp petilil landorus scrafty yamask kricketune exeggcute emboar registeel loudred darmanitan nosepass simisear rufflet trapinch heatmor relicanth haxorus seaking girafarig gabite emolga audino
Tcl
<lang tcl>proc search {path arcs} {
set solutions {}
set c [string index [lindex $path end] end]
set i -1
foreach arc $arcs {
incr i if {[string index $arc 0] ne $c} continue set soln [search [concat $path [list $arc]] [lreplace $arcs $i $i]] lappend solutions [list [llength $soln] $soln]
}
if {[llength $solutions]} {
return [lindex [lsort -integer -decreasing -index 0 $solutions] 0 1]
} else {
return $path
}
} proc firstlast names {
set solutions {}
set i -1
foreach initial $names {
incr i set soln [search [list $initial] [lreplace $names $i $i]] lappend solutions [list [llength $soln] $soln]
} return [lindex [lsort -integer -decreasing -index 0 $solutions] 0 1]
}
set names {
audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask
} set path [firstlast $names] puts "Path (length: [llength $path]): $path"</lang> Output:
Path (length 23): machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino
Ursala
<lang Ursala>#import std
mon =
~&*~ sep` mat` -[
audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask]-
poke = @iiDrzhK16rlXOASK24PiX ~&llrHiFPrYX^=rxS^|\~&iNCS *=+ ~&rlwNrlCQ^*D/~&+ @h
- show+
example = ~&h poke mon</lang>output:
machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino
VBScript
<lang vb>' Last letter-first letter - VBScript - 11/03/2019
names = array( _
"audino", "bagon", "baltoy", "banette", _
"bidoof", "braviary", "bronzor", "carracosta", "charmeleon", _
"cresselia", "croagunk", "darmanitan", "deino", "emboar", _
"emolga", "exeggcute", "gabite", "girafarig", "gulpin", _
"haxorus", "heatmor", "heatran", "ivysaur", "jellicent", _
"jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba", _
"loudred", "lumineon", "lunatone", "machamp", "magnezone", _
"mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu", _
"pinsir", "poliwrath", "poochyena", "porygon2", "porygonz", _
"registeel", "relicanth", "remoraid", "rufflet", "sableye", _
"scolipede", "scrafty", "seaking", "sealeo", "silcoon", _
"simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga", _
"trapinch", "treecko", "tyrogue", "vigoroth", "vulpix", _
"wailord", "wartortle", "whismur", "wingull", "yamask")
maxPathLength = 0 maxPathLengthCount = 0 maxPathExample = "" t1=timer
For i = 0 To ubound(names)
'swap names(0), names(i)
temp=names(0): names(0)=names(i): names(i)=temp
Call lastfirst(names, 1)
'swap names(0), names(i)
temp=names(0): names(0)=names(i): names(i)=temp
Next 'i
buf = buf & "Maximum length = " & maxPathLength & vbCrLf
buf = buf & "Number of solutions with that length = " & maxPathLengthCount & vbCrLf
buf = buf & "One such solution: " & vbCrLf & maxPathExample & vbCrLf
t2=timer
MsgBox buf,,"Last letter-first letter - " & Int(t2-t1) & " sec"
Sub lastfirst(names, offset)
dim i, l
If offset > maxPathLength Then
maxPathLength = offset
maxPathLengthCount = 1
ElseIf offset = maxPathLength Then
maxPathLengthCount = maxPathLengthCount + 1
maxPathExample = ""
For i = 0 To offset-1
maxPathExample = maxPathExample & names(i) & vbCrLf
Next 'i
End If
l = Right(names(offset - 1),1)
For i = offset To ubound(names)
If Left(names(i),1) = l Then
'swap names(i), names(offset)
temp=names(offset): names(offset)=names(i): names(i)=temp
Call lastfirst(names, offset+1)
'swap names(i), names(offset)
temp=names(offset): names(offset)=names(i): names(i)=temp
End If
Next 'i
End Sub 'lastfirst </lang>
- Output:
Maximum length = 23 Number of solutions with that length = 1248 One such solution: machamp pinsir rufflet trapinch heatmor remoraid darmanitan nosepass starly yamask kricketune exeggcute emboar relicanth haxorus simisear registeel landorus seaking girafarig gabite emolga audino
Duration : 69 sec
Yabasic
<lang Yabasic>all$ = "audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon " all$ = all$ + "cresselia croagunk darmanitan deino emboar emolga exeggcute gabite " all$ = all$ + "girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan " all$ = all$ + "kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine " all$ = all$ + "nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 " all$ = all$ + "porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking " all$ = all$ + "sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko " all$ = all$ + "tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask"
dim word$(1)
lnames = token(all$, word$())
dim first(256), snext(lnames)
for i = 1 to lnames
ch = asc(left$(word$(i), 1))
if first(ch)=0 then
first(ch) = i
end if
for j=i+1 to lnames
if asc(left$(word$(j), 1))=ch then
snext(i) = j
break
end if
next
next
dim taken(lnames), best(lnames)
sub try(ch, last, n)
local nex, i
nex = first(ch)
while(nex <> 0)
if taken(nex)=0 then
taken(last) = nex
taken(nex) = -1
try(asc(right$(word$(nex), 1)),nex,n+1)
taken(last) = -1
taken(nex) = 0
end if
nex = snext(nex)
wend
if n>maxn then
bstart = tstart
for i = 1 to lnames
best(i) = taken(i)
next
maxn = n
count = 1
elsif n=maxn then
count = count + 1
end if
end sub
for i=1 to lnames
tstart = i taken(i) = -1 try(asc(right$(word$(i), 1)),i,1) taken(i) = 0
next
print "Runtime: ", peek("millisrunning")/1000, " seconds. Max length: ", maxn, ", found ", count, " of such, one of which is:\n" do
print word$(bstart), " "; bstart = best(bstart) if bstart = -1 break
loop</lang>
zkl
This solution creates a hash table to all the possible word/following words to minimize search times.
No speed records were approached but 25sec seems fine for a one off walk the entire tree.
<lang zkl>pokemon:=("audino bagon baltoy banette bidoof braviary "
"bronzor carracosta charmeleon cresselia croagunk darmanitan deino " ... "whismur wingull yamask").split();
tree:=pokemon.pump(Dictionary(),'wrap(name){ //--> Hash("aB":("Bc","Bd",,,) )
T( name, pokemon.filter('wrap(nm){ name[-1]==nm[0] }) )
});
fcn maxPath([(a,_)]ab,[(c,_)]cd){ if(a>c) ab else cd } fcn walk(name,pathLen,path,tree){ //-->longest path for name
names:=tree.find(name,T); tree[name]=T; // nuke cycle
np:=names.reduce('wrap(np,name){
maxPath(np,walk(name,pathLen+1,String(path," ",name),tree));
},T(0,""));
tree[name]=names;
if(np[0]>pathLen) return(np);
return(pathLen,path);
}
pokemon.reduce('wrap(np,name){ maxPath(walk(name,1,name,tree),np) },T(0,"")) .println();</lang>
- Output:
L(23,"machamp pinsir rufflet trapinch heatmor remoraid darmanitan nosepass starly yamask kricketune exeggcute emboar relicanth haxorus simisear registeel landorus seaking girafarig gabite emolga audino")