# Dinesman's multiple-dwelling problem/AutoHotkey

**Dinesman's multiple-dwelling problem/AutoHotkey**is part of

**Dinesman's multiple-dwelling problem**. You may find other members of Dinesman's multiple-dwelling problem at Category:Dinesman's multiple-dwelling problem.

**Dinesman's multiple-dwelling problem/AutoHotkey**is part of

**Zebra puzzle**. You may find other members of Zebra puzzle at Category:Zebra puzzle.

Combined solution for Dinesman's multiple-dwelling problem and Zebra puzzle.

```
#NoEnv
SetBatchLines, -1
#SingleInstance, Force
Backtrack:=0 ; Set to -1 to turn off backtracking.
; Solve this the same way a human would - logic grids.
; To animate solution, uncomment Display(size) lines.
; Parse problem statement intuitively.
demo1 = Four people: Abe Ben Charlie David. Abe not second or top. not adjacent Ben Charlie. David Abe adjacent. David adjacent Ben. Abe?
demo2 = Four: A B C D. A not adjacent D. not B adjacent higher C. C lower D. A ; assumed nothigher = lower
problem1 = Five adjacent floors of an apartment house contain these different tradesmen: Baker, Cooper, Fletcher, Miller, Smith. Baker does not live on the top floor. Cooper does not live on the bottom floor. Fletcher does not live on either the top or the bottom floor. Miller lives on a higher floor than does Cooper. Smith does not live on a floor adjacent to Fletcher's. Fletcher does not live on a floor adjacent to Cooper's. Where does Fletcher live?
problem2 = Seven adjacent floors of an apartment house contain these different people: Baker, Cooper, Fletcher, Miller, Guinan, and Smith. Guinan does not live on either the top or the third or the fourth floor. Baker does not live on the top floor. Cooper does not live on the bottom floor. Fletcher does not live on either the top or the bottom floor. Miller lives on a higher floor than does Cooper. Smith does not live on a floor adjacent to Fletcher's. Fletcher does not live on a floor adjacent to Cooper's. Where does Fletcher live? ; from the Python version
problem3 = Five adjacent houses contain different men of different nationalities and different tastes, one from each of these groups: Dane, Englishman, German, Norwegian, Swede, Blend, Blue_Master, Dunhill, Pall_Mall, Prince, blue, green, red, white, yellow, beer, coffee, milk, water, tea, birds, cats, dog, horse, zebra. The Englishman lives in the red house. The Swede has a dog. The Dane drinks tea. The green house is immediately to the left of the white house. They drink coffee in the green house. The man who smokes Pall_Mall has birds. In the yellow house they smoke Dunhill. In the middle house they drink milk. The Norwegian lives in the first house. The man who smokes Blend lives in the house next to the house with cats. In a house next to the house where they have a horse, they smoke Dunhill. The man who smokes Blue_Master drinks beer. The German smokes Prince. The Norwegian lives next to the blue house. They drink water in a house next to the house where they smoke Blend. Who owns the zebra?
problem4 = Ten adjacent houses contain different men of different nationalities and different tastes, one from each of these groups: Renault, Ferrari, Mercedes, Ford, Volvo, VW, BMW, Porsche, Rolls_Royce, Toyota, White, Red, Magenta, Yellow, Green, Brown, Gray, Pink, Blue, Black, Water, Ice_tea, Beer, Coffee, Tea, Wine, Espresso, Soda, Milk, Lemonade, Orchids, Crocuses, Roses, Cactuses, Tulips, Dahlias, Geraniums, Hyacinth, Daffodils, Lilies, Waffles, Potatoes, Cheese, Chocolate, Cookies, Ice_cream, Eggs, Spaghetti, Pancakes, Steaks, Norseman, Swiss, German, Spaniard, Brit, Italian, Irishman, Greek, Dane, Swede, Dogs, Mice, Tortoises, Butterflies, Snakes, Birds, Cats, Fish, Horses, Turtles, Chesterfields, Pipe, Cubans, Kools, Pall_Mall, Blend, Dunhill, Bluemaster, Marlboro, Prince, Soccer, Badminton, Lacrosse, Tennis, Rugby, Basketball, Football, Baseball, Volleyball, Ice_hockey, Redwoods, Eucalyptus, Oaks, Pines, Birch, Nuts, Firs, Maples, Palms, Willows. The Ford driver lives directly next to the person drinking ice_tea. The person with the cats drinks tea. The fish live directly to the right of the person drinking milk. The Ford driver lives directly to the right of tennis player. The Swede lives directly to the right of the birch trees. The ice_hockey player does not like redwoods. The Renault driver drinks soda. The green house does not have a Ferrari parked in front of it. The second house reeks of Pall_Mall. The blue house reeks of Prince. The house with nuts does not reek of Bluemaster. The driver of the Ford is not Greek. The driver of the Porsche likes steaks. You will be served spaghetti in the first house. Cookies and birch trees do not go together. The person driving the Volvo plays baseball. The tortoises live directly to the right of the horses. The Brit lives directly to the left of the potatoes-eating person. The firs grow directly next to the basketball player. The person eating cheese lives at a number higher than that of the red house. The person in house nine plays soccer. The eucalyptus trees grow directly to the left of the person drinking coffee. The Dane lives directly to the right of the badminton player. The tenth house is gray. The Norseman lives in house nine. The Brit eats pancakes. The Italian lives directly to the right of the Marlboro-smoker. The person with palms lives directly to the right of the person driving the Rolls_Royce. The person liking the geraniums has dogs. The volleyball player lives at a number higher that of the person eating eggs. The Mercedes is parked in front of house nine. The orchids grow at a number higher that of the blue house. The volleyball player lives directly to the left of the person smoking Kools. The first house is magenta. The person in house four smokes Chesterfields. The football player lives directly to the left of the person smoking Dunhill. The oaks grow directly to the left of the cactuses. The dogs live directly to the left of the baseball player. The person eating pancakes lives in the brown house. The Ferrari is parked in front of house four. The person driving the Porsche lives directly to the right of the white house. The turtles live in house seven. The hyacinth grow in front of house eight. The crocuses grow in front of house six. The VW is parked in front of house two. The palms grow directly to the right of the person drinking milk. The Italian grows lilies. The person driving the Renault lives in the red house. The person in house nine drinks tea. The willows grow directly next to the daffodils. The birds live in house five. The person with the turtles drinks wine. The person drinking beer lives at a number higher than that of the person drinking espresso. The orchids grow directly next to the horses. The nuts grow in front of house ten. The person in house one does not play basketball. The person smoking pipe lives directly to the right of the black house. The Irishman lives directly to the left of the Blend-smoking person. The dahlias grow directly to the left of the snakes. The maples grow in front of house seven. The Toyota driver lives directly to the left of the Ford driver. The mice live directly to the right of the person eating chocolate. The person in house one drinks water. The pines grow directly to the right of the person smoking Pall_Mall. The person smoking Dunhill lives directly next to the person drinking tea. The person playing rugby lives directly to the right of the yellow house. The willows grow in front of house four. The Swiss eats waffles. The baseball player lives directly next to the Lacrosse player. The German lives in house one. The tulips grow directly next to the red house. The daffodils grow directly to the right of the badminton player. The person drinking beer lives directly next to the person drinking milk. Who eats ice_cream?
Loop, Parse, problem1, . ; select name of problem here; do not edit below
{
If (A_Index = 1)
{
; Get number of houses/floors.
numerals:="One|Two|Three|Four|Five|Six|Seven|Eight|Nine|Ten|Eleven|Twelve|Thirteen|Fourteen|Fifteen|Sixteen|Seventeen|Eighteen|Nineteen|Twenty"
ordinals:="First|Second|Third|Fourth|Fifth|Sixth|Seventh|Eighth|Ninth|Tenth|Eleventh|Twelfth|Thirteenth|Fourteenth|Fifteenth|Sixteenth|Seventeenth|Eighteenth|Nineteenth|Twentieth"
Loop, Parse, numerals, |
%A_LoopField%:=A_Index
StringSplit, ordinal, ordinals, |
n:=SubStr(A_LoopField, 1, RegExMatch(A_LoopField, "\W")-1)
n:=%n%
; Get list of all properties, and assign each to an index.
Loop, % size:=n+RegExMatchAll(SubStr(A_LoopField, InStr(A_LoopField, ":")+1), "\b\w+\b", "property" )
{
If (A_Index <= n)
i:=A_Index
, name:=ordinal%i%
Else
i:=A_Index-n
, name:=property%i%
all.=name "|"
%name%:=A_Index
}
all:=SubStr(all, 1, -1)
Middle:=(n+1)//2, Last:=n, Bottom:=1, Top:=n ; permissible shortcut properties
re_properties:="i)(\bBottom|Middle|Top|Last|" numerals "|" all "\b)"
re_properties:=RegExReplace(re_properties, "\|", "\b|\b")
re_keywords:="i)(\bhigher\b|\blower\b|\badjacent\b|\bnext\b|\babove\b|\bbelow\b|\bleft\b|\bright\b)"
; Initialize values, with 1's on the diagonal.
Loop, % size
{
j:=A_Index
Loop, % size
{
i:=A_Index
%i%_%j%:=(i = j) ? 1 : -1
}
}
}
Else
{
RegExMatchAll(A_LoopField, re_properties, "properties")
RegExMatchAll(A_LoopField, re_keywords, "keywords")
note:=RegExMatch(A_LoopField, "i)\bnot\b") ? "not" : ""
If (properties0 = 1)
{
find:=properties1 ; at end of loop will contain name in last line
}
Else If (properties0 = 2)
{
properties1:=%properties1%
properties2:=%properties2%
If (keywords0 = 0)
{
%properties1%_%properties2%:=(note ? 0 : 1)
}
Else Loop, % keywords0
{
keyword:=keywords%A_Index%
%note%%keyword% .= properties1 "," properties2 "`n"
}
}
Else Loop, % properties0
{
If (A_Index = 1)
{
properties1:=%properties1%
}
Else
{
properties:=properties%A_Index%
properties:=%properties%
%properties1%_%properties%:=(note ? 0 : 1)
}
}
}
}
; Create a grid of these attributes, and GUI to show it.
Gui +Resize +MinSize +OwnDialogs +LastFound
Gui, Font, s8, Courier New
Gui, Add, Text, w90 h90 x10 y10, Current`n%find%`nState
x:=80, y:=80
Loop, Parse, all, |
{
x+=21+(mod(A_Index,n)=1 ? 5 : 0)
y+=21+(mod(A_Index,n)=1 ? 5 : 0)
Gui, Add, Tab2, w21 h100 x%x% y10 Left Buttons, %A_LoopField%
Gui, Add, Edit, w90 h15 x10 y%y% Right Disabled, %A_LoopField%
}
y:=81, s:=0
Loop, % size
{
j:=A_Index
x:=83
y+=21+(mod(j,n)=1 ? 5 : 0)
Loop, % size
{
i:=A_Index
x+=21+(mod(i,n)=1 ? 5 : 0)
If (++s < 10000-3*size) ; workaround as AHK only supports 11000 controls per gui
Gui, Add, Checkbox, x%x% y%y% w13 h13 v%i%_%j% Check3 CheckedGray ; w13 h13 tricks AHK to not display label
}
}
Gui, Add, Button, xp-55 yp+20 w70, Close
Gui, Add, Button, xp-85 yp w70, Reset
Gui, Add, Button, xp-85 yp w70 Default, Continue
Gui, Add, Text, xm yp w400 r2 vNotify
Gui, Show, NA
; Internal cleanup.
lower.=nothigher ; only implemented for floor puzzles
higher.=notlower ; only implemented for floor puzzles
right.=above ; synonymns for house vs. floor puzzles
left.=below
adjacent.=next
notadjacent.=notnext
adjacent:=SubStr(adjacent, 1, -1)
notadjacent:=SubStr(notadjacent, 1, -1)
right:=SubStr(right, 1, -1)
Loop, Parse, right, `n
{
StringSplit, a, A_LoopField, `,
left.=a2 "," a1 "`n"
}
left:=SubStr(left, 1, -1)
higher:=SubStr(higher, 1, -1)
Loop, Parse, higher, `n
{
StringSplit, a, A_LoopField, `,
lower.=a2 "," a1 "`n"
}
lower:=SubStr(lower, 1, -1)
; Allow user to add constraint mid-process
Display(size) ; required for Gui Submit below
ButtonContinue:
GuiControl, , Notify, Solving...
Gui, Submit, NoHide
Backtrack:
; Five steps:
s:=true
While, s ; loop until solved
{
; 1. Check adjacent properties.
Loop, Parse, adjacent, `n
{
StringSplit, a, A_LoopField, `,
Loop, % n
{
k:=A_Index-1
l:=A_Index+1
If (%A_Index%_%a1% = 1)
If (A_Index = 1) ; there is only one house adjacent the first house
{
m:=1+1
If (%m%_%a2% != 0)
%m%_%a2%:=1
Else Goto Error
}
Else If (A_Index = n) ; there is only one house adjacent the last house
{
m:=n-1
If (%m%_%a2% != 0)
%m%_%a2%:=1
Else Goto Error
}
Else If (%l%_%a2%=0) ; there are two adjacent house but one has already been eliminated
If (%k%_%a2% != 0)
%k%_%a2%:=1
Else Goto Error
Else If (%k%_%a2%=0) ; there are two adjacent house but one has already been eliminated
If (%l%_%a2% != 0)
%l%_%a2%:=1
Else Goto Error
Else If (%A_Index%_%a1% = 0)
If (A_Index = 1+1) ; there is only one house adjacent the first house
If (%1%_%a2% != 1)
%1%_%a2%:=0
Else Goto Error
Else If (A_Index = n-1) ; there is only one house adjacent the last house
If (%n%_%a2% != 1)
%n%_%a2%:=0
Else Goto Error
If (%A_Index%_%a2% = 1) ; repeat with houses switched
If (A_Index = 1)
{
m:=1+1
If (%m%_%a1% != 0)
%m%_%a1%:=1
Else Goto Error
}
Else If (A_Index = n)
{
m:=n-1
If (%m%_%a1% != 0)
%m%_%a1%:=1
Else Goto Error
}
Else If (%l%_%a1%=0)
If (%k%_%a1% != 0)
%k%_%a1%:=1
Else Goto Error
Else If (%k%_%a1%=0)
If (%l%_%a1% != 0)
%l%_%a1%:=1
Else Goto Error
Else If (%A_Index%_%a2% = 0)
If (A_Index = 1+1)
If (%1%_%a1% != 1)
%1%_%a1%:=0
Else Goto Error
Else If (A_Index = n-1)
If (%n%_%a1% != 1)
%n%_%a1%:=0
Else Goto Error
}
}
Loop, Parse, notadjacent, `n
{
StringSplit, a, A_LoopField, `,
Loop, % n
{
k:=A_Index-1
l:=A_Index+1
If (%A_Index%_%a1% = 1) ; if you know where this house is, you know the other is not adjacent it
If (A_Index = 1)
If (%l%_%a2% != 1)
%l%_%a2%:=0
Else Goto Error
Else If (A_Index = n)
If (%k%_%a2% != 1)
%k%_%a2%:=0
Else Goto Error
Else
If (%k%_%a2% != 1 and %l%_%a2% != 1)
%k%_%a2%:=0
, %l%_%a2%:=0
Else Goto Error
If (%A_Index%_%a2% = 1) ; repeat with houses switched
If (A_Index = 1)
If (%l%_%a1% != 1)
%l%_%a1%:=0
Else Goto Error
Else If (A_Index = n)
If (%k%_%a1% != 1)
%k%_%a1%:=0
Else Goto Error
Else
If (%k%_%a1% != 1 and %l%_%a1% != 1)
%k%_%a1%:=0
, %l%_%a1%:=0
Else Goto Error
}
m:=0
Loop, % n
{
j:=A_Index
If (%j%_%a2% = -1) ; find available a2
{
Loop, % n
{
i:=A_Index
If (abs(j-i) > 1 and %i%_%a1% = -1) ; find available a1
k:=i, l:=j, m++
}
}
}
If (m = 1)
If (%k%_%a1% != 0 and %l%_%a2% != 0)
%k%_%a1%:=1
, %l%_%a2%:=1
Else Goto Error
}
Loop, Parse, left, `n
{
StringSplit, a, A_LoopField, `,
If (1_%a2% != 1)
1_%a2%:=0 ; because otw a1 cannot be below it
Else Goto Error
If (%n%_%a1% != 1)
%n%_%a1%:=0 ; because otw a2 cannot be above it
Else Goto Error
Loop, % n
{
k:=A_Index-1
l:=A_Index+1
If (%A_Index%_%a1% = 1) ; a2 is same value as a1 one house to left
If (A_Index < n and %l%_%a2% != 0)
%l%_%a2%:=1
Else Goto Error
Else If (%A_Index%_%a1% = 0)
If (A_Index < n)
If (%l%_%a2% != 1)
%l%_%a2%:=0
Else Goto Error
If (%A_Index%_%a2% = 1) ; and vice versa
If (A_Index > 1 and %k%_%a1% != 0)
%k%_%a1%:=1
Else Goto Error
Else If (%A_Index%_%a2% = 0)
If (A_Index > 1)
If (%k%_%a1% != 1)
%k%_%a1%:=0
Else Goto Error
}
}
Loop, Parse, lower, `n
{
StringSplit, a, A_LoopField, `,
Loop, % n ; find highest available a2
{
If (%A_Index%_%a2% != 0)
{
l:=A_Index
}
}
Loop, % n-(l-1)
{
m:=(l-1)+A_Index
If (%m%_%a1% != 1)
%m%_%a1%:=0 ; because otw a2 cannot be above it
Else Goto Error
}
Loop, % n ; find lowest available a1
{
If (%A_Index%_%a1% != 0)
{
k:=A_Index
Break
}
}
Loop, % k
{
If (%A_Index%_%a2% != 1)
%A_Index%_%a2%:=0 ; because otw a1 cannot be below it
Else Goto Error
}
}
;Display(size)
; 2. Mirror both directions.
Loop, % size
{
j:=A_Index
Loop, % size
{
i:=A_Index
If (%i%_%j% != -1)
If (%j%_%i% = -1)
%j%_%i%:=%i%_%j%
Else If (%j%_%i% != %i%_%j%)
Goto Error
}
}
;Display(size)
; 3. Add 0s around 1s.
Loop, % size
{
j:=A_Index
Loop, % size
{
i:=A_Index
If (%i%_%j% = 1)
{
k:=i-(i//n=i/n ? n : 0)
Loop, % n-1
{
k+=1-(k//n=k/n && k>i ? n : 0)
If (%k%_%j% = -1)
%k%_%j%:=0
Else If (%k%_%j% != 0)
Goto Error
}
}
}
}
;Display(size)
; 4. Flip 0s around 1s.
Loop, % size
{
j:=A_Index
Loop, % size
{
i:=A_Index
If (%i%_%j% = 1)
{
Loop, % size
{
k:=A_Index
If (%k%_%j% = 0)
If (%i%_%k% = -1)
%i%_%k%:=0
Else If (%i%_%k% != 0)
Goto Error
}
}
}
}
;Display(size)
; 5. Add 1s when only one spot remaining.
Loop, % size
{
j:=A_Index
Loop, % size
{
i:=A_Index
If (mod(i,n) = 1)
k:=0, l:=i-1
If (%i%_%j% = 0)
k++
Else
l:=i
If (k = n-1)
{
If (mod(l,n) = 0 and i-l = n-1)
l+=n
If (%l%_%j% != 0)
%l%_%j%:=1
Else Goto Error
k:=0
}
}
l:=0
}
;Display(size)
; Catch infinite loop.
olds:=s
s:=Check(size)
If (s=olds)
{
If (Backtrack = -1)
{
Display(size)
Msgbox, System error! Infinite loop.
ExitApp
}
Backtrack++
Loop, % size
{
j:=A_Index
Loop, % size
{
i:=A_Index
%Backtrack%_%i%_%j%:=%i%_%j%
If (%i%_%j% = -1)
k:=i, l:=j
}
}
%k%_%l%:=1
}
}
; Show results.
Display(size)
m=
StringSplit, a, all, |
Loop, % n
{
j:=A_Index
m.=a%j% " house:`t"
Loop, % size
{
i:=A_Index
If (%i%_%j% and i!=j)
m.=a%i% "`t"
If (%i%_%j% and a%i% = find)
found := a%j%
, m:="The " found " house contains the " find ".`n`n" m
}
m.="`n"
}
If (Backtrack <= 0)
m.="`nThis solution is unique."
Else
m.="`nBacktracking was required; this solution may not be unique."
GuiControl, , Notify, Solved. The %found% house contains the %find%.
MsgBox % m
Return ;--------------------------------------------------------------
; Function to display grid on screen.
Display(size) {
s:=0
Loop, % size
{
j:=A_Index
Loop, % size
{
i:=A_Index
If (++s < 10000-3*size) ; workaround as AHK only supports 11000 controls per gui
GuiControl, , %i%_%j%, % %i%_%j%
}
}
Gui, Show, NA
Sleep 0.5*1000
Return
}
; Function to check completion.
Check(size) {
s:=0
Loop, % size
{
j:=A_Index
Loop, % size
{
i:=A_Index
If (%i%_%j% = -1)
s++
}
}
Return s
}
; modified from http://www.autohotkey.com/board/topic/58737-stdlib-regexmatchall/
RegExMatchAll( Haystack, NeedleRegEx , QuotedOutputVar, StartingPosition = 1 )
{
Local RegExPosition := StartingPosition-1, MatchCount := 0, temp
While RegExPosition := RegExMatch( Haystack, NeedleRegEx, %QuotedOutputVar%, RegExPosition+1 )
{
%QuotedOutputVar%0 := ++MatchCount
%QuotedOutputVar%%MatchCount% := %QuotedOutputVar%
If MatchCount = 1
temp := %QuotedOutputVar%
}
%QuotedOutputVar%0 := MatchCount
%QuotedOutputVar%1 := temp
Return MatchCount
}
; Consistent error check.
Error:
If (Backtrack = -1)
{
Display(size)
Msgbox, System error! Problem unsolvable.
ExitApp
}
Loop, % size
{
j:=A_Index
Loop, % size
{
i:=A_Index
%i%_%j%:=%Backtrack%_%i%_%j%
If (%i%_%j% = -1)
k:=i, l:=j
}
}
%k%_%l%:=0
Backtrack--
Goto Backtrack
ButtonReset:
;~F5::
Reload
; Pause key.
;~^c::
~Pause::
Pause
Return
; Break key.
ButtonClose:
GuiClose:
GuiEscape:
~^Pause::
ExitApp
```

Demo1:

The Third house contains the Abe. First house: Ben Second house: David Third house: Abe Fourth house: Charlie Backtracking was required; this solution may not be unique.

Demo2:

The Second house contains the A. First house: B Second house: A Third house: C Fourth house: D This solution is unique.

Problem1 (Dinesman's multiple-dwelling problem):

The Fourth house contains the Fletcher. First house: Smith Second house: Cooper Third house: Baker Fourth house: Fletcher Fifth house: Miller This solution is unique.

Problem2:

The Fourth house contains the Fletcher. First house: Baker Second house: Cooper Third house: Miller Fourth house: Fletcher Fifth house: Guinan Sixth house: and Seventh house: Smith Backtracking was required; this solution may not be unique.

Problem3 (Zebra puzzle):

The Fourth house contains the zebra. First house: Norwegian Dunhill yellow water cats Second house: Dane Blend blue tea horse Third house: Englishman Pall_Mall red milk birds Fourth house: German Prince green coffee zebra Fifth house: Swede Blue_Master white beer dog This solution is unique.

Problem4:

The Fifth house contains the ice_cream. First house: BMW Magenta Water Roses Spaghetti German Butterflies Bluemaster Ice_hockey Eucalyptus Second house: VW Brown Coffee Geraniums Pancakes Brit Dogs Pall_Mall Lacrosse Oaks Third house: Volvo Blue Espresso Cactuses Potatoes Greek Horses Prince Baseball Pines Fourth house: Ferrari Pink Beer Orchids Eggs Irishman Tortoises Chesterfields Badminton Willows Fifth house: Rolls_Royce Green Milk Daffodils Ice_cream Dane Birds Blend Volleyball Birch Sixth house: Toyota Black Ice_tea Crocuses Cookies Swede Fish Kools Tennis Palms Seventh house: Ford Yellow Wine Tulips Chocolate Spaniard Turtles Pipe Football Maples Eighth house: Renault Red Soda Hyacinth Waffles Swiss Mice Dunhill Rugby Redwoods Ninth house: Mercedes White Tea Dahlias Cheese Norseman Cats Marlboro Soccer Firs Tenth house: Porsche Gray Lemonade Lilies Steaks Italian Snakes Cubans Basketball Nuts This solution is unique.