Set puzzle: Difference between revisions

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(Added Erlang)
m (Better deck/0)
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-module( set ).
-module( set ).


-export( [deck/0, is_set/3, task/0] ).
-export( [deck/0, is_set/3, shuffle_deck/1, task/0] ).


-record( card, {number, symbol, shading, colour} ).
-record( card, {number, symbol, shading, colour} ).


⚫
deck() -> [#card{number=N, symbol=Sy, shading=Sh, colour=C} || N <- [1,2,3], Sy <- [diamond, squiggle, oval], Sh <- [solid, striped, open], C <- [red, green, purple]].
deck() ->
⚫
Sorted = [#card{number=N, symbol=Sy, shading=Sh, colour=C} || N <- [1,2,3], Sy <- [diamond, squiggle, oval], Sh <- [solid, striped, open], C <- [red, green, purple]],
⚫
knuth_shuffle:list( Sorted ).


is_set( Card1, Card2, Card3 ) ->
is_set( Card1, Card2, Card3 ) ->
Line 320: Line 318:
andalso is_shading_correct( Card1, Card2, Card3 )
andalso is_shading_correct( Card1, Card2, Card3 )
andalso is_symbol_correct( Card1, Card2, Card3 ).
andalso is_symbol_correct( Card1, Card2, Card3 ).

⚫
shuffle_deck( Deck ) -> knuth_shuffle:list( Deck ).


task() ->
task() ->
Line 332: Line 332:


common( X, Y ) ->
common( X, Y ) ->
{Sets, Cards} = find_x_sets_in_y_cards( X, Y ),
{Sets, Cards} = find_x_sets_in_y_cards( X, Y, deck() ),
io:fwrite( "Cards ~p~n", [Cards] ),
io:fwrite( "Cards ~p~n", [Cards] ),
io:fwrite( "Gives sets:~n" ),
io:fwrite( "Gives sets:~n" ),
[io:fwrite( "~p~n", [S] ) || S <- Sets].
[io:fwrite( "~p~n", [S] ) || S <- Sets].


find_x_sets_in_y_cards( X, Y ) ->
find_x_sets_in_y_cards( X, Y, Deck ) ->
⚫
{Cards, _T} = lists:split( Y, shuffle_deck(Deck) ),
Deck = deck(),
⚫
{Cards, _T} = lists:split( Y, Deck ),
find_x_sets_in_y_cards( X, Y, Cards, make_sets1(Cards, []) ).
find_x_sets_in_y_cards( X, Y, Cards, make_sets1(Cards, []) ).


find_x_sets_in_y_cards( X, _Y, Cards, Sets ) when erlang:length(Sets) =:= X -> {Sets, Cards};
find_x_sets_in_y_cards( X, _Y, _Deck, Cards, Sets ) when erlang:length(Sets) =:= X -> {Sets, Cards};
find_x_sets_in_y_cards( X, Y, _Cards, _Sets ) -> find_x_sets_in_y_cards( X, Y ).
find_x_sets_in_y_cards( X, Y, Deck, _Cards, _Sets ) -> find_x_sets_in_y_cards( X, Y, Deck ).


is_colour_correct( Card1, Card2, Card3 ) -> is_colour_different( Card1, Card2, Card3 ) orelse is_colour_same( Card1, Card2, Card3 ).
is_colour_correct( Card1, Card2, Card3 ) -> is_colour_different( Card1, Card2, Card3 ) orelse is_colour_same( Card1, Card2, Card3 ).

Revision as of 17:24, 8 December 2013

Task
Set puzzle
You are encouraged to solve this task according to the task description, using any language you may know.

Set Puzzles are created with a deck of cards from the Set Game™. The object of the puzzle is to find sets of 3 cards in a rectangle of cards that have been dealt face up. There are 81 cards in a deck. Each card contains a unique variation of the following four features: color, symbol, number and shading.

there are three colors
red, green, or purple
there are three symbols
oval, squiggle, or diamond
there is a number of symbols on the card
one, two, or three
there are three shadings
solid, open, or striped

Three cards form a set if each feature is either the same on each card, or is different on each card. For instance: all 3 cards are red, all 3 cards have a different symbol, all 3 cards have a different number of symbols, all 3 cards are striped.

There are two degrees of difficulty: basic and advanced. The basic mode deals 9 cards, that contain exactly 4 sets; the advanced mode deals 12 cards that contain exactly 6 sets. When creating sets you may use the same card more than once. The task is to write code that deals the cards (9 or 12, depending on selected mode) from a shuffled deck in which the total number of sets that could be found is 4 (or 6, respectively); and print the contents of the cards and the sets. For instance:

DEALT 9 CARDS:

green, one, oval, striped
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
red, three, oval, open
red, three, diamond, solid

CONTAINING 4 SETS:

green, one, oval, striped
purple, two, squiggle, open
red, three, diamond, solid


green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid


green, one, diamond, open
purple, two, squiggle, open
red, three, oval, open


purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open

C

Brute force. Each card is a unique number in the range of [0,81]. Randomly deal a hand of cards until exactly the required number of sets are found. <lang c>#include <stdio.h>

  1. include <stdlib.h>

char *names[4][3] = { { "red", "green", "purple" }, { "oval", "squiggle", "diamond" }, { "one", "two", "three" }, { "solid", "open", "striped" } };

int set[81][81];

void init_sets(void) { int i, j, t, a, b; for (i = 0; i < 81; i++) { for (j = 0; j < 81; j++) { for (t = 27; t; t /= 3) { a = (i / t) % 3; b = (j / t) % 3; set[i][j] += t * (a == b ? a : 3 - a - b); } } } }

void deal(int *out, int n) { int i, j, t, c[81]; for (i = 0; i < 81; i++) c[i] = i; for (i = 0; i < n; i++) { j = i + (rand() % (81 - i)); t = c[i], c[i] = out[i] = c[j], c[j] = t; } }

int get_sets(int *cards, int n, int sets[][3]) { int i, j, k, s = 0; for (i = 0; i < n; i++) { for (j = i + 1; j < n; j++) { for (k = j + 1; k < n; k++) { if (set[cards[i]][cards[j]] == cards[k]) sets[s][0] = i, sets[s][1] = j, sets[s][2] = k, s++; } } }

return s; }

void show_card(int c) { int i, t; for (i = 0, t = 27; t; i++, t /= 3) printf("%9s", names[i][(c/t)%3]); putchar('\n'); }

void deal_sets(int ncard, int nset) { int c[81]; int csets[81][3]; // might not be enough for large ncard int i, j, s;

do deal(c, ncard); while ((s = get_sets(c, ncard, csets)) != nset);

printf("dealt %d cards\n", ncard); for (i = 0; i < ncard; i++) { printf("%2d:", i); show_card(c[i]); } printf("\nsets:\n");

for (i = 0; i < s; i++) { for (j = 0; j < 3; j++) { printf("%2d:", csets[i][j]); show_card(c[csets[i][j]]); } putchar('\n'); } }

int main(void) { init_sets(); deal_sets(9, 4);

while (1) deal_sets(12, 6);

return 0; }</lang>

D

<lang d>import std.stdio, std.random, std.array, std.conv, std.traits, 

      std.exception;

const class SetDealer { 

   protected {
       enum Color  : ubyte {green, purple, red}
       enum Number : ubyte {one, two, three}
       enum Symbol : ubyte {oval, diamond, squiggle}
       enum Fill   : ubyte {open, striped, solid}

       static struct Card {
           Color c;
           Number n;
           Symbol s;
           Fill f;
       }

       immutable Card[81] deck;
   }

  this() pure nothrow {
       Card[] tmpdeck;

       immutable colors = [EnumMembers!Color];
       immutable numbers = [EnumMembers!Number];
       immutable symbols = [EnumMembers!Symbol];
       immutable fill = [EnumMembers!Fill];

       foreach (immutable i; 0 .. deck.length)
           tmpdeck ~= Card(colors[i / 27],
                     numbers[(i / 9) % 3],
                     symbols[(i / 3) % 3],
                     fill[i % 3]);

        // randomShuffle(tmpdeck); /* not pure nothrow */

        deck = assumeUnique(tmpdeck);
   }

   // randomSample produces a sorted output that's convenient in our
   // case because we're printing to stout. Normally you would want
   // to shuffle.
   immutable(Card)[] deal(in uint numCards) const {
       enforce(numCards < deck.length, "number of cards too large");
       return deck[].randomSample(numCards).array();
   }

   // The summed enums of valid sets are always zero or a multiple
   // of 3.
   bool validSet(in ref Card c1, in ref Card c2, in ref Card c3)
   const pure nothrow {
       return !((c1.c + c2.c + c3.c) % 3 ||
                (c1.n + c2.n + c3.n) % 3 ||
                (c1.s + c2.s + c3.s) % 3 ||
                (c1.f + c2.f + c3.f) % 3);
   }

   immutable(Card)[3][] findSets(in Card[] cards, in uint target = 0)
   const pure nothrow {
       immutable len = cards.length;
       if (len < 3)
           return null;

       typeof(return) sets;
       foreach (immutable i; 0 .. len - 2)
           foreach (immutable j; i + 1 .. len - 1)
               foreach (immutable k; j + 1 .. len)
                   if (validSet(cards[i], cards[j], cards[k])) {
                       sets ~= [cards[i], cards[j], cards[k]];
                       if (target != 0 && sets.length > target)
                           return null;
                   }
       return sets;
   }

}

const final class SetPuzzleDealer : SetDealer { 

   enum {basic = 9, advanced = 12}

   override immutable(Card)[] deal(in uint numCards = basic) const {
       immutable numSets = numCards / 2;
       typeof(return) cards;

       do {
           cards = super.deal(numCards);
       } while (findSets(cards, numSets).length != numSets);

       return cards;
   }

}

void main() { 

   const dealer = new SetPuzzleDealer();
   const cards = dealer.deal();

   writefln("\nDEALT %d CARDS:\n", cards.length);
   foreach (c; cards)
       writeln(cast()c);

   immutable sets = dealer.findSets(cards);
   immutable len = sets.length;
   writefln("\nFOUND %d %s:\n", len, len == 1 ? "SET" : "SETS");
   foreach (set; sets) {
       foreach (c; set)
           writeln(cast()c);
       writeln();
   }

}</lang>

Sample output:
DEALT 9 CARDS:

Card(green, two, diamond, open)
Card(green, three, oval, striped)
Card(green, three, oval, solid)
Card(green, three, squiggle, open)
Card(purple, two, squiggle, open)
Card(red, one, diamond, striped)
Card(red, one, squiggle, open)
Card(red, two, oval, open)
Card(red, three, diamond, open)

FOUND 4 SETS:

Card(green, two, diamond, open)
Card(purple, two, squiggle, open)
Card(red, two, oval, open)

Card(green, three, oval, solid)
Card(purple, two, squiggle, open)
Card(red, one, diamond, striped)

Card(green, three, squiggle, open)
Card(purple, two, squiggle, open)
Card(red, one, squiggle, open)

Card(red, one, squiggle, open)
Card(red, two, oval, open)
Card(red, three, diamond, open)

Erlang

Until a better solution is found this is one. <lang Erlang> -module( set ).

-export( [deck/0, is_set/3, shuffle_deck/1, task/0] ).

-record( card, {number, symbol, shading, colour} ).

deck() -> [#card{number=N, symbol=Sy, shading=Sh, colour=C} || N <- [1,2,3], Sy <- [diamond, squiggle, oval], Sh <- [solid, striped, open], C <- [red, green, purple]].

is_set( Card1, Card2, Card3 ) -> 

       is_colour_correct( Card1, Card2, Card3 )
       andalso is_number_correct( Card1, Card2, Card3 )
       andalso is_shading_correct( Card1, Card2, Card3 )
       andalso is_symbol_correct( Card1, Card2, Card3 ).

shuffle_deck( Deck ) -> knuth_shuffle:list( Deck ).

task() -> 

   basic(),
   advanced().


advanced() -> common( 6, 12 ).

basic() -> common( 4, 9 ).

common( X, Y ) -> 

   {Sets, Cards} = find_x_sets_in_y_cards( X, Y, deck() ),
   io:fwrite( "Cards ~p~n", [Cards] ),
   io:fwrite( "Gives sets:~n" ),
   [io:fwrite( "~p~n", [S] ) || S <- Sets].

find_x_sets_in_y_cards( X, Y, Deck ) -> 

   {Cards, _T} = lists:split( Y, shuffle_deck(Deck) ),
   find_x_sets_in_y_cards( X, Y, Cards, make_sets1(Cards, []) ).

find_x_sets_in_y_cards( X, _Y, _Deck, Cards, Sets ) when erlang:length(Sets) =:= X -> {Sets, Cards}; find_x_sets_in_y_cards( X, Y, Deck, _Cards, _Sets ) -> find_x_sets_in_y_cards( X, Y, Deck ).

is_colour_correct( Card1, Card2, Card3 ) -> is_colour_different( Card1, Card2, Card3 ) orelse is_colour_same( Card1, Card2, Card3 ).

is_colour_different( #card{colour=C1}, #card{colour=C2}, #card{colour=C3} ) when C1 =/= C2, C1 =/= C3, C2 =/= C3 -> true; is_colour_different( _Card1, _Card2, _Card3 ) -> false.

is_colour_same( #card{colour=C}, #card{colour=C}, #card{colour=C} ) -> true; is_colour_same( _Card1, _Card2, _Card3 ) -> false.

is_number_correct( Card1, Card2, Card3 ) -> is_number_different( Card1, Card2, Card3 ) orelse is_number_same( Card1, Card2, Card3 ).

is_number_different( #card{number=N1}, #card{number=N2}, #card{number=N3} ) when N1 =/= N2, N1 =/= N3, N2 =/= N3 -> true; is_number_different( _Card1, _Card2, _Card3 ) -> false.

is_number_same( #card{number=N}, #card{number=N}, #card{number=N} ) -> true; is_number_same( _Card1, _Card2, _Card3 ) -> false.

is_shading_correct( Card1, Card2, Card3 ) -> is_shading_different( Card1, Card2, Card3 ) orelse is_shading_same( Card1, Card2, Card3 ).

is_shading_different( #card{shading=S1}, #card{shading=S2}, #card{shading=S3} ) when S1 =/= S2, S1 =/= S3, S2 =/= S3 -> true; is_shading_different( _Card1, _Card2, _Card3 ) -> false.

is_shading_same( #card{shading=S}, #card{shading=S}, #card{shading=S} ) -> true; is_shading_same( _Card1, _Card2, _Card3 ) -> false.

is_symbol_correct( Card1, Card2, Card3 ) -> is_symbol_different( Card1, Card2, Card3 ) orelse is_symbol_same( Card1, Card2, Card3 ).

is_symbol_different( #card{symbol=S1}, #card{symbol=S2}, #card{symbol=S3} ) when S1 =/= S2, S1 =/= S3, S2 =/= S3 -> true; is_symbol_different( _Card1, _Card2, _Card3 ) -> false.

is_symbol_same( #card{symbol=S}, #card{symbol=S}, #card{symbol=S} ) -> true; is_symbol_same( _Card1, _Card2, _Card3 ) -> false. %% Nested loops 1, 2 and 3 make_sets1( [_Second_to_last, _Last], Sets ) -> Sets; make_sets1( [Card | T], Sets ) -> make_sets1( T, make_sets2(Card, T, Sets) ).

make_sets2( _Card, [_Last], Sets ) -> Sets; make_sets2( Card1, [Card2 | T], Sets ) -> make_sets2( Card1, T, make_sets3( Card1, Card2, T, Sets) ).

make_sets3( _Card1, _Card2, [], Sets ) -> Sets; make_sets3( Card1, Card2, [Card3 | T], Sets ) -> 

       make_sets3( Card1, Card2, T, make_sets_acc(is_set(Card1, Card2, Card3), {Card1, Card2, Card3}, Sets) ).

make_sets_acc( true, Set, Sets ) -> [Set | Sets]; make_sets_acc( false, _Set, Sets ) -> Sets. </lang>

Output:
53> set:task().
Cards [{card,2,diamond,striped,purple},
       {card,3,squiggle,solid,purple},
       {card,2,squiggle,open,red},
       {card,3,oval,solid,purple},
       {card,1,diamond,striped,green},
       {card,1,oval,open,purple},
       {card,3,squiggle,striped,purple},
       {card,2,diamond,solid,purple},
       {card,1,oval,striped,purple}]
Gives sets:
{{card,1,oval,open,purple},
 {card,3,squiggle,striped,purple},
 {card,2,diamond,solid,purple}}
{{card,2,squiggle,open,red},
 {card,3,oval,solid,purple},
 {card,1,diamond,striped,green}}
{{card,2,diamond,striped,purple},
 {card,3,squiggle,striped,purple},
 {card,1,oval,striped,purple}}
{{card,2,diamond,striped,purple},
 {card,3,squiggle,solid,purple},
 {card,1,oval,open,purple}}
Cards [{card,1,diamond,striped,purple},
       {card,3,diamond,solid,purple},
       {card,2,diamond,solid,green},
       {card,1,diamond,open,green},
       {card,3,oval,striped,red},
       {card,3,squiggle,striped,red},
       {card,2,oval,solid,purple},
       {card,1,squiggle,open,green},
       {card,3,diamond,solid,green},
       {card,2,diamond,striped,red},
       {card,2,squiggle,solid,purple},
       {card,3,oval,open,purple}]
Gives sets:
{{card,3,squiggle,striped,red},
 {card,3,diamond,solid,green},
 {card,3,oval,open,purple}}
{{card,3,squiggle,striped,red},
 {card,1,squiggle,open,green},
 {card,2,squiggle,solid,purple}}
{{card,1,diamond,open,green},
 {card,3,squiggle,striped,red},
 {card,2,oval,solid,purple}}
{{card,1,diamond,open,green},
 {card,3,oval,striped,red},
 {card,2,squiggle,solid,purple}}
{{card,3,diamond,solid,purple},
 {card,1,diamond,open,green},
 {card,2,diamond,striped,red}}
{{card,1,diamond,striped,purple},
 {card,2,squiggle,solid,purple},
 {card,3,oval,open,purple}}

J

Solution: <lang j>require 'stats/base'

Number=: ;:'one two three' Colour=: ;:'red green purple' Fill=: ;:'solid open striped' Symbol=: ;:'oval squiggle diamond' Features=: Number ; Colour ; Fill ;< Symbol Deck=: > ; <"1 { i.@#&.> Features sayCards=: (', ' joinstring Features {&>~ ])"1 drawRandom=: ] {~ (? #) isSet=: *./@:(1 3 e.~ [: #@~."1 |:)"2 getSets=: ([: (] #~ isSet) ] {~ 3 comb #) countSets=: #@:getSets

set_puzzle=: verb define 

target=. <. -: y
whilst. target ~: countSets Hand do. 
  Hand=. y drawRandom Deck
end.
echo 'Dealt ',(": y),' Cards:'
echo sayCards Hand
echo 'Found ',(":target),' Sets:'
echo sayCards getSets Hand

)</lang>

Example: <lang j> set_puzzle 9 Dealt 9 Cards: three, purple, open, oval three, green, open, diamond three, red, solid, squiggle three, green, solid, oval three, purple, striped, oval three, red, open, oval one, red, solid, oval one, green, open, squiggle two, purple, striped, squiggle Found 4 Sets: three, green, open, diamond three, red, solid, squiggle three, purple, striped, oval

three, green, open, diamond one, red, solid, oval two, purple, striped, squiggle

three, red, solid, squiggle one, green, open, squiggle two, purple, striped, squiggle

three, green, solid, oval three, purple, striped, oval three, red, open, oval </lang>

Java

<lang java>import java.util.*; import org.apache.commons.lang3.ArrayUtils;

public class SetPuzzle { 

   enum Color {
       GREEN(0), PURPLE(1), RED(2);

       private Color(int v) {
           val = v;
       }
       public final int val;
   }

   enum Number {
       ONE(0), TWO(1), THREE(2);

       private Number(int v) {
           val = v;
       }
       public final int val;
   }

   enum Symbol {
       OVAL(0), DIAMOND(1), SQUIGGLE(2);

       private Symbol(int v) {
           val = v;
       }
       public final int val;
   }

   enum Fill {
       OPEN(0), STRIPED(1), SOLID(2);

       private Fill(int v) {
           val = v;
       }
       public final int val;
   }

   private static class Card implements Comparable<Card> {
       Color c;
       Number n;
       Symbol s;
       Fill f;

       public String toString() {
           return String.format("[Card: %s, %s, %s, %s]", c, n, s, f);
       }

       public int compareTo(Card o) {
           return (c.val - o.c.val) * 10 + (n.val - o.n.val);
       }
   }

   private static Card[] deck;

   public static void main(String[] args) {
       deck = new Card[81];
       Color[] colors = Color.values();
       Number[] numbers = Number.values();
       Symbol[] symbols = Symbol.values();
       Fill[] fillmodes = Fill.values();
       for (int i = 0; i < deck.length; i++) {
           deck[i] = new Card();
           deck[i].c = colors[i / 27];
           deck[i].n = numbers[(i / 9) % 3];
           deck[i].s = symbols[(i / 3) % 3];
           deck[i].f = fillmodes[i % 3];
       }
       findSets(12);
   }

   private static void findSets(int numCards) {
       int target = numCards / 2;
       Card[] cards;
       Card[][] sets = new Card[target][3];
       int cnt;
       do {
           Collections.shuffle(Arrays.asList(deck));
           cards = ArrayUtils.subarray(deck, 0, numCards);
           cnt = 0;

           outer:
           for (int i = 0; i < cards.length - 2; i++) {
               for (int j = i + 1; j < cards.length - 1; j++) {
                   for (int k = j + 1; k < cards.length; k++) {
                       if (validSet(cards[i], cards[j], cards[k])) {
                           if (cnt < target)
                               sets[cnt] = new Card[]{cards[i], cards[j], cards[k]};
                           if (++cnt > target) {
                               break outer;
                           }
                       }
                   }
               }
           }
       } while (cnt != target);

       Arrays.sort(cards);

       System.out.printf("GIVEN %d CARDS:\n\n", numCards);
       for (Card c : cards) {
           System.out.println(c);
       }
       System.out.println();

       System.out.println("FOUND " + target + " SETS:\n");
       for (Card[] set : sets) {
           for (Card c : set) {
               System.out.println(c);
           }
           System.out.println();
       }
   }

   private static boolean validSet(Card c1, Card c2, Card c3) {
       int tot = 0;
       tot += (c1.c.val + c2.c.val + c3.c.val) % 3;
       tot += (c1.n.val + c2.n.val + c3.n.val) % 3;
       tot += (c1.s.val + c2.s.val + c3.s.val) % 3;
       tot += (c1.f.val + c2.f.val + c3.f.val) % 3;
       return tot == 0;
   }

}</lang> 

GIVEN 12 CARDS:

[Card: GREEN, ONE, DIAMOND, OPEN]
[Card: GREEN, TWO, SQUIGGLE, OPEN]
[Card: GREEN, THREE, DIAMOND, STRIPED]
[Card: GREEN, THREE, DIAMOND, OPEN]
[Card: PURPLE, ONE, DIAMOND, SOLID]
[Card: PURPLE, ONE, SQUIGGLE, SOLID]
[Card: PURPLE, TWO, SQUIGGLE, SOLID]
[Card: PURPLE, THREE, DIAMOND, OPEN]
[Card: RED, ONE, SQUIGGLE, STRIPED]
[Card: RED, ONE, OVAL, STRIPED]
[Card: RED, TWO, DIAMOND, STRIPED]
[Card: RED, THREE, OVAL, STRIPED]

FOUND 6 SETS:

[Card: GREEN, TWO, SQUIGGLE, OPEN]
[Card: PURPLE, ONE, DIAMOND, SOLID]
[Card: RED, THREE, OVAL, STRIPED]

[Card: GREEN, THREE, DIAMOND, OPEN]
[Card: RED, ONE, OVAL, STRIPED]
[Card: PURPLE, TWO, SQUIGGLE, SOLID]

[Card: GREEN, THREE, DIAMOND, OPEN]
[Card: PURPLE, ONE, DIAMOND, SOLID]
[Card: RED, TWO, DIAMOND, STRIPED]

[Card: RED, ONE, SQUIGGLE, STRIPED]
[Card: RED, THREE, OVAL, STRIPED]
[Card: RED, TWO, DIAMOND, STRIPED]

[Card: RED, ONE, OVAL, STRIPED]
[Card: PURPLE, ONE, SQUIGGLE, SOLID]
[Card: GREEN, ONE, DIAMOND, OPEN]

[Card: GREEN, ONE, DIAMOND, OPEN]
[Card: RED, THREE, OVAL, STRIPED]
[Card: PURPLE, TWO, SQUIGGLE, SOLID]

PARI/GP

<lang parigp>dealraw(cards)=vector(cards,i,vector(4,j,1<<random(3))); howmany(a,b,c)=hammingweight(bitor(a,bitor(b,c))); name(v)=Str(["red","green",0,"purple"][v[1]],", ",["oval","squiggle",0,"diamond"][v[2]],", ",["one","two",0,"three"][v[3]],", ",["solid","open",0,"striped"][v[4]]); check(D,sets)={ 

 my(S=List());
 for(i=1,#D-2,for(j=i+1,#D-1,for(k=j+1,#D,
   for(x=1,4,
     if(howmany(D[i][x],D[j][x],D[k][x])==2,next(2))
   );
   listput(S,[i,j,k]);
   if(#S>sets,return(0))
 )));
 if(#S==sets,Vec(S),0)

}; deal(cards,sets)={ 

 my(v,s);
 until(s,
   s=check(v=dealraw(cards),sets)
 );
 v=apply(name,v);
 for(i=1,cards,print(v[i]));
 for(i=1,sets,
   print("Set #"i);
   for(j=1,3,print("  "v[s[i][j]]))
 )

}; deal(9,4) deal(12,6)</lang>

Output:
green, diamond, one, open
purple, squiggle, three, solid
green, squiggle, two, striped
green, oval, one, striped
purple, oval, two, striped
purple, oval, one, open
red, squiggle, one, open
green, squiggle, one, solid
red, diamond, three, solid
Set #1
  green, diamond, one, open
  green, oval, one, striped
  green, squiggle, one, solid
Set #2
  green, diamond, one, open
  purple, oval, one, open
  red, squiggle, one, open
Set #3
  purple, squiggle, three, solid
  green, squiggle, two, striped
  red, squiggle, one, open
Set #4
  green, squiggle, two, striped
  purple, oval, one, open
  red, diamond, three, solid


purple, squiggle, three, open
red, oval, two, open
purple, oval, two, solid
green, squiggle, two, solid
purple, diamond, two, striped
purple, squiggle, two, solid
green, oval, two, striped
red, oval, one, striped
red, squiggle, two, striped
green, diamond, three, solid
green, diamond, two, open
purple, oval, one, open
Set #1
  red, oval, two, open
  purple, oval, two, solid
  green, oval, two, striped
Set #2
  red, oval, two, open
  green, squiggle, two, solid
  purple, diamond, two, striped
Set #3
  purple, oval, two, solid
  red, squiggle, two, striped
  green, diamond, two, open
Set #4
  green, squiggle, two, solid
  green, oval, two, striped
  green, diamond, two, open
Set #5
  purple, diamond, two, striped
  green, oval, two, striped
  red, squiggle, two, striped
Set #6
  red, squiggle, two, striped
  green, diamond, three, solid
  purple, oval, one, open

Perl 6

Works with: rakudo version 2013-02-11

This uses the combine routine from Combinations#Perl_6 task. The trick here is to allocate three different bits for each enum, with the result that the cards of a matching set OR together to produce a 4-digit octal number that contains only the digits 1, 2, 4, or 7. This OR is done by funny looking [+|], which is the reduction form of +|, which is the numeric bitwise OR. (Because Perl 6 stole the bare | operator for composing junctions instead.) <lang perl6>enum Color (red => 0o1000, green => 0o2000, purple => 0o4000); enum Count (one => 0o100, two => 0o200, three => 0o400); enum Shape (oval => 0o10, squiggle => 0o20, diamond => 0o40); enum Style (solid => 0o1, open => 0o2, striped => 0o4);

my @deck := (Color.enums X Count.enums X Shape.enums X Style.enums).tree;

sub MAIN($DRAW = 9, $GOAL = $DRAW div 2) { 

   my @combinations = combine(3, [^$DRAW]);
   my @draw;
   repeat until (my @sets) == $GOAL {
       @draw = @deck.pick($DRAW);
       my @bits = @draw.map: { [+] @^enums».value }
       @sets = gather for @combinations -> @c {
           take @draw[@c].item when /^ <[1247]>+ $/ given ( [+|] @bits[@c] ).base(8);
       }
   }
   say "Drew $DRAW cards:";
   show-cards @draw;
   for @sets.kv -> $i, @cards {
       say "\nSet {$i+1}:";
       show-cards @cards;
   }

}

sub show-cards(@c) { for @c -> $c { printf "  %-6s %-5s %-8s %s\n", $c».key } }</lang>

Output:
Drew 9 cards:
    red    two   diamond  striped
    purple one   squiggle solid
    purple three squiggle solid
    red    two   squiggle striped
    red    two   oval     striped
    green  one   diamond  open
    red    three diamond  solid
    green  three squiggle open
    purple two   diamond  striped

Set 1:
    red    two   diamond  striped
    red    two   squiggle striped
    red    two   oval     striped

Set 2:
    purple one   squiggle solid
    red    two   squiggle striped
    green  three squiggle open

Set 3:
    purple three squiggle solid
    red    two   oval     striped
    green  one   diamond  open

Set 4:
    green  one   diamond  open
    red    three diamond  solid
    purple two   diamond  striped

Perl

Translation of: Perl6

It's actually slightly simplified, since generating Enum classes and objects would be overkill for this particular task. <lang perl>#!perl use strict; use warnings;

  1. This code was adapted from the perl6 solution for this task.
  1. Each element of the deck is an integer, which, when written
  2. in octal, has four digits, which are all either 1, 2, or 4.

my $fmt = '%4o'; my @deck = grep sprintf($fmt, $_) !~ tr/124//c, 01111 .. 04444;

  1. Given a feature digit (1, 2, or 4), produce the feature's name.
  2. Note that digits 0 and 3 are unused.

my @features = map [split ' '], split /\n/,<<; ! red green  ! purple ! one two  ! three ! oval squiggle ! diamond ! solid open  ! striped

81 == @deck or die "There are ".@deck." cards (should be 81)";

  1. By default, draw 9 cards, but if the user
  2. supplied a parameter, use that.

my $draw = shift(@ARGV) || 9; my $goal = int($draw/2);

  1. Get the possible combinations of 3 indices into $draw elements.

my @combinations = combine(3, 0 .. $draw-1);

my @sets;

do { # Shuffle the first $draw elements of @deck. for my $i ( 0 .. $draw-1 ) { my $j = $i + int rand(@deck - $i); @deck[$i, $j] = @deck[$j, $i]; }

# Find all valid sets using the shuffled elements. @sets = grep { my $or = 0; $or |= $_ for @deck[@$_]; # If all colors (or whatever) are the same, then # a 1, 2, or 4 will result when we OR them together. # If they're all different, then a 7 will result. # If any other digit occurs, the set is invalid. sprintf($fmt, $or) !~ tr/1247//c; } @combinations;

# Continue until there are exactly $goal valid sets. } until @sets == $goal;

print "Drew $draw cards:\n"; for my $i ( 0 .. $#sets ) { print "Set ", $i+1, ":\n"; my @cards = @deck[ @{$sets[$i]} ]; for my $card ( @cards ) { my @octal = split //, sprintf '%4o', $card; my @f = map $features[$_][$octal[$_]], 0 .. 3; printf "  %-6s %-5s %-8s %s\n", @f; } }

exit;

  1. This function is adapted from the perl5i solution for the
  2. RosettaCode Combinations task.

sub combine { my $n = shift; return unless @_; return map [$_], @_ if $n == 1; my $head = shift; my @result = combine( $n-1, @_ ); unshift @$_, $head for @result; @result, combine( $n, @_ ); }

__END__ </lang>

Output:
Drew 12 cards:
Set 1:
    red    three oval     striped
    green  three diamond  striped
    purple three squiggle striped
Set 2:
    red    three oval     striped
    purple three squiggle open
    green  three diamond  solid
Set 3:
    purple one   diamond  striped
    red    three diamond  striped
    green  two   diamond  striped
Set 4:
    green  three diamond  striped
    green  three diamond  open
    green  three diamond  solid
Set 5:
    red    three diamond  striped
    green  three oval     solid
    purple three squiggle open
Set 6:
    green  two   diamond  striped
    purple three squiggle striped
    red    one   oval     striped

Python

<lang python>#!/usr/bin/python

from itertools import product, combinations from random import sample

    1. Major constants

features = [ 'green purple red'.split(), 

            'one two three'.split(),
            'oval diamond squiggle'.split(),
            'open striped solid'.split() ]

deck = list(product(list(range(3)), repeat=4))

dealt = 9

    1. Functions

def printcard(card): 

   print(' '.join('%8s' % f[i] for f,i in zip(features, card)))

def getdeal(dealt=dealt): 

   deal = sample(deck, dealt)
   return deal

def getsets(deal): 

   good_feature_count = set([1, 3])
   sets = [ comb for comb in combinations(deal, 3)
            if all( [(len(set(feature)) in good_feature_count)
                    for feature in zip(*comb)]
                  ) ]
   return sets

def printit(deal, sets): 

   print('Dealt %i cards:' % len(deal))
   for card in deal: printcard(card)
   print('\nFound %i sets:' % len(sets))
   for s in sets:
       for card in s: printcard(card)
       print()

if __name__ == '__main__': 

   while True:
       deal = getdeal()
       sets = getsets(deal)
       if len(sets) == dealt / 2:
          break
   printit(deal, sets)

</lang> Note: You could remove the inner square brackets of the 'if all( [...] )' part of the sets computation in the getsets function. It is a remnant of Python 2.7 debugging which gives access to the name feature. The code works on Python 3.X too, but not that access.

Output:
Dealt 9 cards:
   green    three squiggle    solid
   green    three squiggle     open
  purple      two squiggle    solid
   green      one  diamond    solid
     red    three     oval    solid
   green      two     oval    solid
     red      two     oval     open
  purple      one  diamond  striped
     red      two     oval    solid

Found 4 sets:
   green    three squiggle    solid
   green      one  diamond    solid
   green      two     oval    solid

   green    three squiggle    solid
     red      two     oval     open
  purple      one  diamond  striped

   green    three squiggle     open
  purple      one  diamond  striped
     red      two     oval    solid

  purple      two squiggle    solid
   green      one  diamond    solid
     red    three     oval    solid

Racket

<lang Racket>

  1. lang racket

(struct card [bits name])

(define cards 

 (for/list ([C '(red   green    purple )] [Ci '(#o0001 #o0002 #o0004)]
            #:when #t
            [S '(oval  squiggle diamond)] [Si '(#o0010 #o0020 #o0040)]
            #:when #t
            [N '(one   two      three  )] [Ni '(#o0100 #o0200 #o0400)]
            #:when #t
            [D '(solid open     striped)] [Di '(#o1000 #o2000 #o4000)])
   (card (bitwise-ior Ci Si Ni Di) (format "~a, ~a, ~a, ~a" C S N D))))

(define (nsubsets l n) 

 (cond [(zero? n) '(())] [(null? l) '()]
       [else (append (for/list ([l2 (nsubsets (cdr l) (- n 1))])
                       (cons (car l) l2))
                     (nsubsets (cdr l) n))]))

(define (set? cards) 

 (regexp-match? #rx"^[1247]*$"
                (number->string (apply bitwise-ior (map card-bits cards)) 8)))

(define (deal C S) 

 (define hand  (take (shuffle cards) C))
 (define 3sets (filter set? (nsubsets hand 3)))
 (cond [(not (= S (length 3sets))) (deal C S)]
       [else (printf "Dealt ~a cards:\n" C)
             (for ([c hand]) (printf "  ~a\n" (card-name c)))
             (printf "\nContaining ~a sets:\n" S)
             (for ([set 3sets])
               (for ([c set]) (printf "  ~a\n" (card-name c)))
               (newline))]))

(deal 9 4) (deal 12 6) </lang>

Ruby

Brute force. <lang ruby>COLORS = %i(red green purple) #use [:red, :green, :purple] in Ruby < 2.0 SYMBOLS = %i(oval squiggle diamond) NUMBERS = %i(one two three) SHADINGS = %i(solid open striped) FEATURES = [COLORS, SYMBOLS, NUMBERS, SHADINGS]

@hand_size = 9 @num_sets_goal = 4

  1. create an enumerator which deals all combinations of @hand_size cards

@dealer = FEATURES[0].product(*FEATURES[1..-1]).shuffle.combination(@hand_size)

def get_all_sets(hand) 

 hand.combination(3).select do |candidate|
   grouped_features = candidate.flatten.group_by{|f| f}
   grouped_features.values.none?{|v| v.size == 2}
 end

end

def get_puzzle_and_answer 

 sets = []
 until sets.size == @num_sets_goal do
   hand = @dealer.next
   sets = get_all_sets(hand)
 end
 [hand, sets]

end

def print_cards(cards) 

 cards.each{|card| puts card.join(", ")}
 puts

end

puzzle, sets = get_puzzle_and_answer puts "Dealt #{puzzle.size} cards:" print_cards(puzzle) puts "Containing #{sets.size} sets:" sets.each{|set| print_cards(set)}</lang>

Output:
Dealt 9 cards:
purple, diamond, one, open
red, oval, two, striped
purple, oval, two, open
purple, oval, one, striped
purple, diamond, two, open
green, squiggle, two, open
red, squiggle, three, striped
purple, squiggle, one, solid
green, oval, two, solid

Containing 4 sets:
purple, diamond, one, open
purple, oval, one, striped
purple, squiggle, one, solid

purple, diamond, one, open
red, squiggle, three, striped
green, oval, two, solid

red, oval, two, striped
purple, oval, two, open
green, oval, two, solid

green, squiggle, two, open
red, squiggle, three, striped
purple, squiggle, one, solid

Tcl

The principle behind this code is that the space of possible solutions is a substantial proportion of the space of possible hands, so picking a random hand and verifying that it is a solution, repeating until that verification succeeds, is a much quicker way to find a solution than a systematic search. It also makes the code substantially simpler. <lang tcl># Generate random integer uniformly on range [0..$n-1] proc random n {expr {int(rand() * $n)}}

  1. Generate a shuffled deck of all cards; the card encoding was stolen from the
  2. Perl6 solution. This is done once and then used as a constant. Note that the
  3. rest of the code assumes that all cards in the deck are unique.

set ::AllCards [apply {{} { 

   set cards {}
   foreach color {1 2 4} {

foreach symbol {1 2 4} { foreach number {1 2 4} { foreach shading {1 2 4} { lappend cards [list $color $symbol $number $shading] } } } 

   }
   # Knuth-Morris-Pratt shuffle (not that it matters)
   for {set i [llength $cards]} {$i > 0} {} {

set j [random $i] set tmp [lindex $cards [incr i -1]] lset cards $i [lindex $cards $j] lset cards $j $tmp 

   }
   return $cards

}}]

  1. Randomly pick a hand of cards from the deck (itself in a global for
  2. convenience).

proc drawCards n { 

   set cards $::AllCards;    # Copies...
   for {set i 0} {$i < $n} {incr i} {

set idx [random [llength $cards]] lappend hand [lindex $cards $idx] set cards [lreplace $cards $idx $idx] 

   }
   return $hand

}

  1. Test if a particular group of three cards is a valid set

proc isValidSet {a b c} { 

   expr {

([lindex $a 0]|[lindex $b 0]|[lindex $c 0]) in {1 2 4 7} && ([lindex $a 1]|[lindex $b 1]|[lindex $c 1]) in {1 2 4 7} && ([lindex $a 2]|[lindex $b 2]|[lindex $c 2]) in {1 2 4 7} && ([lindex $a 3]|[lindex $b 3]|[lindex $c 3]) in {1 2 4 7} 

   }

}

  1. Get all unique valid sets of three cards in a hand.

proc allValidSets {hand} { 

   set sets {}
   for {set i 0} {$i < [llength $hand]} {incr i} {

set a [lindex $hand $i] set hand [set cards2 [lreplace $hand $i $i]] for {set j 0} {$j < [llength $cards2]} {incr j} { set b [lindex $cards2 $j] set cards2 [set cards3 [lreplace $cards2 $j $j]] foreach c $cards3 { if {[isValidSet $a $b $c]} { lappend sets [list $a $b $c] } } } 

   }
   return $sets

}

  1. Solve a particular version of the set puzzle, by picking random hands until
  2. one is found that satisfies the constraints. This is usually much faster
  3. than a systematic search. On success, returns the hand found and the card
  4. sets within that hand.

proc SetPuzzle {numCards numSets} { 

   while 1 {

set hand [drawCards $numCards] set sets [allValidSets $hand] if {[llength $sets] == $numSets} { break } 

   }
   return [list $hand $sets]

}</lang> Demonstrating: <lang tcl># Render a hand (or any list) of cards (the "."s are just placeholders). proc PrettyHand {hand {separator \n}} { 

   set Co {. red green . purple}
   set Sy {. oval squiggle . diamond}
   set Nu {. one two . three}
   set Sh {. solid open . striped}
   foreach card $hand {

lassign $card co s n sh lappend result [format "(%s,%s,%s,%s)" \ [lindex $Co $co] [lindex $Sy $s] [lindex $Nu $n] [lindex $Sh $sh]] 

   }
   return $separator[join $result $separator]

}

  1. Render the output of the Set Puzzle solver.

proc PrettyOutput {setResult} { 

   lassign $setResult hand sets
   set sep "\n   "
   puts "Hand (with [llength $hand] cards) was:[PrettyHand $hand $sep]"
   foreach s $sets {

puts "Found set [incr n]:[PrettyHand $s $sep]" 

   }

}

  1. Demonstrate on the two cases

puts "=== BASIC PUZZLE =========" PrettyOutput [SetPuzzle 9 4] puts "=== ADVANCED PUZZLE ======" PrettyOutput [SetPuzzle 12 6]</lang>

Sample output:
=== BASIC PUZZLE =========
Hand (with 9 cards) was:
   (purple,squiggle,one,solid)
   (green,diamond,two,striped)
   (green,oval,two,striped)
   (purple,diamond,three,striped)
   (red,oval,three,open)
   (green,squiggle,three,solid)
   (red,squiggle,one,solid)
   (red,oval,one,solid)
   (purple,oval,three,open)
Found set 1:
   (purple,squiggle,one,solid)
   (green,diamond,two,striped)
   (red,oval,three,open)
Found set 2:
   (green,oval,two,striped)
   (purple,oval,three,open)
   (red,oval,one,solid)
Found set 3:
   (red,oval,three,open)
   (green,squiggle,three,solid)
   (purple,diamond,three,striped)
Found set 4:
   (red,squiggle,one,solid)
   (green,diamond,two,striped)
   (purple,oval,three,open)
=== ADVANCED PUZZLE ======
Hand (with 12 cards) was:
   (green,diamond,two,open)
   (red,diamond,one,solid)
   (purple,diamond,one,solid)
   (red,squiggle,two,open)
   (green,diamond,three,open)
   (red,oval,two,striped)
   (red,diamond,two,solid)
   (purple,diamond,two,striped)
   (purple,diamond,three,open)
   (purple,diamond,three,striped)
   (purple,oval,three,open)
   (purple,squiggle,two,striped)
Found set 1:
   (green,diamond,two,open)
   (red,diamond,one,solid)
   (purple,diamond,three,striped)
Found set 2:
   (green,diamond,two,open)
   (purple,diamond,two,striped)
   (red,diamond,two,solid)
Found set 3:
   (purple,diamond,one,solid)
   (purple,diamond,three,open)
   (purple,diamond,two,striped)
Found set 4:
   (purple,diamond,one,solid)
   (purple,oval,three,open)
   (purple,squiggle,two,striped)
Found set 5:
   (green,diamond,three,open)
   (red,diamond,one,solid)
   (purple,diamond,two,striped)
Found set 6:
   (red,diamond,two,solid)
   (red,oval,two,striped)
   (red,squiggle,two,open)
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