プロジェクトオイラー問11

Problem 11 「格子内の最大の積」 †

上の 20×20 の格子のうち, 対角線に沿って4つの数字が赤くマークされている.

08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

それらの数字の積は 26 × 63 × 78 × 14 = 1788696 となる.

上の 20×20 の格子のうち, 上下左右斜めのいずれかの方向で連続する4つの数字の積のうち最大のものはいくつか?

http://odz.sakura.ne.jp/projecteuler/index.php?cmd=read&page=Problem%2011

解法

Ｐｒｏｌｏｇ言語。

マトリックス化するか丁寧に全パターンを記述するかは好みが分かれるらしい。

今回は丁寧に全パターンを記述してみました。

max([],Max,Max):-!.

max([X|Xs],Max,Result):-

    X>Max,

    !,

    max(Xs,X,Result).

max([_|Xs],Max,Result):-

    !,

    max(Xs,Max,Result).

search2([_,_,_],_,_,_,Ans,Ans):-!.

search2([D11,D12,D13,D14|Rest1],

    [D21,D22,D23,D24|Rest2],

    [D31,D32,D33,D34|Rest3],

    [D41,D42,D43,D44|Rest4],

    Ans,Result):-

    !,

    S1 is D11*D12*D13*D14,

    S2 is D11*D21*D31*D41,

    S3 is D14*D23*D32*D41,

    S4 is D11*D22*D33*D44,

    max([S1,S2,S3,S4,Ans],0,Ans1),

    search2([D12,D13,D14|Rest1],[D22,D23,D24|Rest2],

        [D32,D33,D34|Rest3],[D42,D43,D44|Rest4],Ans1,Result).

slideRow([_,_,_],Ans):-!,write(Ans).

slideRow([R1,R2,R3,R4|Rest],Ans):-

    search2(R1,R2,R3,R4,Ans,Ans1),

    slideRow([R2,R3,R4|Rest],Ans1).

main11:-

    Map=[[08,02,22,97,38,15,00,40,00,75,04,05,07,78,52,12,50,77,91,08],

         [49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,04,56,62,00],

         [81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,03,49,13,36,65],

         [52,70,95,23,04,60,11,42,69,24,68,56,01,32,56,71,37,02,36,91],

         [22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80],

         [24,47,32,60,99,03,45,02,44,75,33,53,78,36,84,20,35,17,12,50],

         [32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70],

         [67,26,20,68,02,62,12,20,95,63,94,39,63,08,40,91,66,49,94,21],

         [24,55,58,05,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72],

         [21,36,23,09,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95],

         [78,17,53,28,22,75,31,67,15,94,03,80,04,62,16,14,09,53,56,92],

         [16,39,05,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57],

         [86,56,00,48,35,71,89,07,05,44,44,37,44,60,21,58,51,54,17,58],

         [19,80,81,68,05,94,47,69,28,73,92,13,86,52,17,77,04,89,55,40],

         [04,52,08,83,97,35,99,16,07,97,57,32,16,26,26,79,33,27,98,66],

         [88,36,68,87,57,62,20,72,03,46,33,67,46,55,12,32,63,93,53,69],

         [04,42,16,73,38,25,39,11,24,94,72,18,08,46,29,32,40,62,76,36],

         [20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,04,36,16],

         [20,73,35,29,78,31,90,01,74,31,49,71,48,86,81,16,23,57,05,54],

         [01,70,54,71,83,51,54,69,16,92,33,48,61,43,52,01,89,19,67,48]],

    slideRow(Map,0).