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holmescn

½ð³æ (ÕýʽдÊÖ)

[½»Á÷] Euler ¹¤³Ì µÚʮһÌ⣺ÏàÁÚÔªËØ³Ë»ý×î´ó ÒÑÓÐ4È˲ÎÓë

In the 20x20 grid below, four numbers along a diagonal line have been marked in red.

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
The product of these numbers is 26x63x78x14 = 1788696.

What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 20x20 grid?

¸øÁËÒ»¸ö20x20µÄÁ½Î»Êý¾ØÕ󣬯äÖеĺì×Ö²¿·ÖµÄ»ýΪ£º
26x63x78x14=1788696
ÄÇô£¬ÈÎÒâ·½ÏòÉÏ£¨ÉÏ¡¢Ï¡¢×ó¡¢ÓÒ¡¢¶Ô½Ç£©4¸öÏàÁÚµÄÊýµÄ×î´ó³Ë»ýÊǶàÉÙ£¿

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holmescn

½ð³æ (ÕýʽдÊÖ)

¡ï ¡ï ¡ï
ÓàÔó³É(½ð±Ò+3, ³ÌÐòÇ¿Ìû+1): ¹ÄÀø½»Á÷£¡ 2011-05-18 17:14:09
дÁ˸öFortran°æµÄ£¬ºÃÏñ½á¹û²»Ò»ÑùÁË¡£²»ÖªµÀÔõô»ØÊ¡£Ö÷ÒªÊǶԽÇÉϵļÆË㣬²»ÖªµÀÊDz»ÊÇËã¶ÔÁ˰¡£¡
CODE:
Program euler11
    Implicit None
    Integer, Dimension(20,20) :: Matrix
    Integer :: M1 = 0, M2 = 0, M3 = 0
    Integer :: M = 0
    Integer :: Prod
    Integer :: I, J, K

    Open(100, File="matrix.txt")
    Do I = 1, 20
        Read(100, "(20(I2,X), I2)"), Matrix(I, :)
    EndDo
    Close(100)

    Do I = 1, 20 - 3
        M1 = MaxVal(Product(Matrix(I:I+3, :), 1))
        M2 = MaxVal(Product(Matrix(:, I:I+3), 2))
        M = Max(M1, M2, M)
    EndDo

    Do I = 1, 20 - 3
        Do J = 1, 20 - 3
            Prod = Product((/(Matrix(I+K, J+K), K=0,3)/))
            M3 = Max(M3, Prod)
        EndDo
    EndDo
    Print *, Max(M, M3)

EndProgram euler11

ÎÒÕâ¶ùµÃ51267216

[ Last edited by holmescn on 2011-5-18 at 16:16 ]
9Â¥2011-05-18 16:14:58
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huycwork

½ð³æ (ÖøÃûдÊÖ)

¡ï ¡ï
Сľ³æ(½ð±Ò+0.5):¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
ÓàÔó³É(½ð±Ò+1): ¹ÄÀøÌÖÂÛ£¡ 2011-05-16 17:47:24
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2Â¥2011-05-16 15:23:04
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libralibra

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

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¡ï ¡ï ¡ï ¡ï
Сľ³æ(½ð±Ò+0.5):¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
ÓàÔó³É(½ð±Ò+3, ³ÌÐòÇ¿Ìû+1): лл²ÎÓë»î¶¯£¡ 2011-05-16 17:47:46
¾ØÕóÔËËã,matlabÇ¿Ïî
CODE:
%% What is the greatest product of four adjacent numbers in any direction
% (up, down, left, right, or diagonally) in the 20¡Á20 grid?
function result = euler11()
tic;
s = [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];
[m,n] = size(s);
result = 0;
for i=1:m-3
    for j=1:n-3
        curgrid = s(i:i+3,j:j+3);
        result = max([result,max([max(prod(curgrid,1)), ... % row -
                    max(prod(curgrid,2)), ... % column |
                    prod(diag(curgrid)), ... % diag \
                    prod(diag(imrotate(curgrid,90)))])]); % sub diag /
    end
end
toc;
end

½á¹û,ʱ¼ä
CODE:
% Elapsed time is 0.158644 seconds.
% ans =
%     70600674

matlab/VB/python/c++/Javaд³ÌÐòÇë·¢QQÓʼþ:790404545@qq.com
3Â¥2011-05-16 15:59:44
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

huycwork

½ð³æ (ÖøÃûдÊÖ)

¡ï
Сľ³æ(½ð±Ò+0.5):¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
ÒýÓûØÌû:
Originally posted by libralibra at 2011-05-16 15:59:44:
¾ØÕóÔËËã,matlabÇ¿Ïî

[code] %% What is the greatest product of four adjacent numbers in any direction
% (up, down, left, right, or diagonally) in the 20¡Á20 grid?
function result = euler11()
...

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