Program1

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本文提供了解决Project Euler网站上第11题的算法，该题要求在20×20网格中找到四个相邻数字（同一方向）的最大乘积。文中附有C++代码实现。

解题链接：http://222.197.91.46/test/program2/

这题光有问题没有题目，出题失误

真正的题目链接：https://projecteuler.net/problem=11

（顺便说一下 projecteuler.net 这个网站，这个网站类似ACM，只不过偏向于用算法解决数学问题）

In the 20×20 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 26 × 63 × 78 × 14 = 1788696.

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

我随便copy一个c++的算法，那个网站还有各种各样的语言实现

<span style="font-size:24px;color:#FF0000;">#include<iostream>

using namespace std;

int main()
{

        int A[20][20] = { {8,02,22,97,38,15,00,40,00,75,04,05,07,78,52,12,50,77,91,8},
                {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},
                {67,26,20,68,02,62,12,20,95,63,94,39,63,8,40,91,66,49,94,21},
                {24,55,58,05,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72},
                {21,36,23,9,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95},
                {78,17,53,28,22,75,31,67,15,94,03,80,04,62,16,14,9,53,56,92},
                {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},
                {04,52,8,83,97,35,99,16,07,97,57,32,16,26,26,79,33,27,98,66},
                {88,36,68,87,57,62,20,72,03,46,33,67,46,55,12,32,63,93,53,69},
                {04,42,16,73,38,25,39,11,24,94,72,18,8,46,29,32,40,62,76,36},
                {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} };
        int B[3];
        string D;
        int M, N, V, H, D1, D2;
        M = 0;
        for(int i = 0; i <= 19; i++)
        for(int j = 0; j <= 19; j++)
        {
                V = 0;
                H = 0;
                D1 = 0;
                D2 = 0;
                if(i <= 16)
                {
                        V = A[i][j]*A[i+1][j]*A[i+2][j]*A[i+3][j];
                        if(j <= 16)
                        {
                                D1 = A[i][j]*A[i+1][j+1]*A[i+2][j+2]*A[i+3][j+3];
                                D2 = A[i][19-j]*A[i+1][18-j]*A[i+2][17-j]*A[i+3][16-j];
                        }
                }
                if(j <= 16)
                        H = A[i][j]*A[i][j+1]*A[i][j+2]*A[i][j+3];
                N = M;
                if(V > M) { M = V; D = "V"; }
                if(H > M) {M = H; D = "H"; }
                if(D1 > M) {M = D1; D = "D1"; }
                if(D2 > M) {M = D2; D = "D2"; }
                if(N != M) { B[0] = i + 1; B[1] = 20 - j;}
        }
        cout << "The greatest product of four numbers in a straight line is " << M << ". It begins at row " << B[0] << ", column " << B[1] << " and goes in direction " << D << "\n";
        return 0;
}</span>

将计算结果输入得到KEY:IL0V3Pr0Gr4m