c# - 检查二维数组的对角线 - 欧拉数 11

Question

所以目标是在一个20X20的方格上，下，左，右，对角线上，求出4个连续数的最大乘积。所以我把所有的代码都写在这里，但我知道我的结果是不正确的，因为我已经手工检查过了。似乎我的程序的对角线检查代码不正确，因为我的垂直和水平检查已经产生了我现在的答案。澄清一下，我不希望有人在这里编写自己的代码，而是简单地解释我的错误所在。任何答案将不胜感激。

public long Prob_11()
    {
        int x = 0;
        int y = 0;
        int z = 0;
        long prod = 0;
        long max = 0;
        //creates a 2 dimensional array: grid, which will save all our values.
        int[,] grid = new int[20,20] { { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, 
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
        //creates an array with all of the required values
        int[] array = new int[] {
        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
        };
        //for each point in "grid" assign the next value
        for (x = 0; x <= 19; x++)
        {
            for (y = 0; y <= 19; y++)
            {
                int b = array[z];
                grid[x, y] = b;
                z++;
            }
        }
        for (x=0; x < 20; x++)
        {
            for (y=0; y < 17; y++)
            {
                // check all horizontal values
                prod = grid[x, y] * grid[x, y + 1] * grid[x, y + 2] * grid[x, y + 3];
                //if the product is greater than the max product, it is the new max
                if (prod > max) max = prod;
                // check all the vertical values
                prod = grid[y, x] * grid[y + 1, x] * grid[y + 2, x] * grid[y + 3, x];
                if (prod > max) max = prod;
            }
        }
        for (x = 0; x < 17; x++)
        {
            for (y = 0; y < 17; y++)
            {
                //check diagonals left to right
                prod = grid[x, y] * grid[x + 1, y + 1] * grid[x + 2, y + 2] * grid[x + 3, y + 3];
                if (prod > max) max = prod;
            }
        }
        for (x = 19; x > 2; x--)
        {
            for (y = 19; y > 2; y--)
            {
                // check diagonals right to left
                prod = grid[x, y] * grid[x - 1, y - 1] * grid[x - 2, y - 2] * grid[x - 3, y - 3];
                if (prod > max) max = prod;
            }
        }
        //return the max product
        return max;

    }
    static void Main(string[] args)
    {
        Program prog = new Program();
        Console.WriteLine(prog.Prob_11());
        Console.ReadLine();
    }
}

Answer 1

你的对角线检查都是同一个方向。 grid[x+1, y+1]和 grid[x-1,y-1]都在同一条对角线上，从左上到右下。对于另一条对角线，您需要添加到一个索引并从另一个索引中减去。

如果i是偏移量，0-3，那么一条对角线就是:

grid[x+i, y+i]

另一条对角线是:

grid[x+i, y-i]

您必须调整最终的 for循环到正确的索引。