C++ ProjectEuler #11

Question

我正在尝试解决 ProjectEuler.net 上的第 11 个问题。本题的目标是在任意方向(上、下、右、左、对角线)的 4 个相邻数字的 20x20 网格中找到最大的产品。

我正在使用 BigInteger 库，因为我不知道这些数字有多大而且我不想溢出 - 但我认为这可能是问题所在。每次我重新启动程序时，我都会得到不同的答案。 :/我还尝试使用 unsigned long long int 只是为了看看会发生什么 - 答案保持不变。

这是代码(没有什么复杂的；我只是测试网格中的每个元素，看它是否在任何方向上有 3 个相邻数字，计算乘积，如果它大于前一个，则将其设置为新的最大的。最后我打印最大的产品。):

//NO.11
#include <iostream>
#include <BigIntegerLibrary.hh>
#include <windows.h>

int main()
{
    int grid[20][20] =
    {
        { 8,  2, 22, 97, 38, 15,  0, 40,  0, 75,  4,  5,  7, 78, 52, 12, 50, 77, 91,  8},
        {49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48,  4, 56, 62,  0},
        {81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30,  3, 49, 13, 36, 65},
        {52, 70, 95, 23,  4, 60, 11, 42, 69, 24, 68, 56, 01, 32, 56, 71, 37,  2, 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,  2, 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,  2, 62, 12, 20, 95, 63, 94, 39, 63,  8, 40, 91, 66, 49, 94, 21},
        {24, 55, 58,  5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72},
        {21, 36, 23,  9, 75,  0, 76, 44, 20, 45, 35, 14,  0, 61, 33, 97, 34, 31, 33, 95},
        {78, 17, 53, 28, 22, 75, 31, 67, 15, 94,  3, 80,  4, 62, 16, 14,  9, 53, 56, 92},
        {16, 39,  5, 42, 96, 35, 31, 47, 55, 58, 88, 24,  0, 17, 54, 24, 36, 29, 85, 57},
        {86, 56,  0, 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,  4, 89, 55, 40},
        { 4, 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,  3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69},
        { 4, 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,  1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57,  5, 54},
        { 1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52,  1, 89, 19, 67, 48}
    };

    BigInteger biggestProduct = 0;
    //unsigned long long int biggestProduct = 0;

    for (int row = 0; row < 20; row++)
    {
        for (int col = 0; col < 20; col++)
        {
            BigInteger product;
            //unsigned long long int product;

            //std::cout << grid[row][col] << ":" << std::endl; system("pause>nul");

            //UP
            if ((row-1 >= 0) && (row-2 >= 0) && (row-3 >= 0))
            {
                product = grid[row][col] * grid[row-1][col] * grid[row-2][col] * grid[row-3][col];
                //std::cout << "  U: " << grid[row][col] << "*" << grid[row-1][col] << "*" << grid[row-2][col] << "*" << grid[row-3][col] << "=  \t" << product << std::endl; system("pause>nul");
                if (product > biggestProduct)
                    biggestProduct = product;
            }
            //DOWN
            if ((row+1 >= 0) && (row+2 >= 0) && (row+3 >= 0))
            {
                product = grid[row][col] * grid[row+1][col] * grid[row+2][col] * grid[row+3][col];
                //std::cout << "  D: " << grid[row][col] << "*" << grid[row+1][col] << "*" << grid[row+2][col] << "*" << grid[row+3][col] << "=  \t" << product << std::endl; system("pause>nul");
                if (product > biggestProduct)
                    biggestProduct = product;
            }
            //RIGHT
            if ((col+1 >= 0) && (col+2 >= 0) && (col+3 >= 0))
            {
                product = grid[row][col] * grid[row][col+1] * grid[row][col+2] * grid[row][col+3];
                //std::cout << "  R: " << grid[row][col] << "*" << grid[row][col+1] << "*" << grid[row][col+2] << "*" << grid[row][col+3] << "=  \t" << product << std::endl; system("pause>nul");
                if (product > biggestProduct)
                    biggestProduct = product;
            }
            //LEFT
            if ((col-1 >= 0) && (col-2 >= 0) && (col-3 >= 0))
            {
                product = grid[row][col] * grid[row][col-1] * grid[row][col-2] * grid[row][col-3];
                //std::cout << "  L: " << grid[row][col] << "*" << grid[row][col-1] << "*" << grid[row][col-2] << "*" << grid[row][col-3] << "=  \t" << product << std::endl; system("pause>nul");
                if (product > biggestProduct)
                    biggestProduct = product;
            }

            //UP-RIGHT
            if ((row-1 >= 0) && (row-2 >= 0) && (row-3 >= 0) && (col+1 >= 0) && (col+2 >= 0) && (col+3 >= 0))
            {
                product = grid[row][col] * grid[row-1][col+1] * grid[row-2][col+2] * grid[row-3][col+3];
                //std::cout << "  U-R: " << grid[row][col] << "*" << grid[row-1][col+1] << "*" << grid[row-2][col+2] << "*" << grid[row-3][col+3] << "=  \t" << product << std::endl; system("pause>nul");
                if (product > biggestProduct)
                    biggestProduct = product;
            }

            //DOWN-RIGHT
            if ((row+1 >= 0) && (row+2 >= 0) && (row+3 >= 0) && (col+1 >= 0) && (col+2 >= 0) && (col+3 >= 0))
            {
                product = grid[row][col] * grid[row+1][col+1] * grid[row+2][col+2] * grid[row+3][col+3];
                //std::cout << "  D-R: " << grid[row][col] << "*" << grid[row+1][col+1] << "*" << grid[row+2][col+2] << "*" << grid[row+3][col+3] << "=  \t" << product << std::endl; system("pause>nul");
                if (product > biggestProduct)
                    biggestProduct = product;
            }

            //DOWN-LEFT
            if ((row+1 >= 0) && (row+2 >= 0) && (row+3 >= 0) && (col-1 >= 0) && (col-2 >= 0) && (col-3 >= 0))
            {
                product = grid[row][col] * grid[row+1][col-1] * grid[row+2][col-2] * grid[row+3][col-3];
                //std::cout << "  D-L: " << grid[row][col] << "*" << grid[row+1][col-1] << "*" << grid[row+2][col-2] << "*" << grid[row+3][col-3] << "=  \t" << product << std::endl; system("pause>nul");
                if (product > biggestProduct)
                    biggestProduct = product;
            }

            //UP-LEFT
            if ((row-1 >= 0) && (row-2 >= 0) && (row-3 >= 0) && (col-1 >= 0) && (col-2 >= 0) && (col-3 >= 0))
            {
                product = grid[row][col] * grid[row-1][col-1] * grid[row-2][col-2] * grid[row-3][col-3];
                //std::cout << "  U-L: " << grid[row][col] << "*" << grid[row-1][col-1] << "*" << grid[row-2][col-2] << "*" << grid[row-3][col-3] << "=  \t" << product << std::endl; system("pause>nul");
                if (product > biggestProduct)
                    biggestProduct = product;
            }
        }
    }

    std::cout << biggestProduct;

    return 0;
}

谁知道这是怎么回事？

谢谢，通图尼。

Answer 1

你的问题是你的范围检查:

例子:

// DOWN
if ((row+1 >= 0) && (row+2 >= 0) && (row+3 >= 0))

应该是:

// DOWN
//if ((row+1 < 20 ) && (row+2 < 20 ) && (row+3 < 20 ))
//which still contains redundant comparisons (as pointed out by Blastfurnace), 
//and thus can be can be simplified to : 
if( row + 3 < 20 ) 

如果您在程序的每次运行中都有随机结果，并且您没有使用并发、随机数生成器或类似的东西，那么随机性很可能是由未定义的行为引起的，例如读取未分配的内存或使用未初始化的变量进行读取。