马兰过河卒

 

 二、设计思想

　　首先将所有点设置为可通行，将控制点设置为不可通行。因为只可以向下或者向右行走，所以要想到达目标点只需要到达其左边的点或者上边的点，以此类推，计算从起点到达中间任何一个点的路径条数，并用数组tripnum[][]保存到达这个点的路径条数。

三、代码

#include<iostream>
#include<cstdio>
using namespace std;
int main()
{
    int a[9] = { 0,-1,-1,-2,-2,1,1,2,2 };
    int b[9] = { 0,2,-2,1,-1,2,-2,1,-1 };
    int map[16][16] = { 0 };
    long long tripnum[16][16] = { 0 };
    int n, m, x, y;
    scanf_s("%d %d %d %d", &n, &m, &x, &y);
    for (int i = 0; i < 16; i++)
        for (int j = 0; j < 16; j++)
            map[i][j] = 1;
    for (int i = 0; i < 9; i++)
    {
        if (x + a[i] <= 15 && x + a[i] >= 0 && y + b[i] <= 15 && y + b[i] >= 0)
            map[x + a[i]][y + b[i]] = 0;
    }
    for (int i = 0; i < 16; i++)
    {
        if (map[0][i] == 1)
        {
            tripnum[0][i] = 1;
        }
        else
            break;
    }
    for (int i = 0; i < 16; i++)
    {
        if (map[i][0] == 1)
        {
            tripnum[i][0] = 1;
        }
        else
            break;
    }
    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= m; j++)
        {
            if (map[i][j] == 1)
                tripnum[i][j] = tripnum[i - 1][j] +
                tripnum[i][j - 1];
        }
    }
    printf("%lld", tripnum[n][m]);
    return 0;
}