题解 | #[NOIP2002 普及组] 过河卒#

#include <iostream>
#include <vector>
using namespace std;

void DP13() {
    int n, m, x, y;
    while (cin >> n >> m >> x >> y) {
        vector<long long> row(m + 5, 0);//注意这个一定要给long long类型
        vector<vector<long long>> dps(n + 5, row);//dps表示给定坐标点的路径数
        //初始化边界条件
        for (int i = 1; i < m + 1; i++) {
            if (i == y && x == 0) {
                dps[0][i] = 0;
                break;
            }
            if (abs(x) + abs(i - y) == 3 && x != 0 && y != i) {
                dps[0][i] = 0;
                break;
            }
            dps[0][i] = 1;
        }
        for (int i = 1; i < n + 1; i++) {
            if (i == x && y == 0) {
                dps[i][0] = 0;
                break;
            }
            if (abs(y) + abs(i - x) == 3 && x != i && y != 0) {
                dps[i][0] = 0;
                break;
            }
            dps[i][0] = 1;
        }
        //迭代
        for (int i = 1; i < m + 1; i++) {
            for (int j = 1; j < n + 1; j++) {
                if (i == y && j == x) {
                    dps[j][i] = 0;
                    continue;
                }
                if (abs(i - y) + abs(j - x) == 3 && i != y && j != x) {
                    dps[j][i] = 0;
                    continue;
                }
                dps[j][i] = dps[j - 1][i] + dps[j][i - 1];
            }
        }
        //输出
        cout << dps[n][m] << endl;
    }
}
int main() {
    DP13();
}
// 64 位输出请用 printf("%lld")