思路还是DP，用memo做备忘录，处理重叠子问题。

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.StreamTokenizer;
import java.util.Arrays;

/**
 * @author iceewei
 * @Description: P1002 [NOIP2002 普及组] 过河卒
 * @date 2024/12/12
 */
public class Main {

    long[][] memo;
    private int ans;
    private int hX, hY;
    private int destX, destY;
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StreamTokenizer st = new StreamTokenizer(br);
        Main p1002 = new Main();
        for (int i = 0; i < 2; i++) {
            st.nextToken();
            int x = (int)st.nval;
            st.nextToken();
            int y = (int)st.nval;
            if (i == 0) {
                p1002.destX = x;
                p1002.destY = y;
            } else {
                p1002.hX = x;
                p1002.hY = y;
            }
        }
        p1002.memo = new long[p1002.destX + 1][p1002.destY + 1];
        for (int i = 0; i < p1002.destX + 1; i++) {
            Arrays.fill(p1002.memo[i], -1);
        }
        p1002.memo[0][0] = 1;
        // 判断是否出界、是否被马袭击
        int[][] horseDirs = new int[][]{{1, 2}, {1, -2},{-1, 2}, {-1, -2}, {2, 1}, {2, -1}, {-2, 1}, {-2, -1}};
        p1002.memo[p1002.hX][p1002.hY] = 0;
        int horseStepX, horseStepY;
        for (int i = 0; i < horseDirs.length; i++) {
            horseStepX = p1002.hX + horseDirs[i][0];
            horseStepY = p1002.hY + horseDirs[i][1];
            if (!p1002.exceedBorder(horseStepX, horseStepY)) {
                p1002.memo[horseStepX][horseStepY] = 0;
            }
        }
        System.out.println(p1002.dp(p1002.destX, p1002.destY));
        return;
    }
    private long dp(int i, int j) {
        if (exceedBorder(i, j)) {
            return 0;
        }
        if (memo[i][j] != -1) {
            return memo[i][j];
        }
        return memo[i][j] = dp(i - 1, j) + dp(i, j - 1);
    }

    private boolean exceedBorder(int x, int y) {
        if (x > this.destX || y > this.destY || x < 0 || y < 0) {
            return true;
        }
        return false;
    }
}