Code02_HorseJump.java

package class20;

public class Code02_HorseJump {

	// 当前来到的位置是（x,y）
	// 还剩下rest步需要跳
	// 跳完rest步，正好跳到a，b的方法数是多少？
	// 10 * 9
	public static int jump(int a, int b, int k) {
		return process(0, 0, k, a, b);
	}

	public static int process(int x, int y, int rest, int a, int b) {
		if (x < 0 || x > 9 || y < 0 || y > 8) {
			return 0;
		}
		if (rest == 0) {
			return (x == a && y == b) ? 1 : 0;
		}
		int ways = process(x + 2, y + 1, rest - 1, a, b);
		ways += process(x + 1, y + 2, rest - 1, a, b);
		ways += process(x - 1, y + 2, rest - 1, a, b);
		ways += process(x - 2, y + 1, rest - 1, a, b);
		ways += process(x - 2, y - 1, rest - 1, a, b);
		ways += process(x - 1, y - 2, rest - 1, a, b);
		ways += process(x + 1, y - 2, rest - 1, a, b);
		ways += process(x + 2, y - 1, rest - 1, a, b);
		return ways;
	}

	public static int dp(int a, int b, int k) {
		int[][][] dp = new int[10][9][k + 1];
		dp[a][b][0] = 1;
		for (int rest = 1; rest <= k; rest++) {
			for (int x = 0; x < 10; x++) {
				for (int y = 0; y < 9; y++) {
					int ways = pick(dp, x + 2, y + 1, rest - 1);
					ways += pick(dp, x + 1, y + 2, rest - 1);
					ways += pick(dp, x - 1, y + 2, rest - 1);
					ways += pick(dp, x - 2, y + 1, rest - 1);
					ways += pick(dp, x - 2, y - 1, rest - 1);
					ways += pick(dp, x - 1, y - 2, rest - 1);
					ways += pick(dp, x + 1, y - 2, rest - 1);
					ways += pick(dp, x + 2, y - 1, rest - 1);
					dp[x][y][rest] = ways;
				}
			}
		}
		return dp[0][0][k];
	}

	public static int pick(int[][][] dp, int x, int y, int rest) {
		if (x < 0 || x > 9 || y < 0 || y > 8) {
			return 0;
		}
		return dp[x][y][rest];
	}

	public static int ways(int a, int b, int step) {
		return f(0, 0, step, a, b);
	}

	public static int f(int i, int j, int step, int a, int b) {
		if (i < 0 || i > 9 || j < 0 || j > 8) {
			return 0;
		}
		if (step == 0) {
			return (i == a && j == b) ? 1 : 0;
		}
		return f(i - 2, j + 1, step - 1, a, b) + f(i - 1, j + 2, step - 1, a, b) + f(i + 1, j + 2, step - 1, a, b)
				+ f(i + 2, j + 1, step - 1, a, b) + f(i + 2, j - 1, step - 1, a, b) + f(i + 1, j - 2, step - 1, a, b)
				+ f(i - 1, j - 2, step - 1, a, b) + f(i - 2, j - 1, step - 1, a, b);

	}

	public static int waysdp(int a, int b, int s) {
		int[][][] dp = new int[10][9][s + 1];
		dp[a][b][0] = 1;
		for (int step = 1; step <= s; step++) { // 按层来
			for (int i = 0; i < 10; i++) {
				for (int j = 0; j < 9; j++) {
					dp[i][j][step] = getValue(dp, i - 2, j + 1, step - 1) + getValue(dp, i - 1, j + 2, step - 1)
							+ getValue(dp, i + 1, j + 2, step - 1) + getValue(dp, i + 2, j + 1, step - 1)
							+ getValue(dp, i + 2, j - 1, step - 1) + getValue(dp, i + 1, j - 2, step - 1)
							+ getValue(dp, i - 1, j - 2, step - 1) + getValue(dp, i - 2, j - 1, step - 1);
				}
			}
		}
		return dp[0][0][s];
	}

	// 在dp表中，得到dp[i][j][step]的值，但如果(i，j)位置越界的话，返回0；
	public static int getValue(int[][][] dp, int i, int j, int step) {
		if (i < 0 || i > 9 || j < 0 || j > 8) {
			return 0;
		}
		return dp[i][j][step];
	}

	public static void main(String[] args) {
		int x = 7;
		int y = 7;
		int step = 10;
		System.out.println(ways(x, y, step));
		System.out.println(dp(x, y, step));

		System.out.println(jump(x, y, step));
	}
}