package com.jiucaiyuan.net.question;



/**

 * @Author jiucaiyuan  2022/6/5 23:00

 * @mail services@jiucaiyuan.net

 */



public class BobWalkOnGrid {



    /**

     * 在N*M的区域范围内，Bob在(i,j)位置，走step步之后，仍然在区域内的点数

     *

     * @param N

     * @param M

     * @param i

     * @param j

     * @param k

     * @return

     */

    public static double bob1(int N, int M, int i, int j, int k) {

        //所有走法数目

        long all = (long) Math.pow(4, k);

        System.out.println("all=" + all);



        //走完k步后，bob仍然在区域中的走法数目

        long live = process(N, M, i, j, k);

        System.out.println("live=" + live);

        //最大公约数

        long gcd = gcd(all, live);

        System.out.println("gcd=" + gcd);

        return (double) live / all;

    }



    /**

     * 求m和n的最大公约数

     *

     * @param m

     * @param n

     * @return

     */

    public static long gcd(long m, long n) {

        return n == 0 ? m : gcd(n, m % n);

    }



    private static long process(int N, int M, int i, int j, int step) {

        System.out.println("i=" + i + ",j=" + j + ",step=" + step);

        if (i < 0 || i == N || j < 0 || j == M) {

            //当前Bob已经在N*M区域外

            return 0;

        }

        //如果走完了，未出界，存活

        if (step == 0) {

            System.out.println("已经走完了");

            return 1;

        }

        long live = process(N, M, i - 1, j, step - 1);

        live += process(N, M, i + 1, j, step - 1);

        live += process(N, M, i, j - 1, step - 1);

        live += process(N, M, i, j + 1, step - 1);



        return live;

    }



    public static double dpBob(int N, int M, int row, int col, int k) {

        long[][][] dp = new long[N][M][k + 1];

        for (int i = 0; i < N; i++) {

            for (int j = 0; j < M; j++) {

                dp[i][j][0] = 1;

            }

        }

        for (int rest = 1; rest <= k; rest++) {

            for (int r = 0; r < N; r++) {

                for (int c = 0; c < M; c++) {

                    dp[r][c][rest] = pick(dp, N, M, r - 1, c, rest - 1);

                    dp[r][c][rest] += pick(dp, N, M, r + 1, c, rest - 1);

                    dp[r][c][rest] += pick(dp, N, M, r, c - 1, rest - 1);

                    dp[r][c][rest] += pick(dp, N, M, r, c + 1, rest - 1);

                }

            }

        }

        return (double) dp[row][col][k] / Math.pow(4, k);

    }



    public static long pick(long[][][] dp, int N, int M, int r, int c, int rest) {

        if (r < 0 || r == N || c < 0 || c == M) {

            return 0;

        }

        return dp[r][c][rest];

    }



    public static void main(String[] args) {

        System.out.println("bob1");

        int k = 30;

        //System.out.println(bob1(6, 6, 3, 4, k));  //跑的太慢了

        System.out.println("dpBob");

        System.out.println(dpBob(6, 6, 3, 4, k));

    }



}