【动态规划模板】标准的dp模板

//标准的dp模板
class Solution {
    int m;
    int n;
    int[][] dp;

    public int minPathSum(int[][] grid) {

        m = grid.length;
        n = grid[0].length;
        dp = new int[m][n];//dp[i][j]代表走到第[i][j]格子的最小总和
        
        //初始化第一行和第一列
        dp[0][0] = grid[0][0];
        for(int j = 1; j < n; j++)      dp[0][j] = dp[0][j-1] + grid[0][j];
        for(int i = 1; i < m; i++)      dp[i][0] = dp[i-1][0] + grid[i][0];

        //开始推算
        for(int i = 1; i < m; i++){
            for(int j = 1; j < n; j++){
                dp[i][j] = Math.min(dp[i-1][j], dp[i][j-1]) + grid[i][j];
            }
        }

        show();//展示dp数组

        System.out.println(findPath(grid));//展示最小路径
        
        return dp[m-1][n-1];//最终落在[m-1][n-1]格子上
    }


    //从终点倒着开始推算最小路径
    public String findPath(int[][] grid){
        
        String path = "";//记录最小路径
        path += grid[m-1][n-1];//终点格子要加上
        int i = m-1;//2
        int j = n-1;//2 终点

        //开始推算
        while(i != 0 || j != 0){
                if(j == 0){    
                    path += "->" + grid[i-1][j]; 
                    i--;
                }else if(i == 0){
                    path += "->" + grid[i][j-1];
                    j--;
                }else if(dp[i-1][j] < dp[i][j-1]){
                    path += "->" + grid[i-1][j]; 
                    i--;
                }else if(dp[i-1][j] > dp[i][j-1]){
                    path += "->" + grid[i][j-1];
                    j--;
                }
        }

       return path;
    }


    //展示dp数组
    void show(){
        for(int i = 0; i < m; i++){
            for(int j = 0; j < n; j++){
                System.out.print(dp[i][j] + " ");
            }
            System.out.println();
        }
    }
    
    
}

64. 最小路径和