二维动态规划----2.最小路径和-优快云博客

/**

minPathSum[i][j]:到达(i,j)的最小路径和

对于第0行、第0列的元素,都只有一种走法一直向右或一直向下,路径和是唯一的

(1,1):(0,1)向下或 (1,0)向右 minPathSum[1][1] = Math.min(minPathSum[0][1],minPathSum[1][0]) + grid[1][1]

(1,2):(0,2)向下或 (1,1)向右 minPathSum[1][2] = Math.min(minPathSum[0][2],minPathSum[1][1]) + grid[1][2]

........

(i,j):(i - 1,j)向下或 (i,j - 1)向右 minPathSum[i][j] = Math.min(minPathSum[i- 1][j],minPathSum[i][j - 1]) + grid[i][j]

class Solution {
    /**
        minPathSum[i][j]:到达(i,j)的最小路径和
        对于第0行、第0列的元素,都只有一种走法一直向右或一直向下,路径和是唯一的

        (1,1):(0,1)向下 或 (1,0)向右 minPathSum[1][1] = Math.min(minPathSum[0][1],minPathSum[1][0]) + grid[1][1]
        (1,2):(0,2)向下 或 (1,1)向右 minPathSum[1][2] = Math.min(minPathSum[0][2],minPathSum[1][1]) + grid[1][2]
        ........
        (i,j):(i - 1,j)向下 或 (i,j - 1)向右 minPathSum[i][j] = Math.min(minPathSum[i- 1][j],minPathSum[i][j - 1]) + grid[i][j]
    */
    public int minPathSum(int[][] grid) {
        int row = grid.length;
        int col = grid[0].length;
        
        int dp[][] = new int[row][col];
        dp[0][0] = grid[0][0];

        //初始化
        for(int i = 1; i < row; i++) {
            dp[i][0] += dp[i - 1][0] + grid[i][0];
        }

        for(int j = 1; j < col; j++) {
            dp[0][j] += dp[0][j - 1] + grid[0][j];
        }
        
        //递推
        for(int i = 1; i < row; i++) {
            for(int j = 1; j < col; j++) {
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1])  + grid[i][j];
            }
        }

        return dp[row - 1][col - 1];
    }
}