leetcode -- Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

[解题思路]

与Unique Paths类似，只是把求路径数改成求最小路径和

目标函数：

sum[i][j] = grid[i][j] + Math.min(sum[i+1][j], sum[i][j+1]);

这里为了方便，sum数组分配了[m+2][n+2]个元素，1<=i<=m, 1<=j<=n中存储子问题的解

public int minPathSum(int[][] grid) {
        // Start typing your Java solution below
        // DO NOT write main() function
        int m = grid.length;
        int n = grid[0].length;
        int[][] sum = new int[m+2][n+2];
        for(int i = 0; i < m + 2; i++){
            for(int j = 0; j < n + 2; j++){
                sum[i][j] = Integer.MAX_VALUE;
            }
        }
        sum[m][n+1] = 0;
        for(int i = m; i >= 1; i--){
            for(int j = n; j >= 1; j--){
                sum[i][j] = grid[i-1][j-1] + Math.min(sum[i+1][j], sum[i][j+1]);
            }
        }
        return sum[1][1];
    }