【leetcode】64. Minimum Path Sum【java】

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.

动态规划的思想

public class Solution {
    public int minPathSum(int[][] grid) {
        if (grid == null || grid.length == 0 || grid[0].length == 0){
            return 0;
        }
        int m = grid.length;
        int n = grid[0].length;
        int[][] sum = new int[m][n];
        sum[0][0] = grid[0][0];
        for (int i = 1; i < n; i++){
            sum[0][i] = sum[0][i - 1] + grid[0][i];
        }
        for (int j = 1; j < m; j++){
            sum[j][0] = sum[j - 1][0] + grid[j][0];
        }
        for (int i = 1; i < m; i++){
            for (int j = 1; j < n; j++){
                sum[i][j] = Math.min(sum[i - 1][j], sum[i][j - 1]) + grid[i][j];
            }
        }
        return sum[m - 1][n - 1];
    }
}