LeetCode刷题笔录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.

标准的Dynamic Programming。注意第一行的元素只能从左边走过来，第一列的只能从上边走下来。

public class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[][] result = new int[m][n];
        //fill the first row of result, i.e. result[0]
        int sum = 0;
        for(int i = 0; i < n; i++){
            sum += grid[0][i];
            result[0][i] = sum;
        }
        //fill the first column
        sum = 0;
        for(int j = 0; j < m; j++){
            sum += grid[j][0];
            result[j][0] = sum;
        }
        
        //fill the rest
        for(int i = 1; i < m; i++){
            for(int j = 1; j < n; j++){
                result[i][j] = Math.min(result[i - 1][j], result[i][j - 1]) + grid[i][j];
            }
        }
        return result[m - 1][n - 1];
        
    }
}