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.

题目大意：给定一个矩阵，从左上角走到右下角，找到数字和最小的路径，返回该和，只能向下向右走

题目难度：Medium

/**
 * Created by gzdaijie on 16/5/28
 * 动态规划
 */
public class Solution {
    public int minPathSum(int[][] grid) {
        if (grid.length == 0 || grid[0].length == 0) return 0;

        int m = grid.length;
        int n = grid[0].length;
        int[][] result = new int[m][n];

        result[0][0] = grid[0][0];
        for (int i = 1; i < m; i++) result[i][0] = result[i - 1][0] + grid[i][0];
        for (int i = 1; i < n; i++) result[0][i] = result[0][i - 1] + grid[0][i];

        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];
    }
}