DP------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.

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

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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 < M; i++) {            sum[i][0] = sum[i - 1][0] + grid[i][0];        }//起始条件        for (int i = 1; i < N; i++) {            sum[0][i] = sum[0][i - 1] + grid[0][i];        }//起始条件        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];//状态转移方程            }        }        return sum[M - 1][N - 1];//长度从1开始;    }}