题目：

给定一个只含非负整数的m*n网格，找到一条从左上角到右下角的可以使数字和最小的路径。

样例

 

注意

你在同一时间只能向下或者向右移动一步

解题：

这个和求的最小路径的差不多，这里是个矩阵，第一列和第一行要单独处理，每一点的值等于自身的值加上上一点的值，对于中间节点：grid[i][j] + = min( grid[i-1][j] , grid[i][j-1]) ,也就是说，i j 点的值只能是其左侧的点或者上侧的点加过来，这个时间复杂度比较高O(N²)

Java程序：

public class Solution {    /**     * @param grid: a list of lists of integers.     * @return: An integer, minimizes the sum of all numbers along its path     */    public int minPathSum(int[][] grid) {        // write your code here        int m = grid.length;        if(m == 0 )            return 0;        int n = grid[0].length;        if( n==0 )            return 0;        for(int i=1 ; i

Python程序：

class Solution:    """    @param grid: a list of lists of integers.    @return: An integer, minimizes the sum of all numbers along its path    """    def minPathSum(self, grid):        # write your code here        m = len(grid)        if m == 0:            return 0        n = len(grid[0])        if n==0:            return 0        for i in range(m):            for j in range(n):                if i==0 and j!=0:                    grid[i][j] += grid[i][j-1]                elif j==0 and i!=0:                    grid[i][j] += grid[i-1][j]                elif j!=0 and i!=0:                    grid[i][j] += min(grid[i-1][j] , grid[i][j-1])        return grid[m-1][n-1]