64. 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.

思路：典型动规。

class Solution {public:    int minPathSum(vector<vector<int>>& grid) {        int m = grid.size();        int n = grid[0].size();        vector<vector<int>> sum(m, vector<int>(n,1));        sum[0][0] = grid[0][0];        for(int i = 1; i < m; i++)        {            sum[i][0] = grid[i][0] + sum[i-1][0];        }        for(int j = 1; j < n; j++)        {            sum[0][j] = grid[0][j] + sum[0][j-1];        }        for(int i = 1; i < m; i++)        {            for(int j = 1; j < n; j++)            {                sum[i][j] = min(sum[i-1][j], sum[i][j-1]) + grid[i][j];            }        }        return sum[m-1][n-1];    }};