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：用一个数组存从起点到终点的最短距离。初始化时，全体初始化为最大整数。按行遍历grid，sum就记录从起点到当前行对应sum的列的路径和，每次sum的值取当前值

与前一步路径和的较小值+当前格子的值。sum的最后记录的就是从左上起点到右下终点的最短距离。

class Solution {public:    int minPathSum(vector<vector<int> > &grid) {        // IMPORTANT: Please reset any member data you declared, as        // the same Solution instance will be reused for each test case.        vector<int> sum(grid[0].size()+1, INT_MAX);        sum[1] = 0;        for(int i=0; i<grid.size(); i++){            for(int j=1; j<=grid[0].size(); j++){                sum[j] = min(sum[j-1], sum[j]) + grid[i][j-1];            }        }        return sum.back();    }};