Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right whichminimizes the sum of all numbers along its path.

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

题意：给定m*n矩阵，里面都是非负数，求从左上角，走到右下角的路径，要求这条路径过程中所有数加起来的和最小

分类：数组，动态规划

动态规划：

MPS[i][j] = Min（MPS[i-1][j]，MPS[i][j-1]）+ val[i][j]；

边界处理条件：

for(int j=1; j<res[0].size(); ++j){              res[0][j] += res[0][j-1];          }          for(int j=1; j<res.size(); ++j){              res[j][0] += res[j-1][0];          }  

class Solution {public:    int minPathSum(vector<vector<int> > &grid) {        if(grid.size()==0)            return 0;        vector<vector<int>> res(grid);        int i, j;        for(int j=1; j<res[0].size(); ++j){            res[0][j] += res[0][j-1];        }        for(int j=1; j<res.size(); ++j){            res[j][0] += res[j-1][0];        }        for(i=1; i<res.size(); ++i){            for(int j=1; j<res[i].size(); ++j){                res[i][j] = min(res[i-1][j], res[i][j-1])+grid[i][j];            }        }        return res[grid.size()-1][grid[0].size()-1];    //注意行列的size不一定一样    }};