题目：
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.
代码：
class Solution { public: int minPathSum(vector<vector<int>>& grid) { if ( grid.empty() ) return 0; const int m = grid.size(); const int n = grid[0].size(); vector<int> dp(n, INT_MAX); dp[0] = 0; for ( int i=0; i<m; ++i ) { dp[0] += grid[i][0]; for ( int j=1; j<n; ++j ) { dp[j] = grid[i][j] + std::min(dp[j-1], dp[j]); } } return dp[n-1]; } };
tips：
典型的“DP+滚动数组”，时间复杂度O(m*n)，空间复杂度O(n)。
原文：http://www.cnblogs.com/xbf9xbf/p/4550146.html