题目链接
tag:

• Medium；
• DP；

question：
  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.

Example:

Input:
[
[1,3,1],
[1,5,1],
[4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

思路：
  这道题需要用动态规划Dynamic Programming来做，这算是DP问题中比较简单的一类，维护一个二维的dp数组，其中dp[i][j]表示当前位置的最小路径和，递推式也容易写出来 dp[i][j] = grid[i][j] + min(dp[i - 1][j]，dp[i][j-1]) 反正难度不算大，代码如下：

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