LeetCode-64-Minimum Path Sum

算法描述：

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.

解题思路：求最小路径和，用动态规划法。dp[i][j] = min(dp[i-1][j],dp[i][j-1]) + grid[i][j];

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