【leetcode】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.

 

//DP，f[i][j] = min(f[i-1][j], f[i][j-1]) + a[i][j]

 

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