[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.

解题思路：

一个简单的dp，从上往下，从左往右扫一遍即可。

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
    // IMPORTANT: Please reset any member data you declared, as
    // the same Solution instance will be reused for each test case.
    if(grid.size() == 0) return 0;
    int m = grid.size(), n = grid[0].size();
    int **dp = new int*[m];
    for(int i = 0;i < m;i++)
        dp[i] = new int[n];
    
    for(int i = 0;i < m;i++)
    {
        for(int j = 0;j < n;j++)
        {
            if(i == 0)
            {
                if(j == 0) dp[i][j] = grid[i][j];
                else dp[i][j] = dp[i][j - 1] + grid[i][j];
            }
            else
            {
                if(j == 0) dp[i][j] = dp[i - 1][j] + grid[i][j];
                else dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }
    }
    
    return dp[m - 1][n - 1];
    }
};