学步园

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.

hint: 跟上题一样的简单动态规划 转移方程： dp[i][j] =  min {dp[i][j-1],dp[i-1][j]} + grid[i][j]

cpp:

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        // Note: The Solution object is instantiated only once and is reused by each test case.
        int m = grid.size();
        if(m == 0)
            return 0;
        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 j = 1; j < n; j++)
        {
            dp[0][j] = dp[0][j-1] + grid[0][j];
        }
        for(int i = 1; i < m; i++)
        {
            for(int j = 1; j < n; j++)
            {
                dp[i][j] = min(dp[i][j-1],dp[i-1][j])+grid[i][j];
            }
        }
        int res = dp[m-1][n-1];
        for(int i = 0; i < m; i++)
        {
            delete [] dp[i];
        }
        delete [] dp;
        return res;
    }
};