[leetcode] Minimum Path Sum

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.

 思路：

只能向下和向右移动，那就很简单了。动态规划，当前最小和=当前值+当前点上方或者左方最小和，注意边界情况。

题解：

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