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：典型的动态规划问题。result[i][j]表示(0,0)到(i,j)的最小值。result[i][j]=min(result[i][j-1],result[i-1][j])+grid[i][j];

class Solution {

public:

    int minPathSum(vector<vector<int> > &grid) {

        int m=grid.size();

        int n=grid[0].size();

        if(m==0||n==0)

            return 0;

        int result[m][n];

        for(int i=0;i<m;i++)

        {

            for(int j=0;j<n;j++)

            {

                if(i==0)

                {

                    if(j==0)

                        result[i][j]=grid[i][j];

                    else

                        result[i][j]=result[i][j-1]+grid[i][j];

                }

                else

                {

                    if(j==0)

                        result[i][j]=result[i-1][j]+grid[i][j];

                    else

                        result[i][j]=min(result[i-1][j],result[i][j-1])+grid[i][j];

                }

            }

        }

        return result[m-1][n-1];

    }

};