[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.

二维 DP。简单~

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int m = grid.size();
        if(m==0) return 0;
        int n = grid[0].size();
        
        vector<vector<int> > minSum (m,(vector<int>)n);
        for(int i=n-1;i>=0;i--)
        {
            minSum[m-1][i] = (i==n-1)? grid[m-1][n-1]:minSum[m-1][i+1]+grid[m-1][i];
        }
        for(int i=m-1;i>=0;i--)
        {
            minSum[i][n-1] = (i==m-1)? grid[m-1][n-1]:minSum[i+1][n-1]+grid[i][n-1];
        }
        
        for(int i=m-2;i>=0;i--)
        {
            for(int j=n-2;j>=0;j--)
            {
                minSum[i][j] = grid[i][j] + min(minSum[i+1][j],minSum[i][j+1]);
            }
        }
        
        return minSum[0][0];
    }
};