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.

 

格子取数问题，另dp[i][j]表示走到(i,j)格子时，取得的最小数字，那么有

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

当i=0时，只能从左边过来，当j=0时，只能从上面过来

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;
        vector< vector<int> > dp(grid);
        for(int i=1; i<n; ++i) dp[0][i] += dp[0][i-1];
        for(int i=1; i<m; ++i) dp[i][0] += dp[i-1][0];
        for(int i=1; i<m; ++i)
            for(int j=1; j<n; ++j)
                dp[i][j] += min(dp[i-1][j], dp[i][j-1]);
        return dp[m-1][n-1];
    }
};