minimum path sum

坐标型DP

code

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();

        vector<vector<int>> dp;
        for(int i = 0; i<m; i++)
        {
            vector<int> tmp(n,0);
            dp.push_back(tmp);
        }

        dp[0][0] = grid[0][0];
        for(int i = 1; i<n; i++)
        {
            dp[0][i] = dp[0][i-1] + grid[0][i];
        }
        for(int i = 1; i<m; i++)
        {
            dp[i][0] = dp[i-1][0] + grid[i][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]) + grid[i][j];
            }
        }

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

    }
};