//方法一：dp，不优化空间
class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        int m = grid.size();
        int n = grid[0].size();
        vector<vector<int> > dp(m , vector<int>(n));
        for(int i=0; i<m; i++)
            for(int j=0; j<n; j++)
            {
                if(i==0)
                {
                    if(j==0)
                        dp[i][j] = grid[i][j];
                    else
                        dp[i][j] = dp[i][j-1] + grid[i][j];
                }
                else if(j==0)
                {
                    dp[i][j] = dp[i-1][j] + grid[i][j];
                }
                else
                    dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i][j];
            }
            
        return dp[m-1][n-1];
    }
};

//方法二：dp，优化空间
class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        int m = grid.size();
        int n = grid[0].size();
        vector<int> dp(n);
        for(int i=0; i<m; i++)
            for(int j=0; j<n; j++)
            {
                if(i==0)
                {
                    if(j==0)
                        dp[j] = grid[i][j];
                    else
                        dp[j] = dp[j-1] + grid[i][j];
                }
                else if(j==0)
                {
                    dp[j] = dp[j] + grid[i][j];
                }
                else
                    dp[j] = min(dp[j], dp[j-1]) + grid[i][j];
            }
            
        return dp[n-1];
    }
};