Unique Paths

方法一：直接使用备忘录

class Solution {
public:
    int uniquePaths(int m, int n) {
        fm = vector<vector<int>>(m, vector<int>(n, 0));
        fm[0][0] = 1;
        return dfs(m-1, n-1);
    }
    
private:
    vector<vector<int>> fm;
    
    int dfs(int m, int n)
    {
        if(m < 0 || n < 0)
            return 0;
        if(m == 0 || n == 0)
            return 1;
            
        if(fm[m][n] > 0)
            return fm[m][n];
        else
            return fm[m][n] = dfs(m-1, n) + dfs(m, n-1);
    }
};

方法二：使用动态规划的方法

class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<vector<int>> fm = vector<vector<int>>(m, vector<int>(n,0));
        
        for(int i=0; i<m; ++i)
        {
            for(int j=0; j<n; ++j)
            {
                if(i == 0 || j == 0)
                    fm[i][j] = 1;
                else
                    fm[i][j] = fm[i-1][j] + fm[i][j-1];
            }
        }
        
        return fm[m-1][n-1];
    }
};