LeetCode_Unique Paths

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).



The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).



How many possible unique paths are there?

　　方法一： DFS 大数据超时

class Solution {

public:

    void DFS(int i, int j, int m, int n){

        if( i== m && j == n){

            result++;

        }

        if(j+1 <= n) DFS(i, j+1,m,n);

        if(i+1 <= m) DFS(i+1,j,m,n);

    }

    int uniquePaths(int m, int n) {

        // Start typing your C/C++ solution below

        // DO NOT write int main() function

        result = 0;

        DFS(1,1,m,n);

        return result;

    }

private:

 int result;

};

View Code

　　方法二：动态规划。 grid[i][j] = grid[i-1][j]+grid[i][j-1]

class Solution {

public:

    int uniquePaths(int m, int n) {

        // Start typing your C/C++ solution below

        // DO NOT write int main() function

        vector<vector<int>> grid(m,vector<int>(n,0));

        for(int i = 0; i< n;i++) grid[0][i] = 1;

        for(int i = 0; i< m;i++) grid[i][0] = 1;

        

        for(int i = 1; i< m; i++)

            for(int j = 1; j < n; j++)

                    grid[i][j] = grid[i-1][j] + grid[i][j-1];

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

        

    }

};