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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

//1.深搜
/*
class Solution {
    int dfs(int m,int n,int r,int c,int end_r,int end_c)
    {
        if(r<0 || r>=m || c<0 || c>=n)
        {
            return 0;
        }
        if(end_r == r && end_c==c){
            return 1;
        }
        return dfs(m,n,r+1,c,end_r,end_c)+dfs(m,n,r,c+1,end_r,end_c);
    }
public:
    int uniquePaths(int m, int n) {
        return dfs(m,n,0,0,m-1,n-1);
    }
};
*/

//2.动态
class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<int> help(n,1);
        for(int i=1;i<m;i++){
            for(int j=0;j<n;j++){
                if(j==0){
                    help[j] = 1;
                }else{
                    help[j] = help[j]+help[j-1];
                }
            }
        }
        return m>0&&n>0 ? help[n-1]:0;
    }
};