Unique paths <leetcode>

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?

 

思路：首先想到的是广度优先搜索（分支限界），方法一就是，但是超时,方法二是动态规划，accepted

 

struct node
{
    int x;
    int y;
};
class Solution {
public:
    int total_path;
    int uniquePaths(int m, int n) {
        total_path=0;
        list<node>  ls;
        node orign;
        orign.x=1;
        orign.y=1;
        ls.push_back(orign);
        while(ls.size()!=0)
        {
            node temp=ls.front();
            ls.pop_front();
            if(temp.x+1<=n)
            {
                node p;
                p.x=temp.x+1;
                p.y=temp.y;
                ls.push_back(p);
                if(temp.x+1==n&&temp.y==m)
                {
                    total_path++;
                }
            }
            if(temp.y+1<=m)
            {
                node p;
                p.x=temp.x;
                p.y=temp.y+1;
                ls.push_back(p);
                if(temp.x==n&&temp.y+1==m)
                {
                    total_path++;
                }
            }
        }
        return total_path;
    }
};

 

 

方法二：动态规划

class Solution {
public:
    int uniquePaths(int m, int n) {
        int f[m][n];
        memset(f,0,sizeof(int)*m*n);
        
        for(int i=0;i<m;i++)
        {
            f[i][0]=1;
        }
        for(int i=0;i<n;i++)
        {
            f[0][i]=1;
        }
        
        for(int i=1;i<m;i++)
        {
            for(int j=1;j<n;j++)
            {
                f[i][j]=f[i-1][j]+f[i][j-1];
            }
        }
        return f[m-1][n-1];
    }
};