【leetcode】Unique Paths

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.

 

可以推到一下公式，对于m+1,n+1来说，只需要向右走m步，向下走n步，就能到达终点了，我们把向下和向右进行排列，所有的排列数就是结果

因此result=(m+n)!/(m!*n!)

直接求会超出范围，因此化简一下：

化简一下(m+1)(m/2+1)……（m/n+1)

 

 

class Solution {
public:
   
    int uniquePaths(int m, int n) {
       
        int result=0;
        double tmp=1;
        m--;
        n--;
        for(int i=0;i<n;i++)
        {
            tmp*=(double)(m)/(i+1)+1;
        }
       
        result=round(tmp);
        return result;
    }
};

 

 

直接用动态规划

 

class Solution {
public:
   
    int uniquePaths(int m, int n) {
       
        if(m==0||n==0) return 0;
 
        int dp[101][101];
       
        dp[0][0]=1;
       
        for(int i=1;i<m;i++)
        {
            dp[i][0]=1;
        }
       
        for(int j=1;j<n;j++)
        {
            dp[0][j]=1;
        }
       
        for(int i=1;i<m;i++)
        {
            for(int j=1;j<n;j++)
            {
                dp[i][j]=dp[i][j-1]+dp[i-1][j];
            }
        }
        return dp[m-1][n-1];
    }
};