62. Unique Paths LeetCode

 62. 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?

 

Example 1:

Input: m = 3, n = 7
Output: 28

Example 2:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down

Example 3:

Input: m = 7, n = 3
Output: 28

Example 4:

Input: m = 3, n = 3
Output: 6

 

Constraints:

• 1 <= m, n <= 100
• It's guaranteed that the answer will be less than or equal to 2 * 109.

the solution to the Above Question

class Solution {

public:

    int dp[101][101];

    int helper(int a,int b,int m,int n){

        if(a==m-1 && b==n-1){

            return 1;

        }

        if(a>m-1 || b>n-1){

            return 0;

        }

        int ans=0;

        {   if(dp[a+1][b]==-1){

            dp[a+1][b]=helper(a+1,b,m,n);

        }

         if(dp[a][b+1]==-1){

             dp[a][b+1]=helper(a,b+1,m,n);

         }

            ans=ans+dp[a+1][b]+ dp[a][b+1];

            

        }

        return ans;

    }

    

    int uniquePaths(int m, int n) {

        for(int i=0; i<100; i++){

            for(int j=0; j<100; j++){

                dp[i][j]-=1;

            }

        }

        int ans=0;

        int a=0,b=0;

        return helper(0,0,m,n);

    }

};