62. Unique Paths | LeetCode Solution

There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.

Given the two integers m and n, return the number of possible unique paths that the robot can take to reach the bottom-right corner.

The test cases are generated so that the answer will be less than or equal to 2 * 109.

 

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

 

Constraints:

  • 1 <= m, n <= 100

class Solution {
public:
    
      int helper(int a,int b,int m,int n,vector<vector<int>>&dp){
        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,dp);
        }
         if(dp[a][b+1]==-1){
             dp[a][b+1]=helper(a,b+1,m,n,dp);
         }
            ans=ans+dp[a+1][b]+ dp[a][b+1];
            
        
        return ans;
    }
    
    int uniquePaths(int m, int n) {
        vector<vector<int>>dp(m+1,vector<int>(n+1,-1));
        helper(0,0,m,n,dp);
        return helper(0,0,m,n,dp);
    }
};