62. Unique Paths LeetCode

 62Unique 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 mint 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);
    }
};

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