# 62. Unique Paths | LeetCode Solution

## 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`). 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);
}
};