# 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;
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);
}
};