# Number of Unique Binary Search Trees - Amazon Top Interview Questions

### Problem Statement :

```Given an integer n, return the number of unique binary search trees you can form with integers from [0, n). Mod the result by 10 ** 9 + 7.

Constraints

n ≤ 1,000

Example 1

Input

n = 3

Output

5

Explanation

There are 5 unique trees.

0
\
1
\
2
0
\
2
/
1

2
/
1
/
0

2
/
0
\
1

1
/ \
0   2```

### Solution :

```                        ```Solution in C++ :

#define m 1000000007
int solve(int n) {
long long dp[n + 1] = {0};
dp[0] = 1;
for (int i = 1; i <= n; i++) {
for (int j = 0; j < i; j++) {
dp[i] = (dp[i] + ((dp[j] * dp[i - j - 1]) % m)) % m;
}
}
return dp[n];
}```
```

```                        ```Solution in Python :

class Solution:
def ans(self, n):
fact = d1 = d2 = 1
for i in range(1, 2 * n + 1):
fact = fact * i
if i == n:
d1 = fact
elif i == n + 1:
d2 = fact
return fact // (d1 * d2)

def solve(self, n):
return self.ans(n) % (10 ** 9 + 7)```
```

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