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 :



title-img 




                        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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