Unique Binary Search Trees LeetCode Solution

Problem – Unique Binary Search Trees LeetCode Solution

Given an integer n, return the number of structurally unique BST’s (binary search trees) which has exactly n nodes of unique values from 1 to n.

Example 1:

Input: n = 3
Output: 5

Example 2:

Input: n = 1
Output: 1

Constraints:

  • 1 <= n <= 19

Unique Binary Search Trees LeetCode Solution in Java

public int numTrees(int n) {
    int [] dp = new int[n+1];
    dp[0]= 1;
    dp[1] = 1;
    for(int level = 2; level <=n; level++)
        for(int root = 1; root<=level; root++)
            dp[level] += dp[level-root]*dp[root-1];
    return dp[n];
}

Unique Binary Search Trees LeetCode Solution in C++

class Solution {
public:
    int dp[20]{};
    int numTrees(int n) {
        if(n <= 1) return 1;
        if(dp[n]) return dp[n];
        for(int i = 1; i <= n; i++) 
            dp[n] += numTrees(i-1) * numTrees(n-i);
        return dp[n];
    }
};

Unique Binary Search Trees LeetCode Solution in Python

class Solution:
    @cache
    def numTrees(self, n: int) -> int:
        if n <= 1: return 1
        return sum(self.numTrees(i-1) * self.numTrees(n-i) for i in range(1, n+1))
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