Leetcode - unique-binary-search-trees
https://leetcode.com/problems/unique-binary-search-trees/
Given n, how many structurally unique BST's (binary search trees) that store values 1 ... n?
Example:
Input: 3
Output: 5
Explanation:
Given n = 3, there are a total of 5 unique BST's:
1 3 3 2 1
\ / / / \ \
3 2 1 1 3 2
/ / \ \
2 1 2 3
This problem is very interesting. It can be solved by Catalan Number
On wikipedia, there are detailed proves for why it can solve this problem.
1 2 3 4 5 6 7 8 9 10 11 12 | func numTrees(n int) int { dp := make([]int, n+1) dp[0] = 1 dp[1] = 1 for i := 2; i <= n; i++ { for j := 0; j < i; j++ { dp[i] += dp[j] * dp[i-j-1] } } return dp[n]} |
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