Unique Binary Search Trees
Given n, how many structurally unique BST's (binary search trees) that store values 1...n?
For example,
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
Analyse: We can select 1~N as the root. Suppose the root is i, then we can put j = 0~i - 1 nodes in its left, and put i - j - 1 nodes in its right.
Runtime: 0ms.
1 class Solution { 2 public: 3 int numTrees(int n) { 4 vector<int> dp(n + 1, 0); 5 dp[0] = 1, dp[1] = 1; 6 for(int i = 2; i <= n; i++) { 7 for(int j = 0; j < i; j++) { 8 dp[i] += dp[j] * dp[i - j - 1]; 9 } 10 } 11 return dp[n]; 12 } 13 };