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
考察二叉树的种类,卡特兰数的例子。这里要注意的是空树也属于二叉搜索树。代码如下:
public class Solution { public int numTrees(int n) { int[] dp = new int[n + 1]; dp[0] = 1; dp[1] = 1; for(int i = 2; i <= n; i++) { for(int j = 0; j < i; j++) { dp[i] += dp[j] * dp[i - j - 1]; } } return dp[n]; } }