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
对1-n组成的ＢＳＴ，如果选定ｉ为根，那１－（ｉ－１）都在根的左子树里，（i+1)-n都在根的右子树里，转换为dp问题。
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++) { // i: number of nodes
for (int j = 0; j < i; j++) { // j: the index of root
dp[i] += dp[j] * dp[i - 1 - j];
}
}
return dp[n];
}
}
96. Unique Binary Search Trees
原文：http://www.cnblogs.com/yuchenkit/p/7192035.html