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Unique Binary Search Trees

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Question

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:

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5
1         3     3      2      1
 \       /     /      / \      \
  3     2     1      1   3      2
 /     /       \                 \
2     1         2                 3

Solution

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/*
@param: int
@return: int
Algorithm: dp, 打着BST的一道DP题，以当前节点为root, 判断左右两边子节点个数，无关大小，然后左右子树乘起来
*/
public int numTrees(int n) {
    if (n <= 0) return 0;
    
    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];
}