96.Unique Binary Search Trees

Given n, how many structurally unique BST‘s (binarysearch trees) that store values 1...n?

For example,
Given n = 3, there are a total of 5 unique BST‘s.

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 Tree Dynamic Programming

#pragma once
#include<queue>
#include<iostream>
using namespace std;

int numTrees(int n) {
	int *a=new int[n+1];
	for (int i = 0; i < n + 1; i++)
		a[i] = 0;
	a[0] = 0;
	a[1] = 1;
	for (int i = 1; i <= n; i++)
	{
		for (int j = 2; j < i; j++)
			a[i] += (a[j - 1] * a[i - j]);//掐头去尾后，2至i-1做根节点时的可能数
		a[i] += 2 * a[i - 1];//a[0]=0不能与a[i]相乘后叠加，掐头去尾单独算
	}
	return a[n];
}

void main()
{
	cout << numTrees(1) << endl;
	cout << numTrees(2) << endl;
	cout << numTrees(3) << endl;
	cout << numTrees(4) << endl;
	system("pause");

}