Unique Binary Search Tree

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


分析：这道题的关键是找出规律，可以举几个例子帮助理解，化抽象为具体。实际上就是左子树书目*右子树的数目。此题用递归和循环都可以。用递归注意超时哦，此题我用的是循环。

class Solution {
public:
    int numTrees(int n) {
        int sum=0;
        if(n<=1)
            return n;
        int* num=new int[n+1];
        num[0]=1;
        num[1]=1;
        for(int i=2;i<=n;++i)
        {
            num[i]=0;
            for(int k=0;k<i;++k)
            {
                int left=num[k];//保存左子树的数目
                int right=num[i-k-1];//保存右子树的数目
                num[i]+=left*right;
            }
        }
        sum=num[n];
        delete[] num;
        return sum;
    }
};

 python实现：

class Solution:
    # @return an integer
    def numTrees(self, n):
        if n<=1:
            return n
        num=[]
        for i in range(n+1):
            num.append(0)
        num[0]=1
        num[1]=1
        for j in range(2,n+1):
            for k in range(j):
                left=num[k]
                right=num[j-k-1]
                num[j]+=left*right
        sum=num[n]
        return sum