【LeetCode】96. Unique Binary Search Trees (2 solutions)

Unique Binary Search Trees

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

Base case: n==0, n==1时，f(n)==1

递推关系：f(n)=∑f(i)*f(n-i-1)。即以第i个为根节点，左右子树数目相乘。

解法一：递归

class Solution {
public:
    int numTrees(int n) {
        if(n == )
            return ;
        else if(n == )
            return ;
        else
        {
            int count = ;
            for(int i = ; i <= (n-)/; i ++)
            {
                if(i < n--i)
                    count += *numTrees(i)*numTrees(n--i);
                else
                    count += numTrees(i)*numTrees(n--i);
            }
            return count;
        }
    }
};

解法二：动态规划

class Solution {
public:
    int numTrees(int n) {
        if(n== || n == )
            return ;

        vector<int> v(n+, );
        v[] = ;//n==0
        v[] = ;//n==1
        for(int i = ; i <= n; i ++)
        {//n == i
            for(int j = ; j < i; j ++)
            {
                v[i] += v[j]*v[i--j];
            }
        }
        return v[n];
    }
};