【LeetCode】96

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

Tree Dynamic Programming

 

Solution 1:  递归

class Solution {
public:
    int numTrees(int n) {
        if(n == 0)
            return 1;
        else if(n == 1)
            return 1;
        else
        {
            int count = 0;
            for(int i = 0; i <= (n-1)/2; i ++)
            {
                if(i < n-1-i)
                    count += 2*numTrees(i)*numTrees(n-1-i);
                else
                    count += numTrees(i)*numTrees(n-1-i);
            }
            return count;
        }
    }
};

Solution 2: dynamic programming . Base case: n==0, n==1时，f(n)==1, 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 

class Solution {
public:
    int numTrees(int n) {
        if(n<2)return 1;
        
        vector<int> v(n+1, 0);
        v[0]=1;
        v[1]=1;
        for(int i=2;i<n+1;i++){
            for(int j=0;j<i;j++){
                v[i]+=v[j]*v[i-1-j];
            }
        }
        return v[n];
    }
};