【LeetCode】96 - 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

Tree Dynamic Programming

 

Solution 1:  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;
         }
     }
 };

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<)return ;

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