LeetCode Q96: 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

Solution:
Different from Unique Binary Search Trees II problem, in this problem, there is no need to know exact information contained in each node. All we need to know is for a given number of nodes, how many different unique BST can be generated. The solution is very similar to Fibonacci sequence problem.

	class Solution {
	public:
	int helper(int Num, vector<int>& map){
	if(map[Num]!=0)
	return map[Num];
	int num=0;
	for(int i=1; i<=Num; i++){
	int n0=helper(i-1, map);
	int n1=helper(Num-i, map);
	num+=n0*n1;
	}
	map[Num]=num;
	return num;
	}
	int numTrees(int Num) {
	vector<int> map(Num+1, 0);
	map[0]=1;
	map[1]=1;
	int num=helper(Num, map);
	return num;
	}
	};

view raw Q96UniqueBST.cpp hosted with ❤ by GitHub