Contents
- 1 How do we generate all different BSTs with N nodes?
- 2 How many BSTs can be possible from 3 unique keys?
- 3 How many different trees are possible with n nodes?
- 4 How many binary search trees can be formed using n keys?
- 5 How to construct all possible BSTs with keys 1 to N?
- 6 Which is the recursive function to create all unique BSTs?
How do we generate all different BSTs with N nodes?
The idea is to maintain a list of roots of all BSTs. Recursively construct all possible left and right subtrees….Below is detailed algorithm.
- Initialize list of BSTs as empty.
- For every number i where i varies from 1 to N, do following ……a) Create a new node with key as ‘i’, let this node be ‘node’ ……
How many BSTs can be possible from 3 unique keys?
3.2. As we may notice, there are only 5 possible BSTs of 3 nodes.
How many trees are possible with N nodes?
For n = 0, 1, 2, 3, … values of Catalan numbers are 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, …. So are numbers of Binary Search Trees. Total number of possible Binary Trees with n different keys (countBT(n)) = countBST(n) * n!
How many different trees are possible with n nodes?
In general: If there are n nodes, there exist 2^n-n different trees.
How many binary search trees can be formed using n keys?
How to construct a list of all BSTs?
The idea is to maintain a list of roots of all BSTs. Recursively construct all possible left and right subtrees. Create a tree for every pair of left and right subtree and add the tree to list. Below is detailed algorithm. 1) Initialize list of BSTs as empty.
How to construct all possible BSTs with keys 1 to N?
For example, with keys 1 to 3 (n =3), below are the unique BSTs possible, As we can see, there are five different Binary search Trees created with keys 1 to 3. There we can see each of the keys has got an opportunity to be the root and then we have constructed picking up possible keys for the left subtree and the right subtree subsequently.
Which is the recursive function to create all unique BSTs?
Say the recursive function to create all unique BST is buildBst which takes the range as an argument and returns all the trees (roots). Find the list of left subtrees recursively which can be found by calling buildBST (left,k-1); Now for each combination from left tree list and right tree list, create the BSTs and store that into list arr.
How many possible BSTs are in the left subtree list?
That’s illustrated below: So we can see that the left subtree list has three possible BSTs namely a, b, c & the right subtree list has 2 possible BST namely e & f. So we can have total 3*2=6 combinations.