Insert the elements 18, 23, 10, 12, 30, 18, 25, 4, 21, 36, 14, 20, 47 into a balanced Binary Search Tree and count the number of comparisons.
Q.) Insert the elements 18, 23, 10, 12, 30, 18, 25, 4, 21, 36, 14, 20, 47 into a balanced Binary Search Tree and count the number of comparisons.
Subject: data structuresA Binary Search Tree (BST) is a tree in which all the nodes follow the below property:
- The left sub-tree of a node has a key less than or equal to its parent node's key.
- The right sub-tree of a node has a key greater than to its parent node's key.
To insert elements into a balanced Binary Search Tree (BST), we follow these steps:
- Start from the root.
- Compare the inserting element with root, if less than root, then recurse for the left subtree. Else, recurse for the right subtree.
- After reaching null, insert the new node at that point.
Let's insert the elements 18, 23, 10, 12, 30, 18, 25, 4, 21, 36, 14, 20, 47 into a balanced Binary Search Tree and count the number of comparisons.
Insertion | Tree Structure | Comparisons |
---|---|---|
18 | 18 | 0 |
23 | 18 - 23 | 1 |
10 | 10 - 18 - 23 | 2 |
12 | 10 - 12 - 18 - 23 | 3 |
30 | 10 - 12 - 18 - 23 - 30 | 4 |
18 | 10 - 12 - 18 - 18 - 23 - 30 | 5 |
25 | 10 - 12 - 18 - 18 - 23 - 25 - 30 | 6 |
4 | 4 - 10 - 12 - 18 - 18 - 23 - 25 - 30 | 7 |
21 | 4 - 10 - 12 - 18 - 18 - 21 - 23 - 25 - 30 | 8 |
36 | 4 - 10 - 12 - 18 - 18 - 21 - 23 - 25 - 30 - 36 | 9 |
14 | 4 - 10 - 12 - 14 - 18 - 18 - 21 - 23 - 25 - 30 - 36 | 10 |
20 | 4 - 10 - 12 - 14 - 18 - 18 - 20 - 21 - 23 - 25 - 30 - 36 | 11 |
47 | 4 - 10 - 12 - 14 - 18 - 18 - 20 - 21 - 23 - 25 - 30 - 36 - 47 | 12 |
So, the total number of comparisons made to insert these elements into a balanced Binary Search Tree is 12.
Note: The above tree structures are simplified for the sake of understanding. In a real BST, each node only has up to 2 children, and the actual layout would look more like a tree. However, the order of the nodes would remain the same.