Asksia AI LOGO

Sia

Question
Computer Science
Posted 2 months ago
For the following list :
4
6
,
 
4
3
,
 
5
5
,
 
3
4
,
 
2
4
,
 
2
5
,
 
6
0
,
 
9
1
,
 
9
8
,
 
7
0
,
 
3
9
,
 
4
1
,
 
9
2
,
 
6
4
,
 
8
2
 
a
.
 construct 
(
draw
)
 the 
(
2
,
4
)
-
tree
b
.
 construct 
(
draw
)
 the red
-
black tree 
(
 by converting the tree from 
(
a 
)
 
 
)
 
inserting their elements successively, starting with the empty tree.
Sign in to unlock the answer
Answer from Sia
Posted 2 months ago
Step-by-step Instruction
Choose to represent the trees visually and insert elements successively
Define concrete use cases and testing cases for the function: when user inserts elements, the tree should maintain its properties


 Constructing a 2-4 Tree

Explanation
A 2-4 tree is a self-balancing tree where every node has either 2, 3, or 4 children.


1. 
Initialize the tree
: Start with an empty tree.
2. 
Insert elements
: Insert each element from the list into the tree while maintaining the 2-4 tree properties.
3. 
Split nodes
: If a node exceeds 4 children, split it into two nodes and propagate the middle element up.

 Constructing a Red-Black Tree

Explanation
A red-black tree is a binary search tree with an extra bit for denoting the color of the node, either red or black.


1. 
Initialize the tree
: Start with an empty tree.
2. 
Insert elements
: Insert each element from the list into the tree while maintaining the red-black tree properties.
3. 
Recolor and rotate
: After each insertion, recolor and rotate the tree to maintain balance.

 Example Code for 2-4 Tree

python


 Example Code for Red-Black Tree

python


 Main Function for Testing

python
Time Complexity
The time complexity for insertion in both 2-4 trees and red-black trees is O(logn)O(\log n).
Space Complexity
The space complexity for both trees is O(n)O(n), where nn is the number of elements in the tree.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages
Strong algorithms that better know you
Early access to new release features
Study Other Question