Binary Trees Definition: A binary tree is a data structure in which each node has at most two children referred to as left child and right child.
Binary Tree using an Array:
Utilizes two main rules for placement:
If the parent index is i, the left child is placed at index 2i + 1.
If the parent index is i, the right child is placed at index 2i + 2.
Advantages:
[35mMemory Efficiency[0m: Arrays store data in consecutive memory locations, leading to less memory overhead.
[35mSimplicity of Implementation[0m: Implementing a binary tree with a Python list is straightforward compared to other methods.
Disadvantages:
Array representation is effective only for complete binary trees, where all levels are fully filled except possibly the last.
Inefficient for operations like insertion, deletion, and traversal in non-ideal cases where the tree is not complete.
Definition: A binary tree where every level, except possibly the last, is fully filled.
Example of representation in arrays and the issue with non-completeness:
If parts of the tree are removed, it leads to wasted space represented by None
values, which is inefficient.
Using classes for nodes allows for a more flexible structure.
Essential components for binary tree nodes:
Value: Holds the data of the node.
Left Child: Reference to its left child node.
Right Child: Reference to its right child node.
Example of constructing a binary tree using objects.
Definition: Accessing all items in a binary tree.
Types of Traversal:
Preorder Traversal: Visit the root first, then traverse the left subtree, followed by the right subtree.
Inorder Traversal: Traverse the left subtree first, visit the root, and then traverse the right subtree.
Postorder Traversal: Traverse the left subtree, then the right subtree, and visit the root last.
Given a binary tree:
Preorder Result: root, left subtree, right subtree.
Inorder Result: left subtree, root, right subtree.
Postorder Result: left subtree, right subtree, root.
Looking forward to other data structures in future classes:
Stacks: Follow Last In First Out (LIFO).
Operations include push (add an item), pop (remove the top item), and top (view the top item).
Uses include recursion management and undo/redo buttons in software applications.
Queues: Follow First In First Out (FIFO).
Operations include enqueue (add an item) and dequeue (remove an item).
Commonly used in real-life scenarios like ticket lines and call centers.
Linked Lists: Unlike arrays, linked lists do not store elements in contiguous memory locations.
Each node contains a value and a reference to the next node, which allows for dynamic memory usage.
Demonstrates how to construct a linked list using nodes and how to add new nodes.