Pointer-Based Data Structures — Arrays, Linked Lists, Stacks, Queues & Trees Explained | Chapter 10 of Intro to Algorithms

Foundational data structures shape the way software manages and manipulates information. Chapter 10 of introduction to algorithms introduces essential pointer-based data structures, including arrays, linked lists, stacks, queues, and tree representations. These structures are critical for building more advanced algorithms and are the backbone of dynamic memory management, search, and efficient computation.

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Array-Based Structures: Arrays, Matrices, Stacks, and Queues

Arrays store elements in contiguous memory and provide constant-time access by index. While arrays are efficient for reading and writing elements, they are inflexible for dynamic operations like frequent insertions or deletions. Matrices (2D arrays) can be stored in row-major or column-major order to optimize for different access patterns.

Stacks and queues are classic structures implemented with arrays:

• Stack (LIFO): Last-In-First-Out with operations PUSH, POP, and STACK-EMPTY — all in O(1) time.
• Queue (FIFO): First-In-First-Out with ENQUEUE and DEQUEUE, often using wrap-around indexing for efficiency.

Stack and queue implementations must handle overflow and underflow gracefully.

Linked Lists: Singly, Doubly, and Circular Lists

Linked lists store elements in nodes connected by pointers, supporting dynamic growth and efficient O(1) insertion or deletion (if the pointer is known). Key variants include:

• Singly linked list: Each node points to its successor.
• Doubly linked list: Nodes have both next and previous pointers for bi-directional traversal.
• Circular linked list: The last node points back to the first, forming a loop.

Searching in a linked list is linear (Θ(n)), but sentinel (dummy) nodes can simplify operations and make code more robust by handling edge cases elegantly.

Stacks and Queues via Pointers

Stacks and queues can also be implemented using linked lists for true dynamic memory management. A pointer to the head or tail (or both, in the case of queues) allows for efficient push, pop, enqueue, and dequeue operations without the need for pre-allocated space. Linked implementations grow or shrink as needed and only fail when system memory is exhausted.

Representing Rooted Trees with Pointers

Trees use nodes with pointers to children and parents. In a binary tree, each node contains a key, a parent pointer, and left/right child pointers. The root has no parent (parent = NIL), and missing children are indicated with NIL. An empty tree is simply a root pointer set to NIL.

Left-Child, Right-Sibling Representation for General Trees

For trees with a variable number of children, the left-child, right-sibling representation is a memory-efficient solution. Each node has a parent pointer, a left-child pointer (to its first child), and a right-sibling pointer (to its next sibling at the same level). This design requires only O(n) space for n nodes and is popular in compilers for syntax trees and expression parsing.

Key Concepts and Glossary

• Array: Contiguous block of memory, accessed by index
• Stack: Last-In-First-Out data structure
• Queue: First-In-First-Out data structure
• Linked List: Sequence of nodes linked by pointers
• Doubly Linked List: Nodes with next and previous pointers
• Sentinel: Dummy node for simpler, robust code
• Wrap-Around: Circular array indexing for efficient queues
• Parent/Left-Child/Right-Sibling Pointers: For tree navigation
• Dynamic Set: Collection supporting insert, delete, search
• Compact List: Linked list emulated with two arrays
• Circular List: Last node points to first
• Heap Mergeable Structures: Special linked-list-based heaps
• Matrix: 2D array structure, possibly ragged

Conclusion: Building Blocks for Dynamic Data

Chapter 10 of introduction to algorithms lays the groundwork for dynamic data management in computer science. Mastering pointer-based structures like arrays, linked lists, stacks, queues, and trees unlocks the power to implement efficient, flexible algorithms in any programming language.

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