Index

Omni-Classification of Data Structures:

Tier 1: The Building Blocks (Primitives)¶

These are the atomic units provided by the hardware/CPU. They don't "hold" other data; they are the data.

Integer, Float, Char, Boolean.
Pointers/References: (The "glue" used to build complex structures).

Tier 2: The Physical Containers (Implementation Layer)¶

These define how data is physically arranged in your RAM. Every complex structure in Tier 3 and 4 must be built using one of these.

Structure	Memory Layout	Key Characteristic
Array	Contiguous	One solid block. Fast access via index, but hard to resize.
Linked List	Non-Contiguous	Scattered nodes connected by pointers. Easy to grow, slow to search.

Tier 3: The Logical Rules (Linear ADTs)¶

These are Linear because the data follows a single sequence (one-after-another). They are just rules applied to Tier 2 containers.

Stack (LIFO): Implementation: Array-based Stack or Linked-List Stack.
Queue (FIFO): Implementation: Array-based Queue or Linked-List Queue.
List/Vector: A dynamic version of an array.

Tier 4: The Hierarchical & Relationship Models (Non-Linear ADTs)¶

These are Non-Linear because one element can connect to multiple other elements. They represent complex relationships.

A) Trees (Hierarchical)¶

Data is organized in a parent-child relationship.

Binary Tree / BST: For fast searching.
Heaps: For priority (Priority Queues).
Tries: For dictionary/string searching.
Note: Trees are usually implemented using Linked Nodes (Physical Tier 2).

B) Graphs (Network/Relational)¶

Data is organized as nodes (vertices) and connections (edges). No strict hierarchy.

Directed/Undirected Graphs: Representing maps, social networks, or circuits.
Implementation: Graphs are represented using an Adjacency Matrix (Physical Tier 2: 2D Array) or an Adjacency List (Physical Tier 2: Array of Linked Lists).

Tier 5: The "Abstracted" Collections (Specialized ADTs)¶

These are high-level concepts that often combine multiple tiers to solve specific problems.

Hash Table / Dictionary: Uses an Array + a Hash Function to provide \(O(1)\) access.
Set: A collection of unique items (can be implemented via Hash Table or Tree).

The Big Picture Summary¶

Category	Type	The "What" (Examples)	The "How" (Realization)
Linear	Physical	Array, Linked List	Direct Memory Mapping.
Linear	Logical (ADT)	Stack, Queue	Rules applied to Arrays/LL.
Non-Linear	Hierarchical	Tree, Heap	Parent-Child pointers.
Non-Linear	Relational	Graph	Network of nodes and edges.

Why this solves your confusion:¶

When you see "Representing a Multi-dimensional Array (Tier 2/3) using a Linked List (Tier 2) as a Stack (Tier 3)," you are just moving between these tiers.

You are taking a Physical Container (Linked List), giving it the Behavioral Rules of a Stack, to store data that looks like a Matrix. It's like using Lego Bricks (Physical) to build a Garage (Logical Rule) for your Toy Cars (The Data).

Does this birds-eye view make the relationship between Trees, Arrays, and ADTs feel more organized?