Ontological Layer: Linear Access Disciplines

Stacks & Queues

The Mechanics of LIFO and FIFO Flow

The Rules of Entrance and Exit

Realm 03 taught us how to link data together. Realm 04 dictates the strict rules of how that data can be accessed. A Stack forces a Last-In, First-Out (LIFO) discipline, creating a temporary holding zone perfect for expression evaluation and function calls. A Queue mandates a First-In, First-Out (FIFO) discipline, forming the foundation of task scheduling and fair resource allocation.

DATA SET → ACCESS RESTRICTION → LIFO (STACK) vs FIFO (QUEUE) → POINTER CONTROL → BOUNDARY CHECKS → EXPRESSION EVALUATION → SCHEDULING

The 11 Discipline Nodes

Ontological Mapping: Linear Data Control

GROUP 01

LIFO Stack Concept

Last-In, First-Out logic
Push operation (Insert)
Pop operation (Remove)
Peek / Top (Access)

GROUP 01

Array Implementation

Static memory allocation
Top index pointer
Top = -1 (Empty state)
Top = N-1 (Full state)

GROUP 02

Infix to Postfix

Expression formats (In/Pre/Post)
Operator precedence handling
Parentheses resolution
Stack holds pending operators

GROUP 02

Postfix Evaluation

Machine execution of math
Operands pushed to stack
Operators pop operands & eval
Final result remains at Top

GROUP 03

FIFO Queue Concept

First-In, First-Out logic
Enqueue (Insert at Rear)
Dequeue (Remove from Front)
Dual-pointer mechanism

GROUP 03

Circular Queues

Solves linear queue wasted space
Rear wraps to beginning
Modulo arithmetic (Rear+1)%N
Full condition (Front == Rear+1)

GROUP 01 & 03

Boundary Conditions

Overflow: Insert into full structure
Underflow: Delete from empty structure
Critical error handling
Bounded vs Unbounded capacity

GROUP 04

Priority Queues

Elements ordered by priority, not time
Highest priority dequeued first
Operating system task scheduling
Bridge to Heaps (Realm 05)

GROUP 04

Deques

Double-Ended Queue
Insert/Delete at FRONT
Insert/Delete at REAR
Input/Output restricted variants

VARIOUS

Implementation Choice

Array: Fixed size, O(1) access
Linked: Dynamic size, pointer overhead
Array queues need shifting or circular logic
Linked queues need simple pointer updates

FINAL PROTOCOL

11 — The Linear Discipline Lab

1. PUSH(A), PUSH(B), POP() -> [A]

2. ENQ(1), ENQ(2), DEQ() -> [2]

3. CIRC: REAR = (REAR+1)%MAX

[1] TRACE STACK STATE [2] EVALUATE POSTFIX [3] MANAGE QUEUE POINTERS [4] DETECT OVERFLOW [5] IMPLEMENT DEQUE

These access disciplines are the unseen engines of computation. The stack manages the deep recursion of functions and execution contexts, while the queue organizes the flow of asynchronous data and tasks. Understanding them prepares us for the hierarchical complexity of Trees & Heaps in Realm 05.

SIMULATION RUNNING