COS102: Problem Solving | Master Study Suite

Course Companion

Your Ultimate Study Guide for COS102 Problem Solving

A highly-optimized interactive suite designed to help you master computing architecture, solvable vs. unsolvable theories, heuristics, and algorithmic reduction patterns.

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Your Exam Readiness Map

Master these 4 key syllabus domains

Problem Anatomy & Computing

Inputs, outputs, variables, constants

Routine vs. Non-Routine Challenges

Defining predictability and structural changes

Solvability Theories (Halting Problem)

computability limits & NP-Completeness

The 10 Master Heuristic Strategies

Decomposition, RCA, testing, and analogies

Custom Revision Pad

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Module 1

Foundations of Computational Anatomy & Structure

Computational problem-solving is fundamentally defined by a conversion process. Raw information is ingested, systematically transformed via operations or mathematical steps, and spat out as a completed result—all within strict rules.

Inputs

The initial datasets, states, or parameters available on launch.

Process

The explicit algorithms, sequences, and logic operations executed.

Outputs

The final state, validated results, or calculated values produced.

Constraints

The limitations (system resources, memory bounds, or rules) enforced.

Core Variables & Constants

Data parameters inside computer programs are held in either constants (fixed memory cells that cannot change value once set) or variables (dynamic placeholders updated during execution).

Syntax Standard

const PI = 3.14159 // Fixed Constant value

var wages = hoursWorked * 1000 // wages & hoursWorked are variables

Core Function Library Cheat-Sheet

Master these core mathematical, string, and type conversion helper utilities:

Utility	Purpose	Input Example	Evaluated Output
abs(n)	Yields absolute magnitude	abs(-4)	4
sqrt(n)	Calculates square root	sqrt(4)	2
ceil(n)	Rounds UP to nearest integer	ceil(3.22)	4
round(N, decimals)	Rounds to specified decimals	round(3.7245, 2)	3.72
Length(s)	Returns characters in string	Length("Maryam")	6
float(n)	Converts integer/string to decimal	float(2)	2.0

Module 2

Routine vs. Non-Routine Challenges

Problem classification determines how we approach the building of algorithms. Problems are categorized by predictability and context:

Routine Problems

Features clear inputs, outputs, and deterministic resolution procedures. Solving them requires executing established, repetitive sequences.

Making a cup of tea
Database record search
User login authentication

Non-Routine Problems

These problems occur in unfamiliar or dynamic contexts. Objectives might be poorly defined, requiring creative adaptation, logic modeling, or custom architectures.

Designing an interface from scratch
Isolating a memory leak in unknown legacy code
Inventing a highly efficient custom search algorithm

Key Context Transition

How Routine transforms into Non-Routine: A completely routine operation transforms instantly into a complex non-routine challenge when variables shift without warning, constraints are tightened mid-process, or hardware limits fluctuate.

Module 3

Solvability Theory & Limits of Computation

Not all problems can be solved computationally. In theoretical computer science, a primary boundary exists between solvable and unsolvable operations:

Computable (Solvable)

Problems that have clear step-by-step algorithms that are guaranteed to halt, finish executing, and return a correct output for all valid inputs.

Examples: Shortest Path search (Dijkstra's), Greatest Common Divisor calculation (GCD).

Non-Computable (Unsolvable)

Problems where it is mathematically impossible to write a single algorithm that is guaranteed to find a correct answer and halt on all possible inputs.

Examples: The Halting Problem, State Entry Problem, Context-Free Grammar equivalence check.

The Halting Problem (Alan Turing, 1936)

Can we write a general program that takes *any* other arbitrary program and input, and correctly decides if that program will finish running or enter an infinite loop? Turing proved mathematically that no such universal decider program can ever be constructed. Any attempt to build one creates a logical contradiction.

Module 4

The 10 Master Heuristic Strategies

When an exact algorithmic solution is unavailable, we deploy **Heuristics** (mental frameworks and shortcuts) to navigate decision spaces quickly and generate highly viable solutions.

1. Trial and Error

Testing solutions successively until a workable option is found. Intuitive and flexible, but highly time-consuming.

2. Brainstorming

Group generation of spontaneous, un-evaluated suggestions. Quantity is prioritized over immediate quality; judgment is deferred.

3. Means-End Analysis (MEA)

Isolating current-state to goal-state disparities, then creating progressive actions to systematically bridge the gap.

4. Root Cause Analysis (RCA)

Bypassing immediate surface symptoms to identify the root failure of a system, using inquiries like the "Five Whys" tool.

5. Literal Thinking

A straightforward, logical path dealing explicitly with visible facts on the surface rather than deeper abstract possibilities.

6. Abstraction

Simplifying vast system challenges by stripping away granular details to focus strictly on structural high-level models.

7. Analogy

Drawing relational parallels between a new problem and a similar, solved past problem to transfer and adapt its solution.

8. Hypothesis Testing

Formulating a precise testable prediction (educated guess) and verifying it using structured experimentation and logging data.

9. Reduction

Simplifying or mapping a complex problem down into a known problem class that already has established, verified algorithms.

10. Divide and Conquer

Dividing an overarching problem into isolated sub-problems, solving them, and merging their completed outputs back together.

Your Ultimate Study Guide for COS102 Problem Solving

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Your Exam Readiness Map

Problem Anatomy & Computing

Routine vs. Non-Routine Challenges

Solvability Theories (Halting Problem)

The 10 Master Heuristic Strategies

Custom Revision Pad

Table of Contents

Foundations of Computational Anatomy & Structure

Inputs

Process

Outputs

Constraints

Core Variables & Constants

Core Function Library Cheat-Sheet

Routine vs. Non-Routine Challenges

Routine Problems

Non-Routine Problems

Key Context Transition

Solvability Theory & Limits of Computation

Computable (Solvable)

Non-Computable (Unsolvable)

The Halting Problem (Alan Turing, 1936)

The 10 Master Heuristic Strategies

1. Trial and Error

2. Brainstorming

3. Means-End Analysis (MEA)

4. Root Cause Analysis (RCA)

5. Literal Thinking

6. Abstraction

7. Analogy

8. Hypothesis Testing

9. Reduction

10. Divide and Conquer

COS102 Practice Sandboxes

Precedence Solver

Algebraic Format

Active Computing Trace Log

ATM Failure Sandbox

Available Parameters

1. Inputs Category

2. Process Action

3. Expected Outputs

4. Enforced Constraints

Interactive Mock Examination

Question Matrix

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