ZIO

Introduction to Algorithms

What an algorithm is, step-wise problem decomposition, pseudocode reading.

Measuring Algorithm Efficiency

Time and space complexity intuition, big-picture growth rates without formal Big-O.

Searching

Linear search, binary search and variants over sorted/unsorted data.

Sorting

Selection, insertion, merge and quick sort intuition; stability and order properties.

Recursion

Recursive thinking, base/recursive cases, recursion tree, divide-and-conquer.

Dynamic Programming Intuition

Overlapping subproblems, memoisation, tabulation on small input sizes.

Greedy Algorithms

Local optimal choices, interval scheduling, coin-change-style ad-hoc greedy.

Basic Graph Concepts

Vertices, edges, directed/undirected graphs, paths, cycles, connectivity.

Graph Traversal

Breadth-first and depth-first traversal as conceptual exploration strategies.

Shortest Paths

Shortest-path intuition on grids and small graphs without formal algorithms.

Trees

Rooted trees, binary trees, parent/child traversal, tree counting puzzles.

Basic Data Structures

Arrays, lists, stacks, queues — used as tools for problem modelling.

Simulation

Mentally or on paper simulating a process or rule on small concrete inputs.

Invariants and Monovariants

Quantities preserved or strictly changing across steps — proving outcomes.

Case Analysis

Splitting a problem into exhaustive cases and resolving each.

Counting Principles

Sum and product rules, permutations, combinations applied to small enumerations.

Pigeonhole Principle

Existence arguments via pigeons/holes — colourings, residues, pairs.

Parity and Modular Reasoning

Even/odd reasoning, basic modular arithmetic for invariants.

Elementary Number Theory

Divisibility, gcd/lcm reasoning, prime factorisation puzzles.

Combinatorial Games

Winning/losing positions, Nim-like games, strategy stealing.

Sets and Logic

Inclusion-exclusion, propositional logic, truth tables in puzzles.

Constructive Problems

Building an explicit example/configuration that satisfies given rules.

Optimisation Puzzles

Finding minimum/maximum of a quantity under given constraints.

Scheduling and Ordering

Sequencing tasks, jobs or moves to satisfy precedence/deadline rules.

Grid and Geometry Puzzles

Reasoning on 2D grids — paths, colourings, tilings, distance puzzles.

Three Concrete Inputs Format

ZIO-style problems — solve three increasingly large concrete inputs by spotting an efficient method.