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Computer Science

Arrays and Dynamic Arrays

Contiguous Memory, Amortized Growth, and the O(1) vs O(n) Tradeoffs — A TLDR Primer

You have a data structures exam coming up, or your professor just flew past arrays and dynamic arrays in twenty minutes and left you with more questions than answers. This guide cuts straight to what you need to know.

**TLDR: Arrays and Dynamic Arrays** is a focused, comprehensive but tight guide covering exactly one topic: how arrays and dynamic arrays store data in memory, how their core operations perform, and how to choose between them. Starting from the hardware level — what it actually means for memory to be contiguous — the guide walks through access, search, insertion, and deletion with clear Big-O analysis and worked examples. It then motivates dynamic arrays by showing where fixed arrays break down, explains the resize-and-copy doubling strategy, and works through the amortized cost argument that makes append O(1) on average despite occasional expensive resizes. A pseudocode walkthrough lets you see a minimal dynamic array built from scratch.

This is for high school students in AP Computer Science Principles or AP CSA, college freshmen hitting their first data structures for beginners course, and anyone who needs a clean mental model fast. It is short by design — no padding, no filler, just the concepts and the reasoning behind them.

If you have been searching for a concise arrays vs linked lists study guide that actually explains the tradeoffs instead of just listing them, this is it. Pick it up and walk into your next class or exam with a clear picture of the structure underneath your code.

What you'll learn
  • Explain how a fixed-size array is laid out in memory and why indexing is constant time
  • Analyze the time complexity of common array operations (access, search, insert, delete)
  • Describe how a dynamic array grows via doubling and why amortized append is O(1)
  • Choose between fixed arrays and dynamic arrays for a given problem
  • Implement basic dynamic array operations and reason about their costs
What's inside
  1. 1. What an Array Actually Is
    Introduces the array as a contiguous block of memory and explains how indexing works at the hardware level.
  2. 2. Core Operations and Their Costs
    Walks through access, search, insertion, and deletion on a fixed array with Big-O analysis and worked examples.
  3. 3. The Problem of Fixed Size: Enter Dynamic Arrays
    Motivates dynamic arrays by showing the limits of fixed arrays and introduces capacity vs. length.
  4. 4. How Dynamic Arrays Grow: Doubling and Amortized Cost
    Explains the resize-and-copy strategy and proves why append is O(1) amortized despite occasional O(n) resizes.
  5. 5. Building Your Own Dynamic Array
    Walks through pseudocode for a minimal dynamic array supporting append, get, set, and remove, with cost analysis at each step.
  6. 6. When to Use Which: Practical Tradeoffs
    Compares arrays and dynamic arrays to linked lists and hash tables, and gives rules of thumb for choosing the right structure.
Published by Solid State Press
Arrays and Dynamic Arrays cover
TLDR STUDY GUIDES

Arrays and Dynamic Arrays

Contiguous Memory, Amortized Growth, and the O(1) vs O(n) Tradeoffs — A TLDR Primer
Solid State Press

Contents

  1. 1 What an Array Actually Is
  2. 2 Core Operations and Their Costs
  3. 3 The Problem of Fixed Size: Enter Dynamic Arrays
  4. 4 How Dynamic Arrays Grow: Doubling and Amortized Cost
  5. 5 Building Your Own Dynamic Array
  6. 6 When to Use Which: Practical Tradeoffs
Chapter 1

What an Array Actually Is

Picture a row of numbered mailboxes in an apartment building. Each box is the same size, they sit right next to each other with no gaps, and you can walk straight to box 47 without checking every box before it. That mental image is almost exactly what a computer uses when it stores an array.

An array is a contiguous block of memory — a sequence of storage slots laid out one after another with no gaps between them. Each slot holds one value, called an element, and every slot is exactly the same size (measured in bytes). The array has a fixed size: the number of slots is decided when the array is created and does not change. These three properties — contiguous, uniform-sized, fixed — are what make arrays both powerful and limited.

Memory Addresses and Why They Matter

Every byte of your computer's RAM has a unique numerical label called a memory address. Think of it like a street address, except instead of identifying a house it identifies a single byte. When the operating system hands your program an array, it gives the program the address of the very first element. That address is called the base address.

Because all elements are the same size and there are no gaps, the address of any element can be computed with one arithmetic step. If each element occupies $s$ bytes and the base address is $b$, then the address of the element at position $i$ (where positions start at 0) is:

$\text{address}(i) = b + i \times s$

That formula is the entire secret behind why arrays are so fast. The hardware does not search; it calculates. It jumps directly to the right memory location in a single operation, regardless of how large the array is.

Example. An array of 32-bit integers (int in most languages) is stored starting at memory address 2000. Each integer occupies 4 bytes. What is the memory address of the element at index 5?

Solution. Use the address formula with $b = 2000$, $s = 4$, and $i = 5$: $\text{address}(5) = 2000 + 5 \times 4 = 2000 + 20 = 2020$ The processor goes directly to address 2020 — no scanning, no searching.

Indexing: Zero-Based and Why

The number used to identify a position in an array is called an index (plural: indices). In most programming languages — C, C++, Java, Python, JavaScript — arrays are zero-indexed, meaning the first element sits at index 0, the second at index 1, and so on. The last element of an array with $n$ elements is at index $n - 1$.

About This Book

If you are a high school student looking for computer science concepts for AP CSP students laid out without the textbook bloat, a college freshman working through an intro to data structures course, or a self-taught programmer who keeps hitting a wall when interviews ask about memory and performance, this book is for you.

This guide covers arrays and dynamic arrays explained simply and precisely — from how raw memory works to big-O notation for arrays in a computer science primer format that respects your time. You will learn how dynamic arrays work with examples drawn from real code, see why arrays vs linked lists is a question worth understanding deeply, and find data structures for beginners at the high school level treated with the same rigor you would get in a college course. A concise overview with no filler.

Read the sections in order — each one builds on the last. Work through every worked example before moving on, then use the problem set at the end to confirm you have it.

Keep reading

You've read the first half of Chapter 1. The complete book covers 6 chapters in roughly fifteen pages — readable in one sitting.

Coming soon to Amazon