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Computer Science

Binary Search

A High School & College Primer on the Algorithm, the Code, and the Common Traps

You have a coding exam, a technical interview, or an AP Computer Science unit coming up, and binary search keeps tripping you up — the off-by-one errors, the loop condition, the question of whether it even applies to your problem. This guide cuts straight to what you need to know.

**TLDR: Binary Search** covers the algorithm from first principles to real-world patterns in under 20 pages. You'll see exactly why binary search requires a sorted array, how to trace the low/high/mid pointers on a concrete example, and how to write clean code that doesn't break on edge cases. A dedicated section on off-by-one bugs names the mistakes students make most often and shows you how to avoid them. The guide then explains why the running time is O(log n) — not just the label, but the actual reasoning — and walks through variants like finding the first occurrence, last occurrence, and insertion point of a value. The final section covers the "binary search on the answer" pattern that shows up repeatedly in coding interviews and contest problems.

This book is written for high school students (grades 9–12) and early college students tackling their first algorithms course. It also works well as a quick reference for students reviewing before an exam or a tutor prepping a session. If you've searched for a computer science algorithms study guide that doesn't waste your time, this is it.

Pick it up, read it in one sitting, and walk into your next exam or interview ready.

What you'll learn
  • Explain in plain English why binary search works and what 'sorted' requirement it depends on.
  • Implement binary search in pseudocode with correct loop conditions and midpoint calculation.
  • Analyze the running time of binary search and compare it to linear search using big-O notation.
  • Recognize binary search variants such as finding the first or last occurrence of a value.
  • Identify problem patterns where binary search applies, including 'binary search on the answer'.
What's inside
  1. 1. What Binary Search Is and Why It Works
    Introduces the algorithm through the guessing-game analogy and pins down the sorted-array precondition.
  2. 2. The Algorithm Step by Step
    Walks through binary search on a concrete array, introducing low, high, and mid pointers and the comparison logic.
  3. 3. Writing the Code Without Off-by-One Bugs
    Presents clean pseudocode for binary search and dissects the most common implementation mistakes.
  4. 4. Running Time: Why It's O(log n)
    Explains logarithmic time by counting halvings and compares binary search to linear search with concrete numbers.
  5. 5. Variants: First Occurrence, Last Occurrence, and Insertion Point
    Extends the basic algorithm to handle duplicates and to find where a value would be inserted.
  6. 6. Where Binary Search Shows Up: Patterns and Applications
    Surveys real uses and the 'binary search on the answer' pattern that shows up in interviews and contests.
Published by Solid State Press
Binary Search cover
TLDR STUDY GUIDES

Binary Search

A High School & College Primer on the Algorithm, the Code, and the Common Traps
Solid State Press

Binary Search

A High School & College Primer on the Algorithm, the Code, and the Common Traps

Copyright © 2026 Solid State Press.

Published by Solid State Press.

All rights reserved. No part of this book may be reproduced or transmitted in any form without prior written permission, except for brief quotations in critical reviews and educational use.

Part of the TLDR Study Guides series.

Who This Book Is For

If you're taking AP Computer Science or an intro programming course, this book is for you. It's also for anyone doing binary search interview prep — whether that's a student grinding LeetCode before a summer internship or a self-taught programmer who never had a formal algorithms class. High school and early college students are the core audience, but any beginner who wants a binary search algorithm explained clearly and concisely will find what they need here.

This is a focused data structures and algorithms short guide covering exactly one topic. You'll learn how binary search works, how to code binary search without bugs creeping in at the boundaries, why it runs in O(log n) time, and how to handle variants like finding the first or last occurrence of a value. Think of it as an algorithms primer for AP Computer Science and beyond — about 15 pages, no padding.

Read straight through in order. Work every example yourself before reading the solution. Then hit the problem set at the end to confirm your understanding.

Contents

  1. 1 What Binary Search Is and Why It Works
  2. 2 The Algorithm Step by Step
  3. 3 Writing the Code Without Off-by-One Bugs
  4. 4 Running Time: Why It's O(log n)
  5. 5 Variants: First Occurrence, Last Occurrence, and Insertion Point
  6. 6 Where Binary Search Shows Up: Patterns and Applications
Chapter 1

What Binary Search Is and Why It Works

Imagine a friend is thinking of a number between 1 and 100, and you have to guess it. Every time you guess, they tell you "too high," "too low," or "correct." What's your strategy?

If you start at 1 and count up — 1, 2, 3, … — you'll find the number eventually, but in the worst case you need 100 guesses. There's a better way: guess 50 first. If your friend says "too low," you've instantly ruled out half the possibilities. The number must be between 51 and 100. Guess 75 next. Too high? Now it's between 51 and 74. Every single guess cuts your remaining candidates in half. You're guaranteed to find any number in 1–100 in at most 7 guesses, because $2^7 = 128 > 100$.

That guessing game is binary search. The algorithm does exactly the same thing on a sorted list of values.

The sorted-array precondition

The guessing game works because numbers have a natural order — you know that everything below your guess is smaller and everything above is larger. Binary search on a list requires the same property: the list must be sorted, meaning the elements appear in order from smallest to largest (or largest to smallest — the direction doesn't matter as long as it's consistent).

This is the central precondition of the algorithm — a condition that must be true before the algorithm can be applied. If the list is not sorted, the "too high / too low" logic breaks down completely. Guessing the middle element of a shuffled list tells you nothing useful about where the target might be.

A common mistake is to apply binary search to any list that "looks mostly sorted" or to forget to sort first. If the precondition isn't met, the algorithm can return a wrong answer with no warning. Always verify — or establish — sorted order before reaching for binary search.

The search space shrinks every step

The key idea is the search space: the set of positions in the array where the target value could possibly be hiding. At the start, every position is a candidate — the search space is the whole array.

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