LeetCopilot

Binary Search

Master binary search patterns for sorted arrays, rotated arrays, 2D matrices, and optimization problems. Learn O(log n) search techniques and binary search on answer.

The Binary Search pattern transforms $O (N)$ linear search into $O (lo g N)$ logarithmic search by repeatedly dividing the search space in half. Master classic binary search, lower/upper bounds for duplicates, rotated sorted arrays, 2D matrix search, and binary search on answer for optimization problems. Learn when to use each variant and how to avoid off-by-one errors and infinite loops.

Featured Guide

Complete Guide

The Complete Binary Search Guide: Master All Patterns, Templates, and Techniques

The ultimate comprehensive guide to binary search. Learn all variants (classic, binary search on answer, rotated arrays), when to use each pattern, complete templates in multiple languages, and a systematic approach to solve any binary search problem.

25 min read

Interactive Tool

Roadmap

Binary Search Visualizer

Master binary search algorithms interactively. Step through Classic, Lower Bound, and Rotated Array search patterns. visualize O(log n) convergence and pointer updates in real-time.

Binary Search Learning Roadmap: From Beginner to Interview-Ready in 6 Weeks

A structured 6-week learning path to master all binary search patterns. Progress from classic search to binary search on answer with curated problems, templates, and milestones.

Tutorials

Binary Search Off-by-One Errors: The Complete Fix for left, right, and mid

Master the exact pointer update patterns to avoid off-by-one errors in binary search. Learn when to use mid, mid+1, mid-1, and how to match loop conditions with pointer updates.

Binary SearchOff-by-One ErrorsDebugging

10 min

Why Your Binary Search Has an Infinite Loop (And How to Fix It in 60 Seconds)

Debug infinite loops in binary search fast. Learn the two root causes, the 60-second fix checklist, and how to ensure your pointer updates always make progress.

Binary SearchInfinite LoopDebugging

8 min

Why Binary Search Only Works on Sorted Data (Mathematical Proof)

Understand the fundamental reason binary search requires sorted data through mathematical proof and visual examples. Learn about monotonicity and why unsorted arrays break the elimination property.

Binary SearchMonotonicitySorted Data

8 min

Why Binary Search on Answer Works: The Monotonicity Insight

Understand the mathematical principle behind binary search on answer. Learn why monotonic feasibility enables the guess-and-check approach and how to verify it for any problem.

Binary SearchBinary Search on AnswerMonotonicity

7 min

Minimize Maximum vs Maximize Minimum in Binary Search: Pattern Recognition Guide

Learn to distinguish between minimize maximum and maximize minimum optimization patterns. Understand the feasibility direction, pointer updates, and how to recognize each pattern instantly.

Binary SearchMinimize MaximumMaximize Minimum

7 min

3 Feasibility Function Mistakes That Break Binary Search on Answer

Learn the three most common mistakes in feasibility functions: wrong monotonicity direction, off-by-one in counting, and incorrect greedy logic. Get debugging tips and fixes.

Binary SearchFeasibility FunctionDebugging

7 min

Lower Bound vs Upper Bound in Binary Search: Common Mistakes and Fixes

Stop confusing lower bound and upper bound. Learn the exact difference, common mistakes (wrong pointer, wrong condition), and how to remember which is which.

Binary SearchLower BoundUpper Bound

6 min

Why Binary Search Works on Rotated Sorted Arrays (Visual Proof)

Understand the mathematical proof of why binary search works on rotated sorted arrays. Learn why one half is always sorted and how to leverage this property for O(log n) search.

Binary SearchRotated ArrayProof

9 min

How Duplicates Break Rotated Array Binary Search (And How to Fix It)

Learn why duplicates change rotated array binary search from O(log n) to O(n) worst case, how to handle the ambiguous cases, and when to use the modified template.

Binary SearchRotated ArrayDuplicates

8 min

2D Matrix Index Mapping in Binary Search: The Formula and Common Mistakes

Master the 1D-to-2D index conversion formula for binary search on matrices. Learn row and column calculation, common off-by-one errors, and how to verify correctness.

Binary Search2D MatrixIndex Mapping

6 min

When Binary Search Is NOT O(log n): Hidden Complexity Traps

Binary search isn't always O(log n). Learn when feasibility checks, duplicates, or matrix searches change the complexity to O(n log m), O(n), or O(m+n).

Binary SearchTime ComplexityAlgorithm Analysis

7 min

How to Recognize Binary Search Problems in 30 Seconds (Interview Pattern Recognition)

Learn to identify binary search opportunities instantly with the 30-second checklist. Recognize sorted data, optimization keywords, monotonic properties, and common disguises.

Binary SearchPattern RecognitionInterview Prep

7 min

Binary Search on Answer: The Ultimate Guide to "Guess and Check" Optimization

Master the binary search on answer pattern used in optimization problems. Learn when to use it, how to identify answer spaces, design feasibility functions, and solve "minimize maximum" and "maximize minimum" problems with production-ready templates.

Binary SearchBinary Search on AnswerOptimization

18 min

Find First and Last Position in Binary Search: Lower Bound and Upper Bound Explained

Master the lower bound and upper bound binary search templates for finding first and last occurrences in sorted arrays with duplicates. Learn the exact pointer update logic, when to use each variant, and how to avoid common mistakes.

Binary SearchLower BoundUpper Bound

15 min

Binary Search on Rotated Sorted Arrays: Complete Guide with Templates

Master binary search on rotated sorted arrays with production-ready templates. Learn the key insight that one half is always sorted, how to identify it, and handle duplicates correctly.

Binary SearchRotated ArrayTemplates

16 min

Binary Search on 2D Matrices: Row-Column Search and Sorted Matrix Techniques

Master binary search on 2D matrices with two approaches: treat as 1D array for fully sorted matrices, and staircase search for row-column sorted matrices. Learn index mapping and when to use each technique.

Binary Search2D MatrixIndex Mapping

10 min

Binary Search vs Linear Search: When to Use Each (With Complexity Analysis)

Learn when binary search is worth the complexity overhead versus simple linear search. Understand the breakeven point, practical decision criteria, and real-world tradeoffs between O(log n) and O(n).

Binary SearchLinear SearchComparison

12 min

7 Binary Search Implementation Mistakes That Cause Infinite Loops and Wrong Answers

Learn the exact implementation mistakes that cause binary search bugs: integer overflow, infinite loops, off-by-one errors, wrong loop conditions, and more. Get debugging checklists and fixes for each mistake.

Binary SearchDebuggingCommon Mistakes

12 min