Episode 7 — DSA with JavaScript / 7.10 — Binary Search

7.10 — Quick Revision: Binary Search

<< Overview

Key concepts

VariantWhenTemplate
Standard BSFind exact matchlo<=hi, return mid
Lower boundFirst >= targetlo<hi, hi=mid
Upper boundLast <= targetlo<hi, lo=mid+1
Rotated arraySorted but rotatedCheck which half sorted
BS on answerOptimizationFeasibility check
Peak findingFind local maxCompare mid vs mid+1
2D matrixRow-col sortedFlatten index

Common pitfalls

  1. Off-by-one: lo<=hi vs lo<hi
  2. Integer overflow in mid calculation
  3. Infinite loop when lo=mid (use lo=mid+1)
  4. Forgetting array must be sorted
  5. Wrong comparison direction

Self-check drill

SC-001

  • Q: BS time?
  • A: O(log n)

SC-002

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-003

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-004

  • Q: Rotated array search?
  • A: Check sorted half

SC-005

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-006

  • Q: BS on answer?
  • A: Search feasible range

SC-007

  • Q: Lower bound?
  • A: First element >= target

SC-008

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-009

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-010

  • Q: Infinite array BS?
  • A: Double bounds first

SC-011

  • Q: BS time?
  • A: O(log n)

SC-012

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-013

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-014

  • Q: Rotated array search?
  • A: Check sorted half

SC-015

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-016

  • Q: BS on answer?
  • A: Search feasible range

SC-017

  • Q: Lower bound?
  • A: First element >= target

SC-018

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-019

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-020

  • Q: Infinite array BS?
  • A: Double bounds first

SC-021

  • Q: BS time?
  • A: O(log n)

SC-022

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-023

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-024

  • Q: Rotated array search?
  • A: Check sorted half

SC-025

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-026

  • Q: BS on answer?
  • A: Search feasible range

SC-027

  • Q: Lower bound?
  • A: First element >= target

SC-028

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-029

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-030

  • Q: Infinite array BS?
  • A: Double bounds first

SC-031

  • Q: BS time?
  • A: O(log n)

SC-032

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-033

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-034

  • Q: Rotated array search?
  • A: Check sorted half

SC-035

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-036

  • Q: BS on answer?
  • A: Search feasible range

SC-037

  • Q: Lower bound?
  • A: First element >= target

SC-038

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-039

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-040

  • Q: Infinite array BS?
  • A: Double bounds first

SC-041

  • Q: BS time?
  • A: O(log n)

SC-042

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-043

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-044

  • Q: Rotated array search?
  • A: Check sorted half

SC-045

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-046

  • Q: BS on answer?
  • A: Search feasible range

SC-047

  • Q: Lower bound?
  • A: First element >= target

SC-048

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-049

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-050

  • Q: Infinite array BS?
  • A: Double bounds first

SC-051

  • Q: BS time?
  • A: O(log n)

SC-052

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-053

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-054

  • Q: Rotated array search?
  • A: Check sorted half

SC-055

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-056

  • Q: BS on answer?
  • A: Search feasible range

SC-057

  • Q: Lower bound?
  • A: First element >= target

SC-058

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-059

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-060

  • Q: Infinite array BS?
  • A: Double bounds first

SC-061

  • Q: BS time?
  • A: O(log n)

SC-062

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-063

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-064

  • Q: Rotated array search?
  • A: Check sorted half

SC-065

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-066

  • Q: BS on answer?
  • A: Search feasible range

SC-067

  • Q: Lower bound?
  • A: First element >= target

SC-068

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-069

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-070

  • Q: Infinite array BS?
  • A: Double bounds first

SC-071

  • Q: BS time?
  • A: O(log n)

SC-072

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-073

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-074

  • Q: Rotated array search?
  • A: Check sorted half

SC-075

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-076

  • Q: BS on answer?
  • A: Search feasible range

SC-077

  • Q: Lower bound?
  • A: First element >= target

SC-078

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-079

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-080

  • Q: Infinite array BS?
  • A: Double bounds first

SC-081

  • Q: BS time?
  • A: O(log n)

SC-082

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-083

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-084

  • Q: Rotated array search?
  • A: Check sorted half

SC-085

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-086

  • Q: BS on answer?
  • A: Search feasible range

SC-087

  • Q: Lower bound?
  • A: First element >= target

SC-088

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-089

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-090

  • Q: Infinite array BS?
  • A: Double bounds first

SC-091

  • Q: BS time?
  • A: O(log n)

SC-092

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-093

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-094

  • Q: Rotated array search?
  • A: Check sorted half

SC-095

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-096

  • Q: BS on answer?
  • A: Search feasible range

SC-097

  • Q: Lower bound?
  • A: First element >= target

SC-098

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-099

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-100

  • Q: Infinite array BS?
  • A: Double bounds first

SC-101

  • Q: BS time?
  • A: O(log n)

SC-102

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-103

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-104

  • Q: Rotated array search?
  • A: Check sorted half

SC-105

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-106

  • Q: BS on answer?
  • A: Search feasible range

SC-107

  • Q: Lower bound?
  • A: First element >= target

SC-108

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-109

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-110

  • Q: Infinite array BS?
  • A: Double bounds first

SC-111

  • Q: BS time?
  • A: O(log n)

SC-112

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-113

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-114

  • Q: Rotated array search?
  • A: Check sorted half

SC-115

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-116

  • Q: BS on answer?
  • A: Search feasible range

SC-117

  • Q: Lower bound?
  • A: First element >= target

SC-118

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-119

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-120

  • Q: Infinite array BS?
  • A: Double bounds first

SC-121

  • Q: BS time?
  • A: O(log n)

SC-122

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-123

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-124

  • Q: Rotated array search?
  • A: Check sorted half

SC-125

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-126

  • Q: BS on answer?
  • A: Search feasible range

SC-127

  • Q: Lower bound?
  • A: First element >= target

SC-128

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-129

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-130

  • Q: Infinite array BS?
  • A: Double bounds first

SC-131

  • Q: BS time?
  • A: O(log n)

SC-132

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-133

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-134

  • Q: Rotated array search?
  • A: Check sorted half

SC-135

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-136

  • Q: BS on answer?
  • A: Search feasible range

SC-137

  • Q: Lower bound?
  • A: First element >= target

SC-138

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-139

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-140

  • Q: Infinite array BS?
  • A: Double bounds first

SC-141

  • Q: BS time?
  • A: O(log n)

SC-142

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-143

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-144

  • Q: Rotated array search?
  • A: Check sorted half

SC-145

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-146

  • Q: BS on answer?
  • A: Search feasible range

SC-147

  • Q: Lower bound?
  • A: First element >= target

SC-148

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-149

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-150

  • Q: Infinite array BS?
  • A: Double bounds first

SC-151

  • Q: BS time?
  • A: O(log n)

SC-152

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-153

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-154

  • Q: Rotated array search?
  • A: Check sorted half

SC-155

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-156

  • Q: BS on answer?
  • A: Search feasible range

SC-157

  • Q: Lower bound?
  • A: First element >= target

SC-158

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-159

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-160

  • Q: Infinite array BS?
  • A: Double bounds first

SC-161

  • Q: BS time?
  • A: O(log n)

SC-162

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-163

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-164

  • Q: Rotated array search?
  • A: Check sorted half

SC-165

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-166

  • Q: BS on answer?
  • A: Search feasible range

SC-167

  • Q: Lower bound?
  • A: First element >= target

SC-168

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-169

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-170

  • Q: Infinite array BS?
  • A: Double bounds first

SC-171

  • Q: BS time?
  • A: O(log n)

SC-172

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-173

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-174

  • Q: Rotated array search?
  • A: Check sorted half

SC-175

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-176

  • Q: BS on answer?
  • A: Search feasible range

SC-177

  • Q: Lower bound?
  • A: First element >= target

SC-178

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-179

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-180

  • Q: Infinite array BS?
  • A: Double bounds first

SC-181

  • Q: BS time?
  • A: O(log n)

SC-182

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-183

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-184

  • Q: Rotated array search?
  • A: Check sorted half

SC-185

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-186

  • Q: BS on answer?
  • A: Search feasible range

SC-187

  • Q: Lower bound?
  • A: First element >= target

SC-188

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-189

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-190

  • Q: Infinite array BS?
  • A: Double bounds first

SC-191

  • Q: BS time?
  • A: O(log n)

SC-192

  • Q: Prerequisite?
  • A: Sorted/monotonic

SC-193

  • Q: Mid formula?
  • A: lo+(hi-lo)/2

SC-194

  • Q: Rotated array search?
  • A: Check sorted half

SC-195

  • Q: Peak element?
  • A: Compare mid vs mid+1

SC-196

  • Q: BS on answer?
  • A: Search feasible range

SC-197

  • Q: Lower bound?
  • A: First element >= target

SC-198

  • Q: 2D matrix BS?
  • A: Flatten to 1D index

SC-199

  • Q: Find min in rotated?
  • A: Compare mid with hi

SC-200

  • Q: Infinite array BS?
  • A: Double bounds first