Episode 7 — DSA with JavaScript / 7.9 — Sorting Algorithms

7.9 — Interview Questions: Sorting Algorithms

Q1. What is the difference between stable and unstable sorting?

Answer: Stable sort preserves relative order of equal elements. Merge sort and insertion sort are stable; quick sort and selection sort are not.

Q2. When would you use insertion sort over merge sort?

Answer: For small arrays (<20 elements) or nearly sorted data where insertion sort's O(n) best case applies.

Q3. Explain merge sort's divide and conquer approach.

Answer: Split array in half recursively until single elements, then merge sorted halves back up. O(n log n) guaranteed.

Q4. Why can quick sort be O(n²) in the worst case?

Answer: When pivot selection is poor (always min or max), one partition has n-1 elements. Fix: random pivot or median-of-three.

Q5. What is cyclic sort? When is it applicable?

Answer: Place each element at its correct index. Only works when elements are in range 1..N or 0..N-1. O(n) time.

Q6. How do you find the kth largest element?

Answer: QuickSelect (partition-based): O(n) average. Or use a min-heap of size k: O(n log k).

Q7. What makes merge sort preferred for linked lists?

Answer: No random access needed; merge can be done in O(1) space on linked lists.

Q8. Compare time and space of all major sorting algorithms.

Answer: See comparison table in the chapter. Key: merge sort guarantees O(n log n) but needs O(n) space; quick sort is O(n log n) average with O(log n) space.

Q9. What is counting sort?

Answer: Count occurrences of each value, then reconstruct. O(n+k) where k is range. Only for integers with small range.

Q10. How does radix sort work?

Answer: Sort by each digit from least significant to most significant using a stable sort (counting sort). O(d × (n+k)).

Q11. When to use which sort?

Situation	Best sort
General purpose	Quick sort / merge sort
Nearly sorted	Insertion sort
Linked list	Merge sort
Integers in range	Counting / radix sort
Elements 1-N	Cyclic sort
Memory constrained	Quick sort / heap sort
Stability required	Merge sort / insertion sort

Q12. Explain Dutch National Flag algorithm.

Answer: 3-pointer partition of 0s, 1s, 2s in single O(n) pass. Used in 3-way quicksort.

Q13. How to sort in O(n) for specific inputs?

Answer: Counting sort (small range), radix sort (fixed digits), cyclic sort (1..N range).

Q14. What is external sorting?

Answer: For data too large for memory. Split into chunks, sort each in memory, merge chunks from disk.

Quick-fire table

#	Question	Answer
1	Merge sort time?	O(n log n) always
2	Quick sort worst?	O(n²) with bad pivot
3	Insertion sort best?	O(n) — nearly sorted
4	Cyclic sort time?	O(n) for 1..N range
5	Stable sorts?	Merge, insertion, counting
6	Unstable sorts?	Quick, selection, heap
7	Merge sort space?	O(n)
8	Quick sort space?	O(log n) stack
9	Counting sort time?	O(n+k)
10	Best general sort?	Quick sort (avg O(n log n))

Rapid self-check cards

SC-001

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-002

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-003

Q: Is merge sort stable?
A: Yes

SC-004

Q: Is quick sort stable?
A: No

SC-005

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-006

Q: Insertion sort best case?
A: O(n) — already sorted

SC-007

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-008

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-009

Q: Counting sort constraint?
A: Need small integer range

SC-010

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-011

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-012

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-013

Q: Is merge sort stable?
A: Yes

SC-014

Q: Is quick sort stable?
A: No

SC-015

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-016

Q: Insertion sort best case?
A: O(n) — already sorted

SC-017

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-018

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-019

Q: Counting sort constraint?
A: Need small integer range

SC-020

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-021

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-022

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-023

Q: Is merge sort stable?
A: Yes

SC-024

Q: Is quick sort stable?
A: No

SC-025

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-026

Q: Insertion sort best case?
A: O(n) — already sorted

SC-027

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-028

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-029

Q: Counting sort constraint?
A: Need small integer range

SC-030

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-031

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-032

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-033

Q: Is merge sort stable?
A: Yes

SC-034

Q: Is quick sort stable?
A: No

SC-035

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-036

Q: Insertion sort best case?
A: O(n) — already sorted

SC-037

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-038

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-039

Q: Counting sort constraint?
A: Need small integer range

SC-040

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-041

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-042

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-043

Q: Is merge sort stable?
A: Yes

SC-044

Q: Is quick sort stable?
A: No

SC-045

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-046

Q: Insertion sort best case?
A: O(n) — already sorted

SC-047

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-048

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-049

Q: Counting sort constraint?
A: Need small integer range

SC-050

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-051

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-052

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-053

Q: Is merge sort stable?
A: Yes

SC-054

Q: Is quick sort stable?
A: No

SC-055

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-056

Q: Insertion sort best case?
A: O(n) — already sorted

SC-057

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-058

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-059

Q: Counting sort constraint?
A: Need small integer range

SC-060

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-061

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-062

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-063

Q: Is merge sort stable?
A: Yes

SC-064

Q: Is quick sort stable?
A: No

SC-065

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-066

Q: Insertion sort best case?
A: O(n) — already sorted

SC-067

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-068

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-069

Q: Counting sort constraint?
A: Need small integer range

SC-070

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-071

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-072

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-073

Q: Is merge sort stable?
A: Yes

SC-074

Q: Is quick sort stable?
A: No

SC-075

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-076

Q: Insertion sort best case?
A: O(n) — already sorted

SC-077

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-078

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-079

Q: Counting sort constraint?
A: Need small integer range

SC-080

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-081

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-082

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-083

Q: Is merge sort stable?
A: Yes

SC-084

Q: Is quick sort stable?
A: No

SC-085

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-086

Q: Insertion sort best case?
A: O(n) — already sorted

SC-087

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-088

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-089

Q: Counting sort constraint?
A: Need small integer range

SC-090

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-091

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-092

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-093

Q: Is merge sort stable?
A: Yes

SC-094

Q: Is quick sort stable?
A: No

SC-095

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-096

Q: Insertion sort best case?
A: O(n) — already sorted

SC-097

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-098

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-099

Q: Counting sort constraint?
A: Need small integer range

SC-100

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-101

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-102

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-103

Q: Is merge sort stable?
A: Yes

SC-104

Q: Is quick sort stable?
A: No

SC-105

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-106

Q: Insertion sort best case?
A: O(n) — already sorted

SC-107

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-108

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-109

Q: Counting sort constraint?
A: Need small integer range

SC-110

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-111

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-112

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-113

Q: Is merge sort stable?
A: Yes

SC-114

Q: Is quick sort stable?
A: No

SC-115

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-116

Q: Insertion sort best case?
A: O(n) — already sorted

SC-117

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-118

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-119

Q: Counting sort constraint?
A: Need small integer range

SC-120

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-121

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-122

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-123

Q: Is merge sort stable?
A: Yes

SC-124

Q: Is quick sort stable?
A: No

SC-125

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-126

Q: Insertion sort best case?
A: O(n) — already sorted

SC-127

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-128

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-129

Q: Counting sort constraint?
A: Need small integer range

SC-130

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-131

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-132

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-133

Q: Is merge sort stable?
A: Yes

SC-134

Q: Is quick sort stable?
A: No

SC-135

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-136

Q: Insertion sort best case?
A: O(n) — already sorted

SC-137

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-138

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-139

Q: Counting sort constraint?
A: Need small integer range

SC-140

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-141

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-142

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-143

Q: Is merge sort stable?
A: Yes

SC-144

Q: Is quick sort stable?
A: No

SC-145

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-146

Q: Insertion sort best case?
A: O(n) — already sorted

SC-147

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-148

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-149

Q: Counting sort constraint?
A: Need small integer range

SC-150

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-151

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-152

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-153

Q: Is merge sort stable?
A: Yes

SC-154

Q: Is quick sort stable?
A: No

SC-155

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-156

Q: Insertion sort best case?
A: O(n) — already sorted

SC-157

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-158

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-159

Q: Counting sort constraint?
A: Need small integer range

SC-160

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-161

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-162

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-163

Q: Is merge sort stable?
A: Yes

SC-164

Q: Is quick sort stable?
A: No

SC-165

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-166

Q: Insertion sort best case?
A: O(n) — already sorted

SC-167

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-168

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-169

Q: Counting sort constraint?
A: Need small integer range

SC-170

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-171

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-172

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-173

Q: Is merge sort stable?
A: Yes

SC-174

Q: Is quick sort stable?
A: No

SC-175

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-176

Q: Insertion sort best case?
A: O(n) — already sorted

SC-177

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-178

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-179

Q: Counting sort constraint?
A: Need small integer range

SC-180

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-181

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-182

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-183

Q: Is merge sort stable?
A: Yes

SC-184

Q: Is quick sort stable?
A: No

SC-185

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-186

Q: Insertion sort best case?
A: O(n) — already sorted

SC-187

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-188

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-189

Q: Counting sort constraint?
A: Need small integer range

SC-190

Q: When use insertion sort?
A: Small arrays or nearly sorted data

SC-191

Q: Merge sort complexity?
A: O(n log n) time, O(n) space

SC-192

Q: Quick sort worst case?
A: O(n²) with bad pivot choice

SC-193

Q: Is merge sort stable?
A: Yes

SC-194

Q: Is quick sort stable?
A: No

SC-195

Q: Cyclic sort range?
A: Only for elements 1..N or 0..N-1

SC-196

Q: Insertion sort best case?
A: O(n) — already sorted

SC-197

Q: Selection sort swaps?
A: O(n) — one swap per pass

SC-198

Q: What is QuickSelect?
A: Find kth element in O(n) average

SC-199

Q: Counting sort constraint?
A: Need small integer range

SC-200

Q: When use insertion sort?
A: Small arrays or nearly sorted data