7.9 — Quick Revision: Sorting

<< Overview

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Sorting comparison table

Algorithm	Best	Avg	Worst	Space	Stable
Selection	O(n²)	O(n²)	O(n²)	O(1)	No
Insertion	O(n)	O(n²)	O(n²)	O(1)	Yes
Merge	O(n log n)	O(n log n)	O(n log n)	O(n)	Yes
Quick	O(n log n)	O(n log n)	O(n²)	O(log n)	No
Cyclic	O(n)	O(n)	O(n)	O(1)	No*
Counting	O(n+k)	O(n+k)	O(n+k)	O(k)	Yes
Heap	O(n log n)	O(n log n)	O(n log n)	O(1)	No

When to use which

• Small data / nearly sorted: Insertion sort
• General purpose: Quick sort (avg) or Merge sort (guaranteed)
• Stability needed: Merge sort
• Memory constrained: Heap sort or Quick sort
• Integers 1..N: Cyclic sort
• Small range integers: Counting sort

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Self-check drill

SC-001

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-002

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

SC-003

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-004

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-005

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-006

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-007

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-008

• Q: Counting sort limit?
• A: Only for small integer range

SC-009

• Q: Merge sort space?
• A: O(n) auxiliary

SC-010

• Q: Quick sort space?
• A: O(log n) call stack

SC-011

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-012

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

SC-013

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-014

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-015

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-016

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-017

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-018

• Q: Counting sort limit?
• A: Only for small integer range

SC-019

• Q: Merge sort space?
• A: O(n) auxiliary

SC-020

• Q: Quick sort space?
• A: O(log n) call stack

SC-021

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-022

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

SC-023

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-024

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-025

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-026

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-027

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-028

• Q: Counting sort limit?
• A: Only for small integer range

SC-029

• Q: Merge sort space?
• A: O(n) auxiliary

SC-030

• Q: Quick sort space?
• A: O(log n) call stack

SC-031

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-032

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

SC-033

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-034

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-035

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-036

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-037

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-038

• Q: Counting sort limit?
• A: Only for small integer range

SC-039

• Q: Merge sort space?
• A: O(n) auxiliary

SC-040

• Q: Quick sort space?
• A: O(log n) call stack

SC-041

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-042

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

SC-043

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-044

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-045

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-046

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-047

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-048

• Q: Counting sort limit?
• A: Only for small integer range

SC-049

• Q: Merge sort space?
• A: O(n) auxiliary

SC-050

• Q: Quick sort space?
• A: O(log n) call stack

SC-051

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-052

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

SC-053

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-054

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-055

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-056

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-057

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-058

• Q: Counting sort limit?
• A: Only for small integer range

SC-059

• Q: Merge sort space?
• A: O(n) auxiliary

SC-060

• Q: Quick sort space?
• A: O(log n) call stack

SC-061

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-062

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

SC-063

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-064

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-065

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-066

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-067

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-068

• Q: Counting sort limit?
• A: Only for small integer range

SC-069

• Q: Merge sort space?
• A: O(n) auxiliary

SC-070

• Q: Quick sort space?
• A: O(log n) call stack

SC-071

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-072

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

SC-073

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-074

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-075

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-076

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-077

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-078

• Q: Counting sort limit?
• A: Only for small integer range

SC-079

• Q: Merge sort space?
• A: O(n) auxiliary

SC-080

• Q: Quick sort space?
• A: O(log n) call stack

SC-081

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-082

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

SC-083

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-084

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-085

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-086

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-087

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-088

• Q: Counting sort limit?
• A: Only for small integer range

SC-089

• Q: Merge sort space?
• A: O(n) auxiliary

SC-090

• Q: Quick sort space?
• A: O(log n) call stack

SC-091

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-092

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

SC-093

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-094

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-095

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-096

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-097

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-098

• Q: Counting sort limit?
• A: Only for small integer range

SC-099

• Q: Merge sort space?
• A: O(n) auxiliary

SC-100

• Q: Quick sort space?
• A: O(log n) call stack

SC-101

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-102

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

SC-103

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-104

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-105

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-106

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-107

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-108

• Q: Counting sort limit?
• A: Only for small integer range

SC-109

• Q: Merge sort space?
• A: O(n) auxiliary

SC-110

• Q: Quick sort space?
• A: O(log n) call stack

SC-111

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-112

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

SC-113

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-114

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-115

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-116

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-117

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-118

• Q: Counting sort limit?
• A: Only for small integer range

SC-119

• Q: Merge sort space?
• A: O(n) auxiliary

SC-120

• Q: Quick sort space?
• A: O(log n) call stack

SC-121

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-122

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

SC-123

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-124

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-125

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-126

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-127

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-128

• Q: Counting sort limit?
• A: Only for small integer range

SC-129

• Q: Merge sort space?
• A: O(n) auxiliary

SC-130

• Q: Quick sort space?
• A: O(log n) call stack

SC-131

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-132

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

SC-133

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-134

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-135

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-136

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-137

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-138

• Q: Counting sort limit?
• A: Only for small integer range

SC-139

• Q: Merge sort space?
• A: O(n) auxiliary

SC-140

• Q: Quick sort space?
• A: O(log n) call stack

SC-141

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-142

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

SC-143

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-144

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-145

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-146

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-147

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-148

• Q: Counting sort limit?
• A: Only for small integer range

SC-149

• Q: Merge sort space?
• A: O(n) auxiliary

SC-150

• Q: Quick sort space?
• A: O(log n) call stack

SC-151

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-152

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

SC-153

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-154

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-155

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-156

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-157

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-158

• Q: Counting sort limit?
• A: Only for small integer range

SC-159

• Q: Merge sort space?
• A: O(n) auxiliary

SC-160

• Q: Quick sort space?
• A: O(log n) call stack

SC-161

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-162

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

SC-163

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-164

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-165

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-166

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-167

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-168

• Q: Counting sort limit?
• A: Only for small integer range

SC-169

• Q: Merge sort space?
• A: O(n) auxiliary

SC-170

• Q: Quick sort space?
• A: O(log n) call stack

SC-171

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-172

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

SC-173

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-174

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-175

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-176

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-177

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-178

• Q: Counting sort limit?
• A: Only for small integer range

SC-179

• Q: Merge sort space?
• A: O(n) auxiliary

SC-180

• Q: Quick sort space?
• A: O(log n) call stack

SC-181

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-182

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

SC-183

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-184

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-185

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-186

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-187

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-188

• Q: Counting sort limit?
• A: Only for small integer range

SC-189

• Q: Merge sort space?
• A: O(n) auxiliary

SC-190

• Q: Quick sort space?
• A: O(log n) call stack

SC-191

• Q: Merge sort time?
• A: O(n log n) guaranteed

SC-192

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

SC-193

• Q: Stable sorts?
• A: Merge, insertion, counting

SC-194

• Q: Cyclic sort use?
• A: Elements in range 1..N

SC-195

• Q: Insertion sort best?
• A: O(n) — nearly sorted

SC-196

• Q: Selection sort property?
• A: Minimum swaps O(n)

SC-197

• Q: QuickSelect?
• A: Find kth element in O(n) avg

SC-198

• Q: Counting sort limit?
• A: Only for small integer range

SC-199

• Q: Merge sort space?
• A: O(n) auxiliary

SC-200

• Q: Quick sort space?
• A: O(log n) call stack