Complete Summary and Solutions for Sorting – NCERT Class XII Computer Science, Chapter 5 – Introduction, Sorting Techniques, Bubble Sort, Selection Sort, Insertion Sort, Questions, Answers
Detailed summary and explanation of Chapter 5 'Sorting' from the Computer Science textbook for Class XII, covering the concept of sorting, importance of sorting in data organization, different sorting techniques including bubble sort, selection sort, insertion sort, their algorithms and step-by-step execution—along with all NCERT questions, answers, and exercises.
Updated: 4 days ago
Sorting Algorithms in Python
Chapter 5: Computer Science - Ultimate Study Guide | NCERT Class 12 Notes, Questions, Code Examples & Quiz 2025
Full Chapter Summary & Detailed Notes - Sorting Algorithms in Python Class 12 NCERT
Overview & Key Concepts
- Chapter Goal: Understand sorting as arranging elements; focus on Bubble, Selection, Insertion sorts (O(n²)); time complexity analysis. Exam Focus: Algorithms 5.1-5.3, Programs 5-1 to 5-3, Figures 5.1-5.3 passes; 2025 Updates: Emphasis on efficiency for big data, Python optimizations. Fun Fact: Peter Thiel quote on processing power ties to why efficient sorting matters. Core Idea: Overhead worth for search ease; from unsorted chaos to ordered utility. Real-World: Dictionaries, exam seats. Expanded: All subtopics point-wise with evidence (e.g., Fig 5.1 swaps), examples (e.g., numList=[8,7,13,1,-9,4]), debates (e.g., Bubble vs Insertion for near-sorted).
- Wider Scope: From intro to complexity; sources: Algorithms (5.1-5.3), figures (5.1-5.3), programs (5-1 to 5-3).
- Expanded Content: Include modern aspects like sorted() built-in vs manual; point-wise for recall; add 2025 relevance like ML data prep.
Introduction to Sorting
- Definition: Arranging collection in order (asc/desc, alpha/length). Ex: Numbers asc, strings z-a.
- Importance: Eases search (e.g., dictionary); unsorted tedious. Overhead justified vs unsorted lookup time.
- Real Examples: Dictionary words, exam roll numbers, student height/weight lists.
- Expanded: Evidence: Intro para; debates: Sorting vs hashing; real: Big data (e.g., 2025 AI datasets).
Conceptual Diagram: Unsorted to Sorted Flow
Flow: Unsorted List → Algorithm Passes (Swaps/Inserts) → Sorted List → Efficient Search. Ties to Fig 5.1-5.3.
Why This Guide Stands Out
Comprehensive: All sorts point-wise, program integrations; 2025 with big-O visuals, processes analyzed for real code.
Bubble Sort
- Overview: n-1 passes; adjacent swaps if unordered; largest "bubbles" to end. Fig 5.1: 4 passes for [8,7,13,1,-9,4].
- Algorithm 5.1: Nested loops (i=0 to n-1, j=0 to n-i-1); swap if list[j]>list[j+1].
- Program 5-1: Python impl; output: -9 1 4 7 8 13.
- Optimization: Stop if no swaps (already sorted).
- Expanded: Evidence: Green sorted in Fig 5.1; Activity 5.1 desc order (reverse >); real: Simple but inefficient for large n.
Selection Sort
- Overview: n-1 passes; select min from unsorted, swap to sorted front. Left: sorted, right: unsorted. Fig 5.2 arrows show mins.
- Algorithm 5.2: For i=0 to n-1; find min index j>i; swap if flag.
- Program 5-2: Flag for swap; output same sorted list.
- Characteristics: Fewer swaps than Bubble; good for swap-costly.
- Expanded: Evidence: Blue min in Fig 5.2; Activity 5.3 partial after 4 passes; debates: Vs Bubble swaps.
Insertion Sort
- Overview: Build sorted prefix; insert unsorted element backward. Like card sorting. Fig 5.3 shifts right.
- Algorithm 5.3: For i=1 to n-1; temp=list[i]; shift j>=0 where >temp; insert at j+1.
- Program 5-3: While j>=0 and temp
- Best For: Nearly sorted; fewer shifts.
- Expanded: Evidence: Swaps in Fig 5.3; Activity 5.4 partial after 3 passes; real: Online data insertion.
Exam Code Studies
Program 5-1 Bubble; 5-2 Selection; 5-3 Insertion; compare outputs.
Time Complexity of Algorithms
- Definition: Time for input size n; measure loops.
- Rules: No loop: O(1); Single: O(n); Nested: O(n²).
- For Sorts: All three have nested loops → O(n²) quadratic.
- Analysis: Varies with order (e.g., Insertion best near-sorted); real-world: For huge data, use advanced (e.g., QuickSort O(n log n)).
- Expanded: Evidence: Nested in programs; debates: Bubble worst-case swaps; 2025: Big-O graphs.
Summary & Exercise
- Key Takeaways: Sorting organizes for efficiency; learn three basics (all O(n²)); complexity guides choice.
- Exercise Tease: Partial passes; swaps comparison; median via sort; percentile calc.
Key Definitions & Terms - Complete Glossary
All terms from chapter; detailed with examples, relevance. Expanded: 30+ terms grouped by subtopic; added advanced like "Pass", "Swap" for depth/easy flashcards.
Sorting
Arranging elements in order. Ex: Asc numbers. Relevance: Eases search.
Bubble Sort
Adjacent swaps in passes. Ex: Largest bubbles up. Relevance: Simple impl.
Selection Sort
Select min, swap front. Ex: Build sorted prefix. Relevance: Fewer swaps.
Insertion Sort
Insert into sorted part. Ex: Shift right for place. Relevance: Near-sorted efficient.
Time Complexity
Time vs input size. Ex: O(n²). Relevance: Efficiency measure.
Pass
One iteration over list. Ex: n-1 passes. Relevance: Algorithm step.
Swap
Exchange positions. Ex: list[j], list[j+1]. Relevance: Reorder.
Unsorted/Sorted List
Right: unsorted; left grows sorted. Ex: Selection. Relevance: Divide strategy.
Min Index
Smallest in unsorted. Ex: Flag in Selection. Relevance: Find target.
Temp Variable
Holds insert value. Ex: Insertion shift. Relevance: Avoid overwrite.
Ascending Order
Increasing sequence. Ex: -9,1,4,7,8,13. Relevance: Common sort.
Descending Order
Decreasing. Ex: Activity 5.1 reverse >. Relevance: Variant.
Nested Loop
Loop in loop. Ex: O(n²). Relevance: Complexity source.
Quadratic Time
O(n²). Ex: All three sorts. Relevance: Inefficient large n.
Overhead
Extra sort time. Ex: Worth vs unsorted search. Relevance: Justification.
Flag
Swap indicator. Ex: Selection min found. Relevance: Optimize.
Shift
Move elements right. Ex: Insertion. Relevance: Make space.
Adjacent Elements
Next to each other. Ex: Bubble compare. Relevance: Local check.
Linear Time
O(n). Ex: Single loop. Relevance: Better but not here.
Constant Time
O(1). Ex: No loop. Relevance: Ideal, rare for sort.
Median
Middle value post-sort. Ex: Exercise 4. Relevance: Stats.
Percentile
Relative position. Ex: Exercise 5 sort + index. Relevance: Ranking.
Partially Sorted
After some passes. Ex: Activity 5.2-5.4. Relevance: Trace steps.
Optimization
Early stop. Ex: No swaps in Bubble. Relevance: Efficiency.
Big-O Notation
Worst-case time. Ex: n². Relevance: Analysis.
Real-World Sorting
Dict, exams. Ex: Alphabetical. Relevance: Application.
Custom Sort
User-defined (e.g., length). Ex: Strings. Relevance: Flexible.
Input Size n
List length. Ex: Complexity scales. Relevance: Growth.
Tip: Group by sort; examples for recall. Depth: Debates (e.g., Insertion adaptive). Historical: Early algos. Interlinks: To Ch4 stacks. Advanced: QuickSort. Real-Life: Database queries. Graphs: Complexity table. Coherent: Evidence → Interpretation. For easy learning: Flashcard per term with code.
60+ Questions & Answers - NCERT Based (Class 12) - From Exercises & Variations
Based on chapter + expansions. Part A: 10 (1 mark, one line), Part B: 10 (3 marks, four lines), Part C: 10 (4 marks, six lines), Part D: 10 (6 marks, eight lines). Answers point-wise in black text. Include code where apt.
Part A: 1 Mark Questions (10 Qs - Short)
1. What is sorting?
Arranging in order.
2. Name one sorting algorithm.
Bubble Sort.
3. Passes in Bubble Sort?
n-1.
4. What bubbles in Bubble Sort?
Largest element.
5. Key in Selection Sort?
Min selection.
6. Insertion Sort like what?
Card placing.
7. Time complexity of sorts?
O(n²).
8. Nested loops mean?
Quadratic time.
9. Overhead in sorting?
Extra time worth it.
10. Best for near-sorted?
Insertion Sort.
Part B: 3 Marks Questions (10 Qs - Medium, Exactly 4 Lines Each)
1. Differentiate Bubble vs Selection.
- Bubble: Adjacent swaps.
- Selection: Min swap front.
- Bubble more swaps.
- Both n-1 passes.
2. Steps in Bubble pass.
- Compare adjacent.
- Swap if > (asc).
- Largest to end.
- Reduce range next.
3. Algorithm 5.1 key.
- i=0 to n-1 passes.
- j=0 to n-i-1 compares.
- Swap if list[j]>j+1.
- Ascending order.
4. Selection flag use.
- Flag=0 init.
- Update if smaller found.
- Swap if flag=1.
- Min index track.
5. Insertion shift.
- Temp = list[i].
- While j>=0 and >temp: shift right.
- Insert temp at j+1.
- Backward search.
6. Complexity rules.
7. Why sort? Ex.
- Fast search.
- Ex: Dictionary alpha.
- Exam roll order.
- Student height list.
8. Bubble optimization.
- Check swaps in pass.
- No swaps: Stop.
- Already sorted early.
- Fig 5.1 5th redundant.
9. Selection passes.
- n-1 passes.
- Each: Find min in unsorted.
- Swap with i.
- nth auto placed.
10. Insertion pass 1.
- Sorted: First elem.
- Unsorted: Rest n-1.
- Compare second with first.
- Shift if smaller.
Part C: 4 Marks Questions (10 Qs - Medium-Long, Exactly 6 Lines Each)
1. Explain Bubble Sort with Fig 5.1.
- Adjacent compares/swaps.
- n-1 passes; largest end.
- Fig 5.1: [8,7,13,1,-9,4] → Pass1:13 end.
- Blue compares, green sorted.
- 4 passes sorted.
- Redundant 5th.
2. Algorithm 5.2 steps.
- i=0 to n-1.
- min=i, flag=0.
- j=i+1 to n-1: if smaller, min=j, flag=1.
- If flag: swap i,min.
- Build sorted left.
- Fig 5.2 mins blue.
3. Insertion vs others.
- Insertion: Insert with shifts.
- Bubble: Many swaps.
- Selection: Min swaps.
- All O(n²) nested.
- Insertion adaptive.
- Fig 5.3 shifts.
4. Program 5-1 code key.
- for i in range(n): passes.
- for j in range(n-i-1): compares.
- if list1[j]>j+1: swap.
- numList example.
- Print sorted.
- Output -9 to 13.
5. Time complexity calc.
- Nested loops: n * (n-1)/2 ~ n².
- All three quadratic.
- Input growth: Slows much.
- Real: Huge data need better.
- Tips: Loop count.
- Ex: n=6, passes reduce.
6. Activity 5.2 Bubble [8,7,6,5,4].
- Pass1: [4,7,6,5,8] wait full trace.
- After Pass1: [7,6,5,4,8].
- Pass2: [6,5,4,7,8].
- Pass3: [5,4,6,7,8].
- Last swap Pass4.
- Sorted [4,5,6,7,8].
7. Why O(n²) bad?
- n=1000: 1M ops.
- Slow for big data.
- Compare linear O(n).
- Real: Use mergesort.
- Chapter basics only.
- Overhead analysis.
8. Desc Bubble mod.
- Change > to < in if.
- Smallest bubbles end.
- Activity 5.1.
- Passes same.
- Ex: [1,2,3] → [3,2,1].
- Reverse logic.
9. Selection partial [7,11,3,...].
10. Insertion partial Array.
- Pass1: [7,11,3,...] → [7,11,3,...].
- Pass2: Insert 3: [3,7,11,10,...].
- Pass3: Insert 10: [3,7,10,11,17,...].
- Activity 5.4.
- Shifts for place.
- Sorted prefix grows.
Part D: 6 Marks Questions (10 Qs - Long, Exactly 8 Lines Each)
1. Trace Bubble [7,11,3,10,17,23,1,4,21,5] 3 passes.
- Pass1: Max 23 end: [7,11,3,10,17,1,4,21,5,23].
- Pass2: Next max 21: [7,11,3,10,17,1,4,5,21,23].
- Pass3: 17 end partial: [7,11,3,10,1,4,5,17,21,23].
- Exercise 1.
- Swaps adjacent.
- Green sorted end.
- Full trace Fig like.
- n=10, 9 passes total.
2. Swaps: List1 [63,42,21,9] Bubble vs Selection.
- Bubble: Pass1 3 swaps → [42,21,9,63]; Pass2 2 → [21,9,42,63]; Pass3 1 → [9,21,42,63]. Total 6.
- Selection: Pass1 min9 swap0: [9,42,21,63]; Pass2 min21 swap1: [9,21,42,63]; Pass3 min42 no. Total 2.
- Selection better swaps.
- Compares: Both ~n².
- Exercise 2.
- Bubble more local.
- Selection global min.
- Choose per cost.
3. Insertion compares: List1 [2,3,5,7,11] vs List2 [11,7,5,3,2].
- List1 sorted: Few compares (each insert 1-2).
- Total ~5-10.
- List2 reverse: Many shifts/compares (e.g., 2 insert: 4 compares).
- Total ~20.
- List1 min compares.
- Diagram: List1 shifts minimal.
- Exercise 3.
- Adaptive nature.
4. Median program with Bubble.
- Def median(lst): bubble_sort(lst).
- n=len(lst); if n%2: return lst[n//2].
- Else: (lst[n//2-1] + lst[n//2])/2.
- Ex: [1,3,2] → sort [1,2,3] → 2.
- Code below.
- Exercise 4.
- User func.
- Odd/even handle.
def bubble_sort(lst): ... # From 5-1
def median(lst):
bubble_sort(lst)
n = len(lst)
if n % 2 == 1:
return lst[n//2]
else:
return (lst[n//2 - 1] + lst[n//2]) / 25. Percentile program Selection.
- Def percentile(marks, x): selection_sort(marks).
- import math; index = math.round(x/100 * len(marks)).
- Return marks[index-1] (0-index).
- Steps: Sort asc, calc index, display.
- Ex: 90th for 120: index=108.
- Exercise 5.
- Relative performance.
- XYZ school apt.
6. Ascending names insert program.
- Def insert_name(names, new): Insertion logic for strings.
- Find pos backward where >new.
- Shift right, insert.
- Global list append each call.
- Exercise 6.
- Online insertion.
- Alpha order.
- Admission use.
names = []
def add_name(new):
i = len(names)
while i > 0 and names[i-1] > new:
names[i] = names[i-1]
i -= 1
names[i] = new7. Compare three sorts swaps/complexity.
- All O(n²) nested.
- Bubble: Many swaps worst.
- Selection: Min swaps.
- Insertion: Shifts, adaptive.
- Ex: Reverse list Bubble bad.
- Near-sorted Insertion best.
- Choose per data.
- Figs 5.1-5.3 evidence.
8. Trace Selection [63,42,21,9].
- Pass1: Min9 swap0: [9,42,21,63].
- Pass2: Min21 swap1: [9,21,42,63].
- Pass3: Min42 no swap: [9,21,42,63].
- 2 swaps total.
- Blue mins Fig style.
- Sorted left grows.
- Unsorted right shrinks.
- nth placed.
9. Why complexity important?
- Predict performance.
- n large: n² explodes.
- Compare algos.
- Ex: n=1000 Bubble slow.
- Real apps: Choose fit.
- Chapter: All quadratic.
- Tips: Count operations.
- Ch XI prime link.
10. Custom sort length strings.
- Modify compare by len(str).
- Bubble: if len(s[j])>len(s[j+1]).
- Ex: ["a","bb","c"] → ["a","c","bb"].
- Intro strings mention.
- Flexible orders.
- Python sorted(key=len).
- But manual here.
- App: File names.
Tip: Include traces/code; practice variations. Additional 30 Qs: More partials, mods.
Key Concepts - In-Depth Exploration
Core ideas with examples, pitfalls, interlinks. Expanded: All concepts with steps/examples/pitfalls for easy learning. Depth: Debates, analysis.
Sorting Importance
Steps: 1. Unsorted → Passes → Ordered. Ex: Dict search. Pitfall: Overhead ignore. Interlink: Search ease. Depth: Utility.
Bubble Sort
Steps: 1. Adjacent compare, 2. Swap up, 3. Reduce end. Ex: Fig 5.1. Pitfall: Many swaps reverse. Interlink: Simple. Depth: Bubbles max.
Selection Sort
Steps: 1. Find min, 2. Swap front, 3. Unsorted shrink. Ex: Fig 5.2. Pitfall: Full scan each. Interlink: Swaps min. Depth: Global select.
Insertion Sort
Steps: 1. Take next, 2. Backward shift >, 3. Insert. Ex: Fig 5.3. Pitfall: Reverse worst. Interlink: Adaptive. Depth: Local insert.
Time Complexity
Steps: 1. Count loops, 2. O(f(n)). Ex: Nested n². Pitfall: Ignore input. Interlink: Analysis. Depth: Growth rate.
Passes
Steps: 1. Full traversal, 2. Reduce range. Ex: n-1. Pitfall: Redundant. Interlink: Optimization. Depth: Iteration.
Swaps/Shifts
Steps: 1. Exchange/ move, 2. Position correct. Ex: Bubble swap. Pitfall: Costly ops. Interlink: Efficiency. Depth: Operation type.
Asc/Desc Order
Steps: 1. > for desc, 2. < asc. Ex: Modify if. Pitfall: Wrong logic. Interlink: Variants. Depth: Direction.
Nested Loops
Steps: 1. Outer passes, 2. Inner compares. Ex: O(n²). Pitfall: Inefficient large. Interlink: Complexity. Depth: Quadratic.
Optimization
Steps: 1. Check swaps, 2. Early stop. Ex: Bubble no swap. Pitfall: Miss impl. Interlink: Adaptive. Depth: Improve.
Partially Sorted
Steps: 1. After k passes, 2. Prefix sorted. Ex: Activities. Pitfall: Trace error. Interlink: Trace. Depth: Intermediate.
Real-World Apps
Steps: 1. Sort data, 2. Query fast. Ex: Exams. Pitfall: Wrong type. Interlink: Ch6 files. Depth: Practical.
Adaptive Sorting
Steps: 1. Fewer ops sorted input. Ex: Insertion. Pitfall: Assume random. Interlink: Complexity vary. Depth: Input dep.
Big-O
Steps: 1. Worst case, 2. Asymp. Ex: n². Pitfall: Avg ignore. Interlink: Analysis. Depth: Math bound.
Overhead Justification
Steps: 1. Sort once, 2. Search many. Ex: Dict. Pitfall: Small data. Interlink: Intro. Depth: Trade-off.
Advanced: Stable sort, inversions. Pitfalls: Off-by-one loops. Interlinks: To tuples Ch3. Real: E-commerce sort. Depth: 12 concepts details. Examples: Real traces. Graphs: Pass tables. Errors: Wrong range. Tips: Steps evidence; compare tables (swaps Bubble vs Selection).
Code Examples & Programs - From Text with Simple Explanations
Expanded with evidence, analysis; focus on applications. Added variations for practice.
Example 1: Bubble Sort (Program 5-1)
Simple Explanation: Nested loops swap adjacent.
def bubble_Sort(list1):
n = len(list1)
for i in range(n):
for j in range(0, n-i-1):
if list1[j] > list1[j+1]:
list1[j], list1[j+1] = list1[j+1], list1[j]
numList = [8, 7, 13, 1, -9, 4]
bubble_Sort(numList)
print("The sorted list is :")
for i in range(len(numList)):
print(numList[i], end=" ")- Step 1: Passes outer i.
- Step 2: Inner j compares/swaps.
- Step 3: Output: -9 1 4 7 8 13.
- Simple Way: Asc order.
Example 2: Selection Sort (Program 5-2)
Simple Explanation: Find min, swap front.
def selection_Sort(list2):
n = len(list2)
for i in range(n):
min = i
flag = 0
for j in range(i + 1, len(list2)):
if list2[j] < list2[min]:
min = j
flag = 1
if flag == 1:
list2[min], list2[i] = list2[i], list2[min]
numList = [8, 7, 13, 1, -9, 4]
selection_Sort(numList)
# Print same as above- Step 1: Outer i position.
- Step 2: Inner find min.
- Step 3: Swap if flag.
- Simple Way: Fewer swaps.
Example 3: Insertion Sort (Program 5-3)
Simple Explanation: Shift and insert.
def insertion_Sort(list3):
n = len(list3)
for i in range(1, n):
temp = list3[i]
j = i-1
while j >= 0 and temp < list3[j]:
list3[j+1] = list3[j]
j = j-1
list3[j+1] = temp
numList = [8, 7, 13, 1, -9, 4]
insertion_Sort(numList)
# Print same- Step 1: i from 1, temp hold.
- Step 2: While shift larger.
- Step 3: Insert temp.
- Simple Way: Like cards.
Example 4: Optimization Bubble (Variation)
Simple Explanation: Early stop.
def optimized_bubble(lst):
n = len(lst)
for i in range(n):
swapped = False
for j in range(0, n-i-1):
if lst[j] > lst[j+1]:
lst[j], lst[j+1] = lst[j+1], lst[j]
swapped = True
if not swapped:
break- Step 1: Flag swapped.
- Step 2: Break if no.
- Step 3: Faster sorted input.
- Simple Way: Avoid redundant.
Example 5: Median via Sort (Exercise 4)
Simple Explanation: Sort then middle.
# Use bubble_Sort
def find_median(nums):
bubble_Sort(nums)
n = len(nums)
if n % 2 == 1:
return nums[n//2]
else:
return (nums[n//2 - 1] + nums[n//2]) / 2
print(find_median([3,1,4,1,5])) # 3.0 or int- Step 1: Sort nums.
- Step 2: Odd/even mid.
- Step 3: Return avg/center.
- Simple Way: Stats tool.
Tip: Run traces; vary desc. Added for exercises, optimizations.
Interactive Quiz - Master Sorting Algorithms
10 MCQs in full sentences; 80%+ goal. Covers sorts, complexity.
Quick Revision Notes & Mnemonics
Concise, easy-to-learn summaries for all subtopics. Structured in tables for quick scan: Key points, examples, mnemonics. Covers intro, sorts, complexity. Bold key terms; short phrases for fast reading.
| Subtopic | Key Points | Examples | Mnemonics/Tips |
|---|---|---|---|
| Intro |
|
Alpha words; height list. | SO (Sort-Order). Tip: "Sort Once, Search Often" – Efficiency. |
| Bubble Sort |
|
Program 5-1; [8,7..] → -9..13. | BAP (Bubble-Adjacent-Pass). Tip: "Bubbles Rise" – Largest end. |
| Selection Sort |
|
Program 5-2; Blue mins. | SMF (Select-Min-Flag). Tip: "Select Smallest First" – Prefix grow. |
| Insertion Sort |
|
Program 5-3; Card like. | IST (Insert-Shift-Temp). Tip: "Insert in Place" – Shifts right. |
| Complexity |
|
n=6 ~36 ops. | ONR (O-nested-Rules). Tip: "Nested = Nightmare" – Slow large n. |
| Activities |
|
5.2 last swap Pass4. | PTS (Partial-Trace-Swaps). Tip: "Pass by Pass" – Visualize Figs. |
Overall Tip: Use SO-BAP-SMF-IST-ONR for full scan (5 mins). Flashcards: Front (term), Back (points + mnemonic). Print table for wall revision. Covers 100% chapter – easy for exams!
Key Terms & Processes - All Key
Expanded table 30+ rows; quick ref. Added advanced (e.g., Adaptive, Stable).
| Term/Process | Description | Example | Usage |
|---|---|---|---|
| Sorting | Arrange order | Asc numbers | Search ease |
| Bubble Sort | Adjacent swaps | Alg 5.1 | Simple |
| Selection Sort | Min swap front | Alg 5.2 | Few swaps |
| Insertion Sort | Shift insert | Alg 5.3 | Adaptive |
| Time Complexity | Time vs n | O(n²) | Efficiency |
| Pass | One iteration | n-1 | Step |
| Swap | Exchange pos | list[j],j+1 | Reorder |
| Unsorted List | Right part | Initial all | Target |
| Sorted List | Left grows | Green Fig | Result |
| Min Index | Smallest pos | Flag update | Select |
| Temp Var | Hold value | Insertion | Shift |
| Ascending | Increasing | -9 to 13 | Common |
| Descending | Decreasing | Reverse if | Variant |
| Nested Loop | Loop in loop | O(n²) | Quadratic |
| Quadratic Time | n² growth | All sorts | Slow large |
| Overhead | Extra time | Sort cost | Justified |
| Flag | Indicator | Swap yes | Optimize |
| Shift | Move right | Insertion | Space |
| Adjacent | Next elems | Bubble | Local |
| Linear Time | O(n) | Single loop | Better |
| Constant Time | O(1) | No loop | Rare |
| Median | Middle post-sort | Exercise 4 | Stats |
| Percentile | Position % | Exercise 5 | Ranking |
| Partially Sorted | After passes | Activities | Trace |
| Optimization | Early stop | No swaps | Fast |
| Big-O | Worst time | n² | Analysis |
| Adaptive | Input dep | Insertion | Near-sorted |
| Stable Sort | Equal order preserve | Insertion yes | Advanced |
| Inversions | Out-order pairs | Reverse many | Measure |
| Online Sorting | Insert one-by-one | Exercise 6 | Dynamic |
| Custom Key | Non-num order | String len | Flexible |
| Input Size n | List len | Complexity | Growth |
| Redundant Pass | No change | Fig 5.1 pass5 | Opt target |
Tip: Examples memory; sort subtopic. Easy: Table scan. Added 10 rows depth.
Sorting Processes Step-by-Step
Step-by-step breakdowns of core processes, structured as full questions followed by detailed answers with steps. Visual descriptions for easy understanding; focus on actionable Q&A with examples from chapter.
Question 1: How does Bubble Sort process Pass 1 for [8,7,13,1,-9,4] (Fig 5.1)?
- Step 1: j=0: 8>7 swap → [7,8,13,1,-9,4].
- Step 2: j=1: 8<13 no.
- Step 3: j=2: 13>1 swap → [7,8,1,13,-9,4].
- Step 4: j=3: 13>-9 swap → [7,8,1,-9,13,4].
- Step 5: j=4: 13>4 swap → [7,8,1,-9,4,13].
- Step 6: Largest 13 end (green).
Visual: Blue pairs → Swap arrows → 13 bubbles right. Example: 4 swaps Pass1.
Question 2: What steps in Selection Sort Pass 1 for same list (Fig 5.2)?
- Step 1: i=0, min=0 (8).
- Step 2: j=1:7<8 min=1.
- Step 3: j=2:13>7 no.
- Step 4: j=3:1<7 min=3.
- Step 5: j=4:-9<1 min=4.
- Step 6: j=5:4>-9 no; swap 0 and 4: [-9,7,13,1,8,4].
Visual: Arrows compare → Blue min -9 → Swap to front. Example: 1 swap, full scan.
Question 3: Trace Insertion Sort Pass 2 for [7,8,13,1,-9,4] (Fig 5.3)?
- Step 1: i=2, temp=13 (sorted [7,8]).
- Step 2: j=1:8<13 no shift.
- Step 3: Insert at j+1=2: No change [7,8,13,1,-9,4].
- Step 4: But full: Later passes insert 1 etc.
- Step 5: For 1 (i=3): Shifts all >1 right.
- Step 6: [7,8,1,13,-9,4] → shifts to [1,7,8,13,-9,4].
Visual: Backward arrow from i → Shift blocks → Insert spot. Example: Multi swaps for small.
Question 4: How does time complexity arise in nested loops (Bubble)?
- Step 1: Outer i: n passes.
- Step 2: Inner j: ~n-i compares each.
- Step 3: Total ~ n(n-1)/2 = O(n²).
- Step 4: Swaps up to n²/2 worst.
- Step 5: Scales bad large n.
- Step 6: All sorts similar.
Visual: Outer circle passes → Inner shrinking loops. Example: n=6: 15 compares.
Question 5: Steps for median calc via sort (Exercise 4)?
- Step 1: Input list, bubble_sort.
- Step 2: n=len; if odd: mid = n//2.
- Step 3: Even: avg (n//2-1, n//2).
- Step 4: Return value.
- Step 5: Ex: [1,3] → 2.0.
- Step 6: Handles odd/even.
Visual: List → Sort arrow → Mid pick. Example: Stats post-sort.
Question 6: Process for percentile with Selection (Exercise 5)?
- Step 1: selection_sort(marks).
- Step 2: index = round(x/100 * n).
- Step 3: Value at index (1-based adjust).
- Step 4: Display.
- Step 5: Ex: 90th n=120: index=108.
- Step 6: Relative rank.
Visual: Sort → % calc → Index point. Example: Aptitude test.
Tip: Treat as FAQ; apply to Figs. Easy: Q → Steps + Visual. Full Q&A for exam-like practice.
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