Complete Summary and Solutions for Stack – NCERT Class XII Computer Science, Chapter 3 – Introduction, Operations, Applications, Implementation, Questions, Answers
Comprehensive summary and explanation of Chapter 3 'Stack' from the Computer Science textbook for Class XII, covering the concept of stack data structure, stack operations like push and pop, applications of stack, implementation using arrays and linked lists, and use cases in expression evaluation and recursion—along with all NCERT questions, answers, and exercises for effective learning.
Updated: 4 days ago
Stack in Python
Chapter 3: Computer Science - Ultimate Study Guide | NCERT Class 12 Notes, Questions, Code Examples & Quiz 2025
Full Chapter Summary & Detailed Notes - Stack in Python Class 12 NCERT
Overview & Key Concepts
- Chapter Goal: Understand stack as LIFO data structure, operations (push/pop), Python implementation via list, notations (infix/prefix/postfix), conversion & evaluation using stack. Exam Focus: Algorithms 3.1-3.2, Fig 3.2-3.4, Programs for stack funcs; 2025 Updates: Emphasis on recursion stacks. Fun Fact: Steve Jobs quote on monitoring ties to stack in OS. Core Idea: Efficient LIFO for reversals, expressions. Real-World: Undo in editors, parentheses matching. Expanded: All subtopics point-wise with evidence (e.g., Fig 3.3 steps), examples (e.g., (x+y)/(z*8) → xy+z8*/), debates (e.g., array vs list impl).
- Wider Scope: From linear DS to applications in compilers; sources: Figs (3.1-3.4), Tables (3.1), Algorithms (3.1-3.2).
- Expanded Content: Include modern aspects like deque for efficient stacks, recursion depth; point-wise for recall; add 2025 relevance like stack in async tasks.
Introduction & Data Structures
- Overview: DS organize data for efficient access/ops; linear (stack/queue) vs others (array/tree/graph).
- Stack Intro: LIFO like plates/books (Fig 3.1); add/remove from top only.
- Applications: Real: Clothes pile, bangles; Prog: String reverse, undo/redo, browser back, parentheses matching.
- Example: Undo: Stack tracks changes; pop for undo. Evidence: Traversing string reverse via push/pop.
- Practical Difficulties: Overflow (full), underflow (empty pop). Solutions: Check size.
- Expanded: Evidence: OS memory allocation via stack; debates: Stack vs queue; real: Function calls in compilers.
Conceptual Diagram: Stack LIFO Flow
Flow: Empty → Push (top grows) → Pop (top shrinks) → Empty. Ties to Fig 3.2 glasses.
Why This Guide Stands Out
Comprehensive: All subtopics point-wise, program integrations; 2025 with deque variants, processes analyzed for real code.
Operations on Stack
- Push: Add to top; overflow if full (Fig 3.2 i-ii).
- Pop: Remove from top; underflow if empty (Fig 3.2 iv,ix).
- Other: isEmpty, size, top (peek).
- Expanded: Evidence: Glasses numbered 1-4; real: No fixed size in Python lists.
Implementation in Python
- Using List: append() for push, pop() for pop; no explicit top.
- Functions: isEmpty, opPush, size, top, opPop, display (as in text).
- Example Program: glassStack with push/pop glass1-3; output shows LIFO.
- Output Evidence: Pushed glass1/2, popped glass2, top glass3, display glass3/glass1.
- Expanded: Evidence: While loop empty check; debates: List vs collections.deque.
Quick Code: Basic Stack
glassStack = []
glassStack.append('glass1') # Push
print(glassStack.pop()) # Pop: glass1Output: glass1 (LIFO)
Notations for Arithmetic Expressions
- Infix: Op between operands; BODMAS (e.g., x+y).
- Prefix (Polish): Op before (e.g., +xy); no parens.
- Postfix (Reverse Polish): Op after (e.g., xy+); single traversal eval.
- Table 3.1: Examples like 3*(4+5) → *3+45 (prefix), 345+* (postfix).
- Expanded: Evidence: Lukasiewicz 1920s; real: Calculators use postfix.
Conversion Infix to Postfix
- Algorithm 3.1: Stack for ops/parens; precedence rules (e.g., * > +).
- Steps: Push (, pop on ); for op, compare prec & pop/append.
- Example 3.1: (x + y)/(z*8) → Steps in Fig 3.3; final xy+z8*/.
- Expanded: Evidence: Left assoc; debates: Handling same prec.
Evaluation of Postfix
- Algorithm 3.2: Push operands; pop two for op, push result.
- Example 3.2: 7 8 2 * 4 / + → Steps Fig 3.4; result 11.
- Expanded: Evidence: Binary ops only; real: Stack machine eval.
Exam Code Studies
Stack funcs; infix "(A+B)*C" → AB+C*; eval "AB+C*" (A=2,B=3,C=4) → 20.
Summary & Exercise
- Key Takeaways: LIFO stack via list; notations for expr; stack for conv/eval.
- Exercise Tease: True/False LIFO; code reverse string; convert/eval expr.
Key Definitions & Terms - Complete Glossary
All terms from chapter; detailed with examples, relevance. Expanded: 30+ terms grouped by subtopic; added advanced like "Overflow", "Precedence" for depth/easy flashcards.
Stack
LIFO linear DS. Ex: Plates pile. Relevance: Top insert/delete.
LIFO
Last In First Out. Ex: Undo recent action. Relevance: Principle.
Push
Add to top. Ex: append(). Relevance: Insertion.
Pop
Remove from top. Ex: pop(). Relevance: Deletion.
Overflow
Push on full stack. Ex: Fixed array limit. Relevance: Exception.
Underflow
Pop on empty. Ex: No elements. Relevance: Check isEmpty.
Top
Peek top element. Ex: glassStack[-1]. Relevance: Read without pop.
Infix
Op between operands. Ex: A+B. Relevance: Human readable.
Prefix
Op before operands. Ex: +AB. Relevance: Polish, no parens.
Postfix
Op after operands. Ex: AB+. Relevance: Reverse Polish, easy eval.
Precedence
Op priority (* > +). Ex: In conv algo. Relevance: Order eval.
Linear Data Structure
Sequential elements. Ex: Stack/List. Relevance: Vs non-linear (tree).
opPush
Function to push. Ex: append(element). Relevance: Impl.
opPop
Function to pop. Ex: pop(). Relevance: Returns deleted.
isEmpty
Check empty stack. Ex: len()==0. Relevance: Avoid underflow.
Size
Number of elements. Ex: len(stack). Relevance: Count.
Display
Print stack contents. Ex: For i in reversed(stack). Relevance: View.
BODMAS
Order of ops in infix. Ex: Brackets/Orders/Division/Multi/Add/Sub. Relevance: Precedence.
PostExp
String for postfix. Ex: In algo 3.1. Relevance: Build result.
Left Parenthesis
'('; Push on stack. Ex: In conv. Relevance: Matching.
Right Parenthesis
')'; Pop till '('. Ex: Discard pair. Relevance: Nesting.
Operand
Variable/num. Ex: x,3. Relevance: Append direct.
Operator
+,*,/. Ex: Push/pop by prec. Relevance: Stack track.
Conversion Algorithm
Infix to postfix steps. Ex: Algo 3.1. Relevance: Compiler use.
Evaluation Algorithm
Postfix to value. Ex: Algo 3.2. Relevance: Calc machines.
GlassStack
Example stack. Ex: ['glass1']. Relevance: Illustrate ops.
Reverse Polish Notation
Postfix alias. Ex: xy+. Relevance: Lukasiewicz reverse.
Tip: Group by ops/notations/impl; examples for recall. Depth: Debates (e.g., fixed vs dynamic size). Historical: 1920s Polish. Interlinks: To queue Ch4. Advanced: Recursion stack. Real-Life: Browser history. Graphs: Notations 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 stack?
LIFO data structure.
2. Define LIFO.
Last In First Out.
3. Name one stack operation.
Push.
4. What is overflow?
Push on full stack.
5. Purpose of pop?
Remove top.
6. What is infix?
Op between operands.
7. Define postfix.
Op after operands.
8. Role of stack in conversion?
Track operators.
9. What is underflow?
Pop empty stack.
10. Example of prefix?
+xy.
Part B: 3 Marks Questions (10 Qs - Medium, Exactly 4 Lines Each)
1. Differentiate linear vs other DS.
- Linear: Sequential (stack).
- Others: Hierarchical (tree/graph).
- Ex: List vs binary tree.
- Stack: LIFO linear.
2. List 3 stack applications.
- Undo/redo in editors.
- Browser back button.
- Parentheses matching.
- Ex: String reverse.
3. Explain push operation.
- Add to top (append).
- Overflow if full.
- Ex: opPush(stack, elem).
- LIFO insertion.
4. What is pop? Give example.
- Remove top (pop).
- Underflow if empty.
- Ex: opPop(stack) returns top.
- LIFO deletion.
5. Need for stack in expressions.
6. Process of push/pop in Python.
- Push: list.append().
- Pop: list.pop().
- No top var needed.
- Dynamic size.
7. Basic infix to postfix syntax.
- Algo 3.1 steps.
- Push ops/parens.
- Ex: (x+y) → xy+.
- Prec rules.
8. Use of stack in eval postfix.
- Push operands.
- Pop for op, push result.
- Ex: 78 2* + → 11.
- Single traversal.
9. Role of isEmpty.
- Check len()==0.
- Avoid underflow.
- Ex: Before pop.
- Returns True/False.
10. When is top used?
- Peek without remove.
- stack[-1].
- Ex: Read top glass.
- If empty: None.
Part C: 4 Marks Questions (10 Qs - Medium-Long, Exactly 6 Lines Each)
1. Explain stack with example.
- LIFO linear DS.
- Top insert/delete.
- Ex: Plates (Fig 3.1).
- Apps: Undo, back.
- Ops: Push/pop.
- Python: List.
2. Describe 4 notations.
- Infix: A+B.
- Prefix: +AB.
- Postfix: AB+.
- BODMAS for infix.
- No parens in pre/post.
- Table 3.1 ex.
3. How does push work? Code example.
- Add top; append().
- Overflow check.
- Ex: opPush(stack, 'glass').
- Fig 3.2 push 1.
- Dynamic in Python.
- No limit.
4. Explain pop with program.
- Remove top; pop().
- Underflow if empty.
- Ex: opPop(stack) returns elem.
- Glass ex output.
- Returns deleted.
- Check isEmpty first.
5. Outline conversion process.
- Algo 3.1: postExp string.
- Push (, pop on ).
- Op: Prec compare, pop/append.
- Ex: Fig 3.3 steps.
- Final pop all.
- Operators only pushed.
6. Catching with eval postfix.
- Algo 3.2: Push operands.
- Pop two for op, push result.
- Ex: Fig 3.4 7 8 2*4/+ =11.
- Single element final.
- Invalid if not.
- Binary ops.
7. Use of display in stack.
- Print reversed for top-down.
- for i in range(len-1,-1,-1).
- Ex: glass3 then glass1.
- Visualize contents.
- After ops.
- Current elements msg.
8. Differentiate notations.
- Infix: Human, BODMAS.
- Prefix: Op first, left-to-right.
- Postfix: Op last, easy eval.
- Ex: 3*(4+5) variants.
- No parens needed.
- Stack for conv/eval.
9. Why use stack for parens?
- Push on (, pop on ).
- Match pairs/nesting.
- Error if mismatch.
- Ex: Compiler check.
- LIFO perfect.
- Algo step 4.
10. Bare stack risks.
- No checks: Underflow crash.
- Ex: Pop empty.
- Always isEmpty first.
- Debug hard.
- Use functions.
- Python list safe.
Part D: 6 Marks Questions (10 Qs - Long, Exactly 8 Lines Each)
1. Justify: Stack follows LIFO but queue FIFO.
- Stack: Last in out first.
- Ex: Plates top only.
- Queue: First in out first.
- Ex: Line waiting.
- Both linear.
- Stack apps: Undo.
- Queue: BFS.
- Evidence: Ch3 intro.
2. When raised: Overflow, underflow, prec low. Examples.
- Overflow: Push full.
- Ex: Fixed size array.
- Underflow: Pop empty.
- Ex: No elems.
- Low prec: Pop higher first.
- Ex: + then * push.
- Algo 3.1.
- Fig 3.3.
3. Use of stack: Code for reverse string.
- Push chars.
- Pop to new string.
- Ex: "ABC" → CBA.
- Code below.
- LIFO reverse.
- App ex.
- Efficient O(n).
- Exercise 3.
s = "ABC"
stack = []
for c in s: stack.append(c)
rev = ""
while stack: rev += stack.pop()
print(rev) # CBA4. Use stack in Q3 for odd numbers.
- Push only odds.
- Pop to find max.
- Ex: Inputs 1-10 → odds stack.
- Modified code.
- Display + max.
- Hint: Pop track max.
- LIFO but max separate.
- Exercise 7.
stack = []
while True:
n = int(input())
if n % 2: stack.append(n)
if n == -1: break
mx = max(stack)
while stack: print(stack.pop())
print("Max odd:", mx)5. Define: Stack, Push, Conversion.
- Stack: LIFO DS.
- Ex: List impl.
- Push: Add top.
- Ex: Append.
- Conversion: Infix-postfix.
- Ex: Algo 3.1.
- Stack ops track.
- Key for expr.
6. Explain eval with code.
- Algo 3.2 steps.
- Push ops, pop for calc.
- Ex: AB+C* A=3 B=5 C=1 → 8.
- Code below.
- Single final value.
- Fig 3.4.
- Exercise 5a.
- Binary only.
post = "3 5 + 1 *"
stack = []; tokens = post.split()
for t in tokens:
if t.isdigit(): stack.append(int(t))
else:
b = stack.pop(); a = stack.pop()
if t == '+': stack.append(a + b)
print(stack.pop()) # 87. Fill blanks in impl code; explain.
- def opPush(stack, elem): stack.append(elem)
- def opPop(stack): return stack.pop() if stack else None
- if not isEmpty(stack): ...
- Code: Full funcs.
- Flow: Create → Push → Pop → Display.
- Glass ex.
- LIFO verify.
- Matches text.
def isEmpty(s): return len(s)==0
# Use in top/pop8. Convert A+B-C*D; show steps.
- Algo 3.1: AB+CD* -.
- Steps: A append, + push (empty), etc.
- Prec: * high, pop for -.
- Ex: Exercise 6a.
- Stack changes.
- Similar TypeError.
- Debug tool.
- Ch link.
# Manual: A B + C D * -9. Use display in Q7 problem.
- Add def display(s): for i in range(len(s)-1,-1,-1): print(s[i])
- After ops.
- Cleanup ex: Print all.
- Top first.
- Ex: glass3 glass1.
- Ensures view.
- Robustness.
- File prep.
10. Stack in languages; Python specifics.
- Used in C++/Java.
- LIFO for calls.
- Python: List append/pop.
- Dynamic.
- Stack search.
- Ex: Expr handlers.
- 2025: Async stacks.
- Clean LIFO.
Tip: Include code in ans; practice run. Additional 30 Qs: Variations on conversions, error scenarios.
Key Concepts - In-Depth Exploration
Core ideas with examples, pitfalls, interlinks. Expanded: All concepts with steps/examples/pitfalls for easy learning. Depth: Debates, analysis.
LIFO Principle
Steps: 1. Push last, 2. Pop first. Ex: Plates. Pitfall: Confuse with FIFO. Interlink: Queue. Depth: OS calls.
Push Operation
Steps: 1. Append to end, 2. Top updates. Ex: Fig 3.2. Pitfall: Overflow in arrays. Interlink: Impl. Depth: O(1) time.
Pop Operation
Steps: 1. Remove end, 2. Return value. Ex: Glass pop. Pitfall: Underflow. Interlink: isEmpty. Depth: O(1).
Python Implementation
Steps: 1. List(), 2. append/pop. Ex: glassStack. Pitfall: Reverse display. Interlink: Built-ins. Depth: Deque alt.
Infix Notation
Steps: 1. Op between, 2. BODMAS. Ex: A+B*C. Pitfall: Parens needed. Interlink: Conv. Depth: Human-friendly.
Postfix Notation
Steps: 1. Op after, 2. No prec worry. Ex: ABC*+. Pitfall: Read hard. Interlink: Eval. Depth: Stack machine.
Conversion Algo
Steps: 1. Scan left-right, 2. Push ops. Ex: Fig 3.3. Pitfall: Assoc rules. Interlink: Parens. Depth: Compiler.
Evaluation Algo
Steps: 1. Push nums, 2. Pop calc. Ex: Fig 3.4. Pitfall: Invalid expr. Interlink: Binary. Depth: Reverse Polish.
Precedence
Steps: 1. * / high, + - low. Ex: Pop high first. Pitfall: Same prec left assoc. Interlink: Algo 3.1. Depth: BODMAS map.
Parentheses Matching
Steps: 1. Push (, 2. Pop on ). Ex: Nested check. Pitfall: Mismatch error. Interlink: Conv. Depth: Compiler syntax.
isEmpty & Size
Steps: 1. len()==0, 2. len(stack). Ex: Before pop. Pitfall: Forget check. Interlink: Underflow. Depth: O(1).
Top/Peek
Steps: 1. stack[-1], 2. If not empty. Ex: Read top. Pitfall: IndexError. Interlink: Non-destructive. Depth: O(1).
Display Function
Steps: 1. Reverse loop print. Ex: Top first. Pitfall: Wrong order. Interlink: View. Depth: Debug tool.
Overflow/Underflow
Steps: 1. Push full/pop empty. Ex: Exceptions. Pitfall: No check crash. Interlink: Fixed vs dynamic. Depth: Array impl.
Applications
Steps: 1. Reverse via pop. Ex: Undo stack. Pitfall: Memory use. Interlink: Real-life. Depth: Function calls.
Advanced: Recursion Stack
Steps: 1. Calls push frames. Ex: Factorial. Pitfall: Depth limit. Interlink: Ch5. Depth: Sys recursion.
Advanced: Deque impl, prefix eval. Pitfalls: Nested unhandled. Interlinks: To queue Ch4. Real: API stacks. Depth: 14 concepts details. Examples: Real outputs. Graphs: Flow Fig 3.3. Errors: Wrong prec. Tips: Steps evidence; compare tables (notations vs ops).
Code Examples & Programs - From Text with Simple Explanations
Expanded with evidence, analysis; focus on applications. Added variations for practice.
Example 1: Basic Stack Ops (Fig 3.2)
Simple Explanation: LIFO demo.
stack = []
stack.append(1) # Push 1
stack.append(2) # Push 2
print(stack.pop()) # Pop 2- Step 1: [1] → [1,2].
- Step 2: Pop → 2, [1].
- Step 3: LIFO.
- Simple Way: Glasses nums.
Example 2: Full Impl Functions
Simple Explanation: Text program.
def isEmpty(s): return len(s)==0
def opPush(s, e): s.append(e)
def opPop(s): return s.pop() if not isEmpty(s) else None
stack = []; opPush(stack, 'glass1'); print(opPop(stack))- Step 1: Define funcs.
- Step 2: Push/pop.
- Step 3: Output glass1.
- Simple Way: Reuse.
Example 3: Display Stack
Simple Explanation: Print top-down.
def display(s):
for i in range(len(s)-1, -1, -1): print(s[i])
stack = ['glass1', 'glass3']; display(stack) # glass3 glass1- Step 1: Reverse range.
- Step 2: Print each.
- Step 3: Top first.
- Simple Way: Visualize.
Example 4: Infix to Postfix Manual
Simple Explanation: Algo 3.1 sim.
infix = "(x + y) / z"
# Steps: Parse, stack ops, build postExp = "xy+ z /"- Step 1: Push (, +.
- Step 2: ) pop + append.
- Step 3: / low prec.
- Simple Way: Prec table.
Example 5: Postfix Eval (Fig 3.4)
Simple Explanation: Calc result.
post = "7 8 2 * 4 / +"
stack = []; tokens = post.split()
for t in tokens:
if t.isdigit(): stack.append(int(t))
else: b=stack.pop(); a=stack.pop(); stack.append(a + (b * 2 // 4) if t=='*' else ...) # Simplified
print(stack.pop()) # 11- Step 1: Push 7,8,2.
- Step 2: * pop 2*8=16 push.
- Step 3: Final + =11.
- Simple Way: Operands push.
Example 6: Reverse String (Exercise 3)
Simple Explanation: App (2025 string ops).
def reverse(s):
stack = []; for c in s: stack.append(c)
rev = ''; while stack: rev += stack.pop()
return rev
print(reverse("ABC")) # CBA- Step 1: Push chars.
- Step 2: Pop build rev.
- Step 3: LIFO reverse.
- Simple Way: Easy traversal.
Tip: Run in shell; troubleshoot (e.g., empty pop). Added for conv, full blocks.
Interactive Quiz - Master Stack
10 MCQs in full sentences; 80%+ goal. Covers LIFO, ops, notations.
Quick Revision Notes & Mnemonics
Concise, easy-to-learn summaries for all subtopics. Structured in tables for quick scan: Key points, examples, mnemonics. Covers ops, notations, impl. Bold key terms; short phrases for fast reading.
| Subtopic | Key Points | Examples | Mnemonics/Tips |
|---|---|---|---|
| Stack Basics |
|
Plates/books. | LIT (LIFO-Insert-Top). Tip: "Last Plate In First Out" – Visualize pile. |
| Operations (Push/Pop) |
|
Fig 3.2 glasses. | PPUS (Push-Pop-Under-Size). Tip: "Push Up, Pop Down" – Top focus. |
| Notations (3) |
|
Table 3.1: *3+45. | IPP (In-Pre-Post). Tip: "In Between, Pre First, Post Last" – Op position. |
| Conversion (Algo 3.1) |
|
Fig 3.3: xy+z8*/. | SPP (Scan-Push-Pop). Tip: "Prec Higher Pops" – Order rule. |
| Evaluation (Algo 3.2) |
|
Fig 3.4: 11. | PEP (Push-Eval-Pop). Tip: "Numbers Nest, Ops Nestle" – Calc flow. |
| Impl & Apps |
|
glassStack output. | LAR (List-Apps-Reverse). Tip: "Stack Like Plates Always Top" – LIFO daily. |
Overall Tip: Use LIT-PPUS-IPP-SPP-PEP 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., Deque, Recursion Depth).
| Term/Process | Description | Example | Usage |
|---|---|---|---|
| Stack | LIFO linear DS | Plates pile | Undo |
| LIFO | Last In First Out | Pop recent | Principle |
| Push | Add top | append(elem) | Insert |
| Pop | Remove top | pop() | Delete |
| Overflow | Push full | Array limit | Exception |
| Underflow | Pop empty | No elems | Check |
| Top | Peek top | stack[-1] | Read |
| Infix | Op between | A+B | Human |
| Prefix | Op before | +AB | Polish |
| Postfix | Op after | AB+ | Eval |
| Precedence | Op priority | * > + | Order |
| Linear DS | Sequential | Stack/list | Access |
| opPush | Push func | append | Impl |
| opPop | Pop func | pop return | Impl |
| isEmpty | Empty check | len()==0 | Avoid err |
| Size | Element count | len(stack) | Count |
| Display | Print contents | Reverse loop | View |
| BODMAS | Infix order | Brackets etc | Eval |
| PostExp | Postfix string | xy+z*/ | Build |
| Left Paren | '(' push | Matching | Conv |
| Right Paren | ')' pop | Discard pair | Conv |
| Operand | Num/var | x,3 | Append |
| Operator | +/ * | Push prec | Track |
| Conv Algo | Infix-post | Algo 3.1 | Compiler |
| Eval Algo | Post-value | Algo 3.2 | Calc |
| GlassStack | Example | ['glass1'] | Demo |
| Reverse Polish | Postfix alias | AB+ | History |
| Undo | Pop changes | Editor | App |
| Browser Back | Pop history | P3→P2 | App |
| Parens Match | Push/pop ( ) | Compiler | Syntax |
| Deque | Efficient stack | collections.deque | Advanced |
| Recursion Depth | Call stack limit | sys.setrecursionlimit | Advanced |
Tip: Examples memory; sort subtopic. Easy: Table scan. Added 10 rows depth.
Stack 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 push/pop work in glasses example (Fig 3.2)?
- Step 1: Empty stack.
- Step 2: Push 1 → [1] top=1.
- Step 3: Push 2 → [1,2] top=2.
- Step 4: Pop → 2 out, top=1.
- Step 5: Push 3 → [1,3].
- Step 6: LIFO: Last 3 out first.
Visual: Growing/shrinking tower – Bottom fixed, top changes. Example: Num glasses 1-4.
Question 2: What steps in infix to postfix for (x + y)/(z*8) (Ex 3.1)?
- Step 1: postExp="", stack empty.
- Step 2: ( push; x append → "x".
- Step 3: + push; y append → "xy".
- Step 4: ) pop + append → "xy+".
- Step 5: / push (low prec); z append → "xyz+".
- Step 6: * pop? No, push; 8 append → "xyz+8"; pop * / append → "xy+z8*/".
Visual: Input scan → Stack ops → String build. Example: Fig 3.3 arrows.
Question 3: How to implement isEmpty/top as in text?
- Step 1: Def isEmpty: len(s)==0 → True.
- Step 2: Call top: If empty print msg, return None.
- Step 3: Else: s[len(s)-1] return.
- Step 4: Ex: top(['glass3']) → 'glass3'.
- Step 5: Avoid pop err.
- Step 6: Use in opPop.
Visual: Checkmark – Empty? Msg/Peek. Example: glassStack top.
Question 4: What is the full process of postfix eval 7 8 2 * 4 / + (Ex 3.2)?
- Step 1: Push 7,8,2 → [7,8,2].
- Step 2: * pop 2,8 → 16 push [7,16].
- Step 3: Push 4 → [7,16,4].
- Step 4: / pop 4,16 → 4 push [7,4].
- Step 5: + pop 4,7 → 11 push [11].
- Step 6: Pop 11 result.
Visual: Stack grow/shrink – Num push, op calc. Example: Fig 3.4 symbols.
Question 5: How does display enable view in impl program?
- Step 1: len(s), range(len-1,-1,-1).
- Step 2: Print s[i] each.
- Step 3: Top first: glass3 then 1.
- Step 4: After push/pop.
- Step 5: "Current elements" msg.
- Step 6: Verify LIFO (Fig 3.2 v).
Visual: Loop down – Reversed print. Example: Output glass3/glass1.
Question 6: Outline steps to reverse string using stack (Exercise 3).
- Step 1: stack = [], for c in s: push c.
- Step 2: rev="", while stack: rev += pop().
- Step 3: Ex: "ABC" → push A B C → pop C B A → "CBA".
- Step 4: LIFO traversal.
- Step 5: O(n) time.
- Step 6: App: Reverse order.
Visual: Input chars → Stack → Output rev. Example: Handles any string.
Tip: Treat as FAQ; apply to codes. Easy: Q → Steps + Visual. Full Q&A for exam-like practice.
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