Data Structures: Stacks Overview

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Questions and Answers

What is the final result after evaluating the Postfix expression '7 4 -3 * 1 5 + / *'?

  • 5
  • -2
  • -14 (correct)
  • -12

When evaluating an operator in a Postfix expression, what must be done first?

  • The operator should be pushed onto the stack.
  • Evaluate the operator without operands.
  • All operands should be stored in an array.
  • Operands must be popped from the stack. (correct)

In the expression '10 + 2 * 8 - 3', what will be the first output when converting to Postfix notation?

  • 3
  • 2
  • 10 (correct)
  • 8

What is the purpose of popping all operators from the stack at the end of the Postfix conversion?

<p>To ensure no operators are left in the stack. (C)</p> Signup and view all the answers

Which step is NOT part of evaluating a Postfix expression?

<p>Pushing operators onto the stack after evaluation. (A)</p> Signup and view all the answers

What does LIFO stand for in relation to stack operations?

<p>Last-In, First-Out (B)</p> Signup and view all the answers

Which operation would you use to check the element at the top of the stack without removing it?

<p>top (C)</p> Signup and view all the answers

What condition must be met to successfully execute a push operation on a stack implemented with an array?

<p>top must be less than MAXSIZE (C)</p> Signup and view all the answers

What would the value of top be after popping an element from a stack where top was initially 3?

<p>2 (C)</p> Signup and view all the answers

What will isEmpty return if the stack is initialized but has not had any elements pushed onto it?

<p>true (C)</p> Signup and view all the answers

Which of the following is NOT a basic operation available for stack data structures?

<p>insert (B)</p> Signup and view all the answers

In array implementation of a stack, what value should 'top' be initialized to?

<p>-1 (D)</p> Signup and view all the answers

What happens if you try to pop from an empty stack using the described pop operation?

<p>It throws an error (B)</p> Signup and view all the answers

What is the first action taken when encountering an operand during infix to postfix conversion?

<p>Print it to the result. (B)</p> Signup and view all the answers

What should be done when a right parenthesis ')' is encountered?

<p>Pop and print the top operator until the corresponding left parenthesis is found. (B)</p> Signup and view all the answers

When an operator is read, what is the initial check regarding the stack?

<p>If the operator has higher or equal precedence compared to the stack's top. (C)</p> Signup and view all the answers

In the expression (A+B)*(C-D), which operation occurs when encountering the left parenthesis '('?

<p>Push it into the stack. (C)</p> Signup and view all the answers

In the example expression 10 + 2 * 8 - 3, what happens after the operator '+' is read?

<p>It is pushed to the stack. (D)</p> Signup and view all the answers

What is the result of the expression (A+B)*(C-D) in postfix notation?

<p>AB+CD-* (C)</p> Signup and view all the answers

What occurs when the operator '-' is read in the expression 10 + 2 * 8 - 3?

<p>Operators are popped from the stack until the '-' can be placed. (D)</p> Signup and view all the answers

In the sequence of operations during infix to postfix conversion, how are operators handled in relation to their precedence?

<p>Higher or equal precedence operators are popped from the stack first. (C)</p> Signup and view all the answers

What is the primary function of the 'push' operation in a stack implemented with a linked list?

<p>To insert an element at the beginning of the linked list (A)</p> Signup and view all the answers

What happens during the 'pop' operation in a stack using a linked list?

<p>The element at the top is removed and returned (B)</p> Signup and view all the answers

In the context of a stack implemented as a linked list, what does it mean to 'push' elements into the stack?

<p>To add elements into the stack in the last-in-first-out manner (B)</p> Signup and view all the answers

Which of the following applications is not typically associated with stacks?

<p>Sorting an array (A)</p> Signup and view all the answers

When reversing the string 'a b c d e f' using a stack, which sequence applies to the 'pop' operation?

<p>f e d c b a (B)</p> Signup and view all the answers

What is the purpose of maintaining a pointer called 'top' in a linked list stack implementation?

<p>To maintain the head of the linked list (C)</p> Signup and view all the answers

Which of these represents a correct part of the 'push' implementation?

<p>newNode-&gt;next = top; (B)</p> Signup and view all the answers

Why is a singly-linked list suitable for implementing a stack?

<p>It efficiently manages memory by allowing dynamic size (A)</p> Signup and view all the answers

Flashcards

Stack

A list that allows insertion and deletion of elements only at one end, called the top.

Push

Adding an element to the top of a stack.

Pop

Removing an element from the top of a stack.

Peek (or Top)

Retrieving the element at the top of the stack without removing it.

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Stack Implementation using Array

Implementing a stack using an array data structure.

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Stack Overflow

Occurs when you try to push an element onto a full stack.

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Stack Underflow

Occurs when you try to pop an element from an empty stack.

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LIFO

Last-In, First-Out; the order of operations in a stack.

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Postfix Expression

An arithmetic expression where operators follow their operands.

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Postfix Evaluation

Evaluating a postfix expression involves using a stack to compute the result, placing numbers onto the stack and calculating results with operators.

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Infix Expression Conversion

Transforming an arithmetic expression from infix notation (operators between operands) to postfix notation.

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Operator Precedence

The order in which operators are evaluated (e.g., *, / before +, -).

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Stack-Based Calculation

A method of calculating (evaluating) expressions by placing values onto a stack and performing operations on the top elements.

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Stack Implementation using Linked List

A stack data structure implemented using a singly linked list, where all operations (push, pop) happen at the top of the list.

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Push Operation (Stack)

Adds an element to the top of the stack (beginning of the linked list).

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Pop Operation (Stack)

Removes an element from the top of the stack (beginning of the linked list).

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Stack Applications

Stacks are helpful for tasks needing Last-In First-Out (LIFO) behavior like expression evaluation, function calls, and reversing strings.

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Reversing a String (Stack)

Pushing each character of a string onto a stack and then popping them off results in the reverse order.

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Infix to Postfix Conversion

Converting an expression from infix (normal mathematical notation) to postfix (a form that is well-suited for evaluation on a stack).

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Node Structure (Linked List)

A structure containing data and a pointer to the next node in the linked list, enabling linear linked data.

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Stack's Top

Pointer variable pointing to the top element in a stack (top of the linked list).

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Postfix Notation

An arithmetic expression where operators follow their operands.

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Operand

A number or variable in an expression.

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Left Parenthesis '('

In infix to postfix conversion, pushes onto the the stack to hold.

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Right Parenthesis ')'

In infix to postfix conversion, pops until matching '(' is found.

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Operator

Symbol used in an expression to perform a calculation.

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Study Notes

Stacks

  • Stacks are lists with a restriction: insertions and deletions are both performed at the same end, known as the top of the stack.
  • Stacks follow the Last-In, First-Out (LIFO) principle. The last item added is the first one removed.
  • Operations on a stack include:
    • push (add): Adds an element to the top of the stack.
    • pop (remove): Removes the element at the top of the stack and returns it.
    • peek (top): Returns the element at the top of the stack without removing it.
    • isEmpty: Checks if the stack is empty.
    • size: Returns the number of elements in the stack.

Stack Implementations

  • Stacks can be implemented using arrays or linked lists.

Array Implementation

  • Using an array to store the stack elements.
  • Requires defining a MAXSIZE for the array's capacity.
  • A top variable tracks the index of the top element.
  • top is initialized to -1.

Linked List Implementation

  • Using a linked list to store the stack elements.
  • Each element in the list (node) stores a data value and a pointer to the next node.
  • The top pointer points to the first node in the list (the top of the stack).
  • top is initially NULL.

Stack Applications

  • Reversing Strings: Puts characters into a stack, then pops out in reverse order.
  • Bracket Matching: Stacks help check whether opening and closing brackets are matched correctly in a given expression.
  • Postfix Evaluation: Stacks are used to evaluate mathematical expressions in postfix notation.
  • Function Call Stack: Keeps track of function calls in computer programs (like a web browser's history).
  • Line Editing: Stacks are used to store characters during text editing, and can undo/redo changes.

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