Algorithms Quiz: Quicksort and Stacks

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson
Download our mobile app to listen on the go
Get App

Questions and Answers

What type of algorithm is Quicksort?

  • Brute force algorithm
  • Divide and conquer algorithm (correct)
  • Dynamic programming algorithm
  • Greedy algorithm

The best-case running time of the Quicksort algorithm is $O(n^2)$.

False (B)

What is the first number in the list that is processed by Quicksort?

44

Quicksort requires rearranging elements into two sublists called the first sublist and the ______.

<p>second sublist</p> Signup and view all the answers

What is the main characteristic of a stack?

<p>Last-in first-out (LIFO) (A)</p> Signup and view all the answers

Match the running times of Quicksort to their respective cases:

<p>Worst-case = n^2 / 2 Average-case = n log n Best-case = O(n log n)</p> Signup and view all the answers

In the third step of the Quicksort algorithm, which number does 44 interchange with?

<p>40 (A)</p> Signup and view all the answers

A stack allows elements to be removed from both ends.

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

In Quicksort, the pivot is always the last number of the list.

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

Name the operation used to insert an element into a stack.

<p>Push</p> Signup and view all the answers

When an element is removed from a stack, it is called a _____ operation.

<p>pop</p> Signup and view all the answers

How many numbers are initially in the list A?

<p>12</p> Signup and view all the answers

Match the following stack operations with their descriptions:

<p>Push = Insert an element into the stack Pop = Remove an element from the stack Overflow = Indicates the stack is full Underflow = Indicates the stack is empty</p> Signup and view all the answers

After the first interchange, the list becomes ______.

<p>22, 33, 11, 55, 77, 90, 40, 60, 99, 44, 88, 66</p> Signup and view all the answers

If the TOP of a stack is equal to MAXSTK, what does this indicate?

<p>The stack is at maximum capacity (D)</p> Signup and view all the answers

What determines the final position of the pivot in Quicksort?

<p>The counts of numbers less than and greater than it (D)</p> Signup and view all the answers

In a stack, the position of the TOP is always the highest index of the stack array.

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

What is the initial condition of TOP when a stack is empty?

<p>0 or NULL</p> Signup and view all the answers

In an empty stack, both TOP and __________ are set to 0.

<p>MAXSTK</p> Signup and view all the answers

What happens when a pop operation is attempted on an empty stack?

<p>An UNDERFLOW message is printed (D)</p> Signup and view all the answers

What is Polish notation also known as?

<p>Prefix notation (D)</p> Signup and view all the answers

Infix notation requires the use of parentheses to define the order of operations.

<p>True (A)</p> Signup and view all the answers

What is the output of the Postfix expression 'AB+'?

<p>A + B</p> Signup and view all the answers

The equivalent Infix expression for the Postfix expression '5 6 2 + * 12 4 / -' is '5 * (6 + 2) - 12 / 4'.

<p>true</p> Signup and view all the answers

Match the different notations with their descriptions:

<p>Infix notation = Operator is between operands Polish notation = Operator is before operands Reverse Polish notation = Operator is after operands Postfix notation = Another name for Reverse Polish notation</p> Signup and view all the answers

Which of the following correctly represents the transformation of '(A + B) * C' to Polish notation?

<p>*+ABC (A)</p> Signup and view all the answers

One does not need parentheses when using Reverse Polish notation.

<p>True (A)</p> Signup and view all the answers

Describe the fundamental property of Polish notation.

<p>The order of operations is determined by the positions of operators and operands, eliminating the need for parentheses.</p> Signup and view all the answers

In Reverse Polish notation, the expression 'A B +' translates into the Infix expression '______'.

<p>A + B</p> Signup and view all the answers

Which of the following best describes the transformation of Infix to Postfix?

<p>Operators are placed after the operands. (D)</p> Signup and view all the answers

Flashcards

What is a stack?

A data structure that follows the Last-In-First-Out (LIFO) principle, meaning the last element added is the first one removed. Think of a stack of plates - you take the top plate off first.

What is the PUSH operation?

The operation of adding a new element to the top of the stack. It's like placing a new plate on top of your stack of plates.

What is the POP operation?

The operation of removing the top element from the stack. It's like taking the top plate off your stack of plates.

What is the TOP of a stack?

The top of the stack is where the last element added is located. It's the most accessible element to remove.

Signup and view all the flashcards

How are stacks represented using an array?

An array is used to represent the stack in memory. Each element in the array corresponds to a position in the stack.

Signup and view all the flashcards

What is the TOP pointer?

A pointer variable that holds the index of the top element in the stack. It allows you to access the top element easily.

Signup and view all the flashcards

What is the MAXSTK?

The maximum number of elements that can be stored in the stack. This limit is typically defined by the size of the array used to represent the stack.

Signup and view all the flashcards

What is STACK OVERFLOW?

This condition occurs when you attempt to add an element to a stack that is already full. It's like trying to add a plate to a stack when there's no space left.

Signup and view all the flashcards

What is STACK UNDERFLOW?

This occurs when you try to remove an element from an empty stack. It's like trying to take a plate from an empty stack.

Signup and view all the flashcards

How are elements stored in a stack?

The elements in the stack are stored in consecutive memory locations, typically in an array. This makes it efficient to access elements based on their position.

Signup and view all the flashcards

Polish Notation

A notation where the operator symbol is placed before its operands.

Signup and view all the flashcards

Infix Notation

A notation where the operator symbol is placed between its operands.

Signup and view all the flashcards

Reverse Polish Notation (Postfix)

A notation where the operator symbol is placed after its operands.

Signup and view all the flashcards

Fundamental property of Polish notation

The order of operations is determined by the positions of operators and operands. No parentheses are needed.

Signup and view all the flashcards

Transforming Infix to Postfix

A method used to convert Infix to Postfix, where we scan the infix expression symbol by symbol, pushing them onto a stack and popping them according to rules, ultimately producing a postfix expression.

Signup and view all the flashcards

Transforming Postfix to Infix

A method used to convert Postfix to Infix, where we scan the postfix expression symbol by symbol, pushing them onto a stack and popping them according to rules, ultimately producing an infix expression.

Signup and view all the flashcards

Quicksort

A sorting algorithm that uses a stack as a primary data structure.

Signup and view all the flashcards

Stack

A data structure that follows the Last-In, First-Out (LIFO) principle. Think of a stack of plates or a stack of books.

Signup and view all the flashcards

Sorting a list

Rearranging elements in a list to be in a specific order, like numerically or alphabetically.

Signup and view all the flashcards

Reduction Step in Quicksort

In the Quicksort algorithm, the initial step involves finding the right position for the first element in the list.

Signup and view all the flashcards

Scanning from right to left in Quicksort

Repeatedly scanning a list from right to left, comparing each element with a pivot element, and swapping them if the current element is less than the pivot.

Signup and view all the flashcards

Scanning from left to right in Quicksort

Repeatedly scanning a list from left to right, comparing each element with a pivot element, and swapping them if the current element is greater than the pivot.

Signup and view all the flashcards

Interchange in Quicksort

The act of exchanging the positions of two elements in a list.

Signup and view all the flashcards

Partitioning in Quicksort

The process of breaking a list into two sublists based on the position of the pivot. One sublist contains elements smaller than the pivot, and the other contains elements larger than the pivot.

Signup and view all the flashcards

Worst-Case Running Time of Quicksort

The worst-case scenario for Quicksort, where the algorithm might take the longest time to sort the list completely.

Signup and view all the flashcards

Average-Case Running Time of Quicksort

The average time Quicksort takes to sort a list, usually a more efficient scenario compared to the worst-case.

Signup and view all the flashcards

Best-Case Running Time of Quicksort

The most efficient way Quicksort can sort a list, where it takes minimal time.

Signup and view all the flashcards

Study Notes

Stacks

  • A stack is a list where elements are inserted and deleted from one end, called the top.
  • The last item added is the first removed (LIFO).
  • Common operations are "push" (insert) and "pop" (delete).

Basic Operations

  • Push: Adds an element to the top of the stack.
  • Pop: Removes an element from the top of the stack.
  • These operations are unique to stack data structures.

Array Representation of Stacks

  • A stack can be implemented using an array.
  • TOP points to the top element.
  • MAXSTK represents the maximum capacity.
  • An empty stack has TOP = 0 or TOP = NULL.

Push Operation

  • Check if the stack is full (TOP=MAXSTK). If full, print "OVERFLOW" and return.
  • Increase TOP by 1.
  • Insert the new element at STACK[TOP].
  • Return.

Pop Operation

  • Check if the stack is empty (TOP=0). If empty, print "UNDERFLOW" and return.
  • Store the element at STACK[TOP] in ITEM.
  • Decrease TOP by 1.
  • Return the ITEM.

Arithmetic Expressions: Notation

  • Infix Notation: Operator placed between operands (e.g., A + B).
  • Polish Notation (Prefix): Operator placed before operands (e.g., +AB).
  • Reverse Polish Notation (Postfix): Operator placed after operands (e.g., AB+).

Translation between Notations

  • Converting between infix, prefix, and postfix notations requires careful consideration of operator precedence and parentheses.

Quicksort

  • Quicksort is a sorting algorithm.
  • It rearranges elements of a list.
  • It's a divide-and-conquer algorithm.

Quicksort: Reduction Step

  • The quicksort algorithm finds a final position for the first element.
  • A scan across the list occurs to find the proper location for the initial value.
  • This often involves swapping elements.

Quicksort: Complexity

  • Worst-case time complexity is O(n²).
  • Average-case time complexity is O(n log n).
  • Best-case time complexity is O(n log n).

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

More Like This

Quicksort Quiz
8 questions

Quicksort Quiz

SaneIguana avatar
SaneIguana
Quicksort Algorithm
10 questions

Quicksort Algorithm

IntricateLight avatar
IntricateLight
Algorithm Analysis: Quicksort Overview
10 questions
Use Quizgecko on...
Browser
Browser