Algorithm Design: Abstract Data Types and Analysis

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Questions and Answers

What is the time complexity to remove an element from the back of an array?

Θ(1) (correct)

Θ(n^2)

Θ(n)

Θ(log n)

Which of the following operations has a time complexity of Θ(n) for an array?

addLast()

removeLast()

addFirst() (correct)

removeFirst() (correct)

Which characteristic is NOT an advantage of arrays?

Efficient random access

Memory locality

Space efficiency

Dynamic resizing (correct)

In a singly linked list, what do nodes contain?

A reference to the data value and a reference to the next node Signup and view all the answers

What is a disadvantage of using arrays compared to linked lists?

Fixed length Signup and view all the answers

Which algorithm complexity is guaranteed to be slower as $n$ increases significantly?

Θ(n^3) Signup and view all the answers

What could make a Θ(n^2) algorithm slower than a Θ(n^3) algorithm for small values of $n$?

Leading constants being large Signup and view all the answers

At what growth rate does logarithmic complexity exceed a constant time complexity?

When $n$ approaches infinity Signup and view all the answers

When comparing an O(n^3) algorithm and an O(n^2) algorithm, what is typically true as $n$ gets large?

O(n^2) is faster Signup and view all the answers

Which of the following growth rates increases faster than a linear growth rate as $n$ becomes large?

Exponential Signup and view all the answers

Which of the following statements about algorithm performance is correct?

A Θ(n^2) algorithm will eventually outpace a Θ(n^3) algorithm. Signup and view all the answers

What is the significance of comparing growth rates of algorithms?

To predict performance as input size increases. Signup and view all the answers

Which algorithm class is often the slowest as $n$ increases?

Cubic Signup and view all the answers

What defines an Abstract Data Type (ADT)?

The type of data stored, operations supported, and their parameters Signup and view all the answers

How is an Abstract Data Type expressed in Java?

Using an interface that lists method declarations with no body Signup and view all the answers

What is one key characteristic of an Abstract Data Type?

It allows implementation changes without affecting other parts Signup and view all the answers

Which of the following statements about Abstract Data Types is false?

ADTs must always guarantee optimal performance. Signup and view all the answers

What role do parameters play in Abstract Data Types?

They provide data type constraints for the operation arguments. Signup and view all the answers

Which of the following describes a correct relationship between an interface and a class in the context of Abstract Data Types?

The class implements the interface, ensuring all methods are defined. Signup and view all the answers

In terms of data structures, what does encapsulation imply?

It hides the implementation details from the users of the data structure. Signup and view all the answers

What is a primary purpose of analyzing algorithms related to Abstract Data Types?

To provide a measure of performance and efficiency Signup and view all the answers

What is the time complexity to add an element at the back of an array?

Constant time Θ(1) Signup and view all the answers

How long does it take to add an element at the front of an array?

Linear time Θ(n) Signup and view all the answers

If an array contains n elements, how does the runtime change as n increases for adding an element at the front?

It increases linearly Signup and view all the answers

Which of the following statements is true about adding elements to an array?

Adding at back is constant time; adding at front is linear time Signup and view all the answers

What is the primary disadvantage of adding elements at the front of an array?

It requires shifting elements Signup and view all the answers

When adding an element in alphabetical order to a sorted array, what is the expected runtime complexity?

Linear time Θ(n) Signup and view all the answers

If you want to frequently add elements to the front of a collection, which data structure is typically more efficient than an array?

Linked List Signup and view all the answers

For an array of size n, what happens to the performance if every operation is done at the beginning of the array?

Performance degrades to linear time Signup and view all the answers

What is the runtime complexity for inserting a node at the head of a singly linked list?

Θ(1) Signup and view all the answers

Which step is performed first when inserting a node in an empty singly linked list?

Instantiate a Node object Signup and view all the answers

When inserting a new node into a non-empty singly linked list, what should the next pointer of the new node point to?

The current head of the list Signup and view all the answers

What happens immediately after the new node is created and its element is set in an empty list?

The head and tail pointers are set to the new node Signup and view all the answers

Why is the order of pointer assignment significant during insertion in a singly linked list?

To maintain the integrity of the list structure Signup and view all the answers

If a new node is added at the head of a singly linked list, which pointer must be updated to point to the new node?

The head pointer Signup and view all the answers

Which of the following statements about inserting nodes in singly linked lists is true?

Insertion at the head always requires a new node Signup and view all the answers

What is the first action to take when inserting a new node into a non-empty singly linked list?

Create and configure a new Node object Signup and view all the answers

What is the initial action when attempting to remove an element from an empty singly linked list?

Throw an exception Signup and view all the answers

What happens to the head and tail when only one element remains in the list after removal?

Both head and tail are set to null Signup and view all the answers

What is the time complexity for removing the head from a singly linked list with more than one element?

Θ(1) Signup and view all the answers

After removing the head of a list with multiple elements, how is the new head determined?

It is set to the second element in the list Signup and view all the answers

Which statement about singly linked lists is incorrect during the removal process?

The head can never be set to null under any conditions Signup and view all the answers

What condition must be true for a singly linked list to be considered empty?

Head equals null Signup and view all the answers

Why is the runtime for removal from the head of a singly linked list defined as Θ(1)?

Because it requires adjusting only a few pointers Signup and view all the answers

What would happen if the second element is also removed immediately after the head is removed from a list of two elements?

Both head and tail will point to null Signup and view all the answers

Study Notes

Course Information

Course code: CC21120, CS21120
Course title: Algorithm Design and Data Structures
Lecture topic: Abstract Data Types, Basic Data Structures and Analysis of Algorithms
Lecturer: Christine Zarges
Email: [email protected]

Overview

Abstract Data Types (ADTs): Mathematical model of a data structure, defining data types, operations, and their parameters. Specifies what operations do but not how they are implemented. Does not guarantee performance.
Analysis of Algorithms: Aims to classify problems and algorithms, forecast performance, ensure certain performance qualities, compare differing algorithms. Focuses on running time and memory usage.
Arrays: Contiguous memory area with equal-sized elements, indexed by integers. Fixed length. Constant-time access, local memory, space-efficient.
Singly Linked Lists: Collection of nodes, with each node referencing the next node in a sequence. Dynamic length. Efficient to add/remove from beginning/end (but not always from middle), not efficient for random access.

Abstract Data Types in Java

Expressed as interfaces: Includes method declarations with empty bodies. No data/constructors.
Realised by concrete data structures implemented as classes. The implementation is encapsulated, changes don't affect other parts.

Analysis of Algorithms: Motivation

Motivation for Analysis: Problem classification, performance prediction, providing guarantees, comparing algorithms, understanding principles, improving implementations, tuning parameters.

Analysis of Algorithms: Running Time

What is Running Time?: Count primitive operations (statements, assignments, method calls), multiply by how often executed. Focus on the rate of growth as input size increases.

Analysis of Algorithms: Asymptotic Notation

Significant aspect when considering growth: omit multiplicative constants, lower-order terms. Results for smaller input sizes not crucial.

Analysis of Algorithms: Asymptotic Notation - Definitions

Big-O: Asymptotic upper bound (≤)
Big-Omega: Asymptotic lower bound (≥)
Big-Theta: Same asymptotic order (=)

Analysis of Algorithms: Misuse of Big-O notation

Leading constants can be significant. O(n²) is not necessarily faster than O(n³) for all inputs.
Use the correct notation to ensure accuracy and avoid misleading interpretations.

Comparing Growth Rates

Understanding how different rates of growth of functions affect algorithms is essential for optimization.

Arrays

Structure and Implementation: Continuous block of memory space, with elements indexed as contiguous integers. Elements have equal size.
Performance: Constant-time access to elements, efficient memory locality, space efficiency, but fixed length.

Arrays: Adding/Removing

Adding to end: Constant time.
Adding at beginning/middle: Linear time (Θ(n))
Removing from end: Constant time.
Removing from beginning/middle: Linear time (Θ(n))

Singly Linked Lists

Structure and Implementation: Collection of nodes; each node holds an element and a pointer to the next node.
Performance: Dynamic Length. Efficiently add/remove from beginning/end, not efficient to randomly access elements.

Singly Linked Lists: Traversal

Runtime: Θ(n) for traversing the list.

Singly Linked Lists: Inserting at Head/Tail

Runtime: Θ(1) at head/tail. Crucial for implementation details.

Singly Linked Lists: Removing at Head/Tail

Runtime: Θ(1) at head. Θ(n) at tail!

Singly Linked Lists: Summary

Runtime for operations, advantages, and disadvantages are summarized. The efficiency compared to arrays is important to understand when choosing a data structure. Specific use cases affect these conclusions.

Summary

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Description

This quiz covers Abstract Data Types (ADTs), basic data structures like arrays and singly linked lists, and the analysis of algorithms. It focuses on understanding the mathematical models, operational specifications, and performance evaluation of different algorithmic approaches. Test your knowledge and skills in algorithm design and data structures.