Data Structures: Stacks and Queues

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Questions and Answers

What is the primary behavior expected of a stack data structure?

Last In, First Out (LIFO) (correct)

Ordered List

Random Access

First In, First Out (FIFO)

Which operation is typically performed to add an element to a queue?

enqueue(x) (correct)

pop()

push(x)

insert(x)

If you implement a singly linked list (SLL)-backed queue, which operation should be performed at the head and which at the tail for optimal efficiency?

Add to head, remove from head

Add to tail, remove from head (correct)

Add to head, remove from tail

Add to tail, remove from tail

Which of the following statements accurately describes the structure of an array-backed queue?

It tracks capacity, front index, back index, and size. Signup and view all the answers

In what scenario would a queue be most appropriately used?

Managing online orders in a restaurant. Signup and view all the answers

What is the complexity of searching for an unknown index in a singly linked list (SLL)?

O(n) Signup and view all the answers

In a tree, which of the following terms describes nodes with no children?

External/Leaf nodes Signup and view all the answers

When incrementing the front index in a circular buffer implementation of a queue, what should be done with the front variable?

It should be modded by the capacity. Signup and view all the answers

Which property defines the arrangement of data within a tree structure?

Order Signup and view all the answers

What is the depth of the root node in a tree?

0 Signup and view all the answers

Which statement correctly describes a parent node in a tree?

It has at least one child. Signup and view all the answers

What will the back index be set to when it is decremented to -1 in a circular buffer implementation?

Capacity - 1 Signup and view all the answers

Which data structure has an access complexity of O(1) for known indices?

Array Signup and view all the answers

What is the height of a leaf node?

0 Signup and view all the answers

How can the height of a node be determined?

By adding 1 to the maximum height of its children Signup and view all the answers

Which method would you use to find the parent of a specific node in a tree?

parent(x) Signup and view all the answers

What characterizes a binary tree based on its shape?

Each node can have at most two children Signup and view all the answers

Which of the following methods can be classified as a query method?

isRoot() Signup and view all the answers

What happens to the back index when adding an element to an array-backed deque?

It is increased by 1 and then modded by capacity. Signup and view all the answers

Which operation in a deque allows you to remove an element from the back?

removeLast() Signup and view all the answers

In the context of deque operations, what does O(1) time complexity signify?

Operations can be performed in constant time. Signup and view all the answers

What does modding the front index by capacity help achieve?

It allows the deque to maintain a circular structure. Signup and view all the answers

When using an array-backed deque, what should happen if the front index is decremented to -1?

It should be reset to capacity. Signup and view all the answers

What is the main characteristic of a deque compared to other queue types?

It allows adding/removing from both ends. Signup and view all the answers

What operation would be used to add an element to the head of a DLL-backed deque?

addFirst() Signup and view all the answers

What is the initial behavior of the 'size' attribute in an empty array-backed deque?

It is set to 0. Signup and view all the answers

Study Notes

Stacks

Stack ADT operates on a "Last In, First Out" (LIFO) principle.
Implementation can be done using Array, Singly Linked List (SLL), or Doubly Linked List (DLL).

Queues

Queue ADT follows a "First In, First Out" (FIFO) behavior.
Linear structure useful for scenarios like water pipes, waitlists, print queues, and online orders.
Key operations include:
- enqueue(x): Add element to the end.
- dequeue(): Remove element from the front.
- peek(): View the front element without removing it.
- isEmpty(): Check if the queue is empty.
- size(): Get the number of elements in the queue.

SLL-backed Queue

Requires both head and tail pointers for efficiency.
For optimal performance, elements should be added at the tail and removed from the head.
Both operations, adding and removing, run in O(1) time.

Array-backed Queue

Key components:
- capacity: Size of the backing array.
- front index: Index of the first element.
- back index: Index of the last element or the next spot.
- size: Total number of current elements in the queue.
Example of enqueueing and dequeueing elements shown with character management.

Deques

Double Ended Queue (Deque) allows addition/removal of elements from both ends.
Main operations:
- addFirst(x): Adds item to the front.
- addLast(x): Adds item to the rear.
- removeFirst(): Removes item from the front.
- removeLast(): Removes item from the rear.

DLL-backed Deque

Implemented with Doubly Linked List, providing O(1) operations for adding/removing items from either end.

Array-backed Deque

Utilizes a circular array to manage elements efficiently.
Modifications to front and back indices maintain circular structure.
Operations such as adding/removing elements make use of modulo with capacity for proper indexing.

Overview of Worst Case Runtimes

Array access at a known index is O(1); searching for an unknown index is O(n).
Singly Linked List (SLL) and Doubly Linked List (DLL) both have O(n) for access and search.
Stack, Queue, and Deque also demonstrate O(n) for access and search.
Data structures with O(n) complexities serve specific purposes but may not be suitable for access-heavy operations.

Trees Introduction

Trees consist of nodes with no cycles, allowing hierarchical relationships.
Highly recursive structure; best implemented with pointers in linked list-like structures.
Properties defined by shape and order characteristics.

Tree Terminology

Root: Entry point of the tree.
Children: Nodes directly connected to a parent node.
External/Leaf nodes: Nodes without children.
Internal nodes: Nodes with at least one child.
Hierarchical relationships can include parent, grandparent, siblings, cousins, and subtrees.

Depth & Height

Depth: Distance from the root to a specific node; root has a depth of 0.
Height: Distance from a node to the furthest leaf; leaf height is 0, and height of a node is 1 plus the maximum height of its children.

Tree ADT Operations

Information methods: size(), isEmpty(), iterator(), position().
Accessor methods: root(), parent(x), children(x), numChild(x).
Query methods: isInternal(), isExternal(), isRoot() evaluate node attributes.

Binary Trees

Shape allows each node to have a maximum of 2 children.
Nodes can store references to parent, children, and flags for internal/external classification.
Iteration is typically achieved through recursion, enabling access to parent nodes during the return phase of recursive calls.

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Description

Explore the fundamental concepts of stacks and queues in data structures. Understand their ADTs, implementations, and key operations like enqueue and dequeue. This quiz covers both array-backed and linked list-backed solutions for optimal performance.