Priority Queues

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Questions and Answers

What distinguishes a Priority Queue from a simple queue?

Priority queues cannot store integers.

Priority queues do not allow duplicate elements.

Priority queues always remove elements in the order they were inserted.

Priority queues assign a priority to each element. (correct)

In a Priority Queue, a larger priority value indicates higher importance.

False (B)

What is the name of the method that removes the smallest element from a Priority Queue?

extractMin

The priority in a Priority Queue comes from a totally ordered universe called _______.

K Signup and view all the answers

Match the following Priority Queue operations with their descriptions:

insert = Adds a new element with its priority extractMin = Removes and returns the smallest element isEmpty = Checks if the queue has no elements Signup and view all the answers

Which node does not have any children?

Leaf node (B) Signup and view all the answers

In a binary min-heap, the value of a parent node is always greater than the values of its child nodes.

False (B) Signup and view all the answers

What is the position of the root node in an array representation of a binary heap?

0 Signup and view all the answers

A node whose parent is `null` is called the ______ node.

root Signup and view all the answers

Match the following terms related to a binary heap with their descriptions:

Root = Node whose parent is null Leaf = Node without any children Inner node = Node that has at least one child Ordering property = Parent's value is less than or equal to its children Signup and view all the answers

What is the purpose of the `swap(i, j)` function in the BinaryHeap class?

To exchange the elements at positions <code>i</code> and <code>j</code> in the array. (A) Signup and view all the answers

The `isEmpty` method returns `true` if the last index is equal to 0.

False (B) Signup and view all the answers

What is the worst case running time of the `insert` function in a BinaryHeap?

$O(logn)$ Signup and view all the answers

The `bubbleUp` function moves the new element upwards until the ordering property is fulfilled, which means the parent is ______ or equal.

smaller Signup and view all the answers

Match the following methods with their descriptions:

<code>parent(i)</code> = Calculates the index of the parent node for the given index <code>i</code>. <code>lchild(i)</code> = Calculates the index of the left child node for the given index <code>i</code>. <code>rchild(i)</code> = Calculates the index of the right child node for the given index <code>i</code>. <code>bubbleUp(i)</code> = Moves the element at the given index <code>i</code> upwards in the heap to maintain the heap property. Signup and view all the answers

What is the primary purpose of the `Ordering` class in the context of priority queues?

To define a total order among the elements. (D) Signup and view all the answers

In the priority queue sorting algorithm, elements are extracted from the priority queue in ascending order.

True (A) Signup and view all the answers

What is the time complexity of the `extractMin()` operation in the worst case for the linked-nodes implementation when elements are stored in arbitrary order?

$O(n)$ Signup and view all the answers

The dummy-node technique uses an `______` to store the reference to the dummy node.

anchor Signup and view all the answers

Match the following priority queue implementations with their respective properties:

Linked Nodes (Increasing Order) = <code>extractMin()</code> is $O(1)$, <code>insert()</code> is $O(n)$ Linked Nodes (Arbitrary Order) = <code>insert()</code> is $O(1)$, <code>extractMin()</code> is $O(n)$ Array Implementation = More complex, with better running times than linked nodes. Signup and view all the answers

Which of the following best describes the role of `extractMin()`?

It removes a value whose key is minimal among all other keys. (D) Signup and view all the answers

In the linked-node priority queue implementation, using a dummy node to indicate if the list is empty adds complexity to the implementation.

False (B) Signup and view all the answers

Why are array-based priority queue implementations preferred over linked-node implementations in terms of caching?

Arrays have better caching behavior. Signup and view all the answers

What is the worst-case running time of Heapsort?

$O(n \log n)$ (A) Signup and view all the answers

Heapsort is a stable sorting algorithm.

False (B) Signup and view all the answers

What is the memory usage characteristic of Heapsort in its standard implementation?

out-of-place Signup and view all the answers

In-place heapsort avoids copying elements by directly using the ______ processes on the input array.

bubbling Signup and view all the answers

Match the following sorting algorithms with their corresponding time complexities from linked-nodes implementation:

Insertion sort = $O(n^2)$ Selection sort = $O(n^2)$ Signup and view all the answers

What is the first step in the `extractMin()` operation of a min-heap?

Store the root element temporarily. (B) Signup and view all the answers

The `bubbleDown()` method in a min-heap only checks one child node when comparing values.

False (B) Signup and view all the answers

What property of a heap might be violated after removing the root element?

ordering property Signup and view all the answers

The `bubbleDown()` method recurses on the ______ node after a swap.

child Signup and view all the answers

What is the worst-case running time of the `extractMin()` operation in a min-heap?

$O(log n)$ (C) Signup and view all the answers

What does $T_{in}(n)$ represent in the context of the PrioQueue sorting algorithm?

The running time of the insertion method when the heap contains $n$ elements. (D) Signup and view all the answers

Match the following steps with their action in the min-heap deletion process:

Store <code>array(0)</code> = Temporarily store the root element Swap last element with root = Replace the root with the last element Call <code>bubbleDown(0)</code> = Adjust the heap to maintain its properties Signup and view all the answers

The total running time of the priority queue sort is solely dependent on the number of elements to be sorted.

False (B) Signup and view all the answers

Study Notes

Priority Queue (PrioQueue)

Abstract data type (ADT) similar to a queue, but elements have priorities.
Smaller priority values are dequeued first.

ADT Specifications

insert(key: K): Adds an element with priority key.
extractMin(): Removes and returns the element with the smallest key.
isEmpty: Checks if the queue is empty.

Applications

Operating systems: Scheduling processes based on urgency.
Networking: Prioritizing data packets (e.g., voice, video).
Database management: Processing queries/transactions with different priorities.
Algorithms: Efficient element selection (e.g., Dijkstra's shortest path).
Printing: Prioritizing print jobs.

Sorting with Priority Queues

Algorithm prioQueueSort uses a priority queue to sort an array.
Inserts all array elements into a priority queue.
Extracts elements repeatedly from the queue and inserts them into the array in sorted order.

Implementation with Linked Nodes

Variant 1 (increasing order): Elements stored in increasing order.
- extractMin() is O(1).
- insert() is O(n) in the worst case.
Variant 2 (arbitrary order): Elements in arbitrary order.
- insert() is O(1).
- extractMin() is O(n).

Dummy-Node Technique

Used to simplifies insert and extractMin operations, especially in implementation with Linked nodes.
Introduces a dummy node at the anchor, facilitating empty conditions in the priority queue.

Array Implementation (Binary Heap)

Implements a priority queue using an array.
Represented as a binary heap (a binary tree-based structure).
Ordering property: A node's value is smaller than or equal to its children's values.
Time complexity
- Insert: O(log n)
- ExtractMin/RemoveMin: O(log n)

Heapsort Algorithm

In-place algorithm used for sorting.
Sorts elements using a binary heap.
Worst-case time complexity: O(n log n).

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Description

Explore the concept of Priority Queues as an abstract data type and their unique operations such as insert and extractMin. Learn about real-world applications in operating systems, networking, and database management, as well as sorting algorithms that utilize priority queues.

Priority Queues

Choose a study mode

Podcast

Questions and Answers

What distinguishes a Priority Queue from a simple queue?

In a Priority Queue, a larger priority value indicates higher importance.

What is the name of the method that removes the smallest element from a Priority Queue?

The priority in a Priority Queue comes from a totally ordered universe called _______.

Match the following Priority Queue operations with their descriptions:

Which node does not have any children?

In a binary min-heap, the value of a parent node is always greater than the values of its child nodes.

What is the position of the root node in an array representation of a binary heap?

A node whose parent is null is called the ______ node.

Match the following terms related to a binary heap with their descriptions:

What is the purpose of the swap(i, j) function in the BinaryHeap class?

The isEmpty method returns true if the last index is equal to 0.

What is the worst case running time of the insert function in a BinaryHeap?

The bubbleUp function moves the new element upwards until the ordering property is fulfilled, which means the parent is ______ or equal.

Match the following methods with their descriptions:

What is the primary purpose of the Ordering class in the context of priority queues?

In the priority queue sorting algorithm, elements are extracted from the priority queue in ascending order.

What is the time complexity of the extractMin() operation in the worst case for the linked-nodes implementation when elements are stored in arbitrary order?

The dummy-node technique uses an ______ to store the reference to the dummy node.

Match the following priority queue implementations with their respective properties:

Which of the following best describes the role of extractMin()?

In the linked-node priority queue implementation, using a dummy node to indicate if the list is empty adds complexity to the implementation.

Why are array-based priority queue implementations preferred over linked-node implementations in terms of caching?

What is the worst-case running time of Heapsort?

Heapsort is a stable sorting algorithm.

What is the memory usage characteristic of Heapsort in its standard implementation?

In-place heapsort avoids copying elements by directly using the ______ processes on the input array.

Match the following sorting algorithms with their corresponding time complexities from linked-nodes implementation:

What is the first step in the extractMin() operation of a min-heap?

The bubbleDown() method in a min-heap only checks one child node when comparing values.

What property of a heap might be violated after removing the root element?

The bubbleDown() method recurses on the ______ node after a swap.

What is the worst-case running time of the extractMin() operation in a min-heap?

What does $T_{in}(n)$ represent in the context of the PrioQueue sorting algorithm?

Match the following steps with their action in the min-heap deletion process:

The total running time of the priority queue sort is solely dependent on the number of elements to be sorted.

Study Notes

Priority Queue (PrioQueue)

ADT Specifications

Applications

Sorting with Priority Queues

Implementation with Linked Nodes

Dummy-Node Technique

Array Implementation (Binary Heap)

Heapsort Algorithm

Studying That Suits You

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A node whose parent is `null` is called the ______ node.

What is the purpose of the `swap(i, j)` function in the BinaryHeap class?

The `isEmpty` method returns `true` if the last index is equal to 0.

What is the worst case running time of the `insert` function in a BinaryHeap?

The `bubbleUp` function moves the new element upwards until the ordering property is fulfilled, which means the parent is ______ or equal.

What is the primary purpose of the `Ordering` class in the context of priority queues?

What is the time complexity of the `extractMin()` operation in the worst case for the linked-nodes implementation when elements are stored in arbitrary order?

The dummy-node technique uses an `______` to store the reference to the dummy node.

Which of the following best describes the role of `extractMin()`?

What is the first step in the `extractMin()` operation of a min-heap?

The `bubbleDown()` method in a min-heap only checks one child node when comparing values.

The `bubbleDown()` method recurses on the ______ node after a swap.

What is the worst-case running time of the `extractMin()` operation in a min-heap?