"In computer science, a priority queue is an abstract data-type similar to a regular queue or stack data structure."
These data structures are used to efficiently find and retrieve the smallest or largest value in a dataset. Heaps are specialized trees, while priority queues are more general implementations.
Basic data structures: It is important to have a good understanding of basic data structures like arrays, linked lists, trees, and graphs, as heaps and priority queues are built on top of them.
Binary heaps: A binary heap is a binary tree data structure where the parent node is always greater/lesser than its child nodes. It is an important data structure in the implementation of a priority queue.
Priority queues: A priority queue is a data structure that stores elements and assigns priority levels to them based on the key value. It allows the user to insert elements into the queue and remove them based on their priorities.
Operations on priority queue: Operations like insert, delete, find max/min, and change priority are important for working with priority queues.
Implementations of priority queue: Priority queues can be implemented using binary heaps, Fibonacci heaps, etc.
Heapsort: Heapsort is an algorithm that uses a heap to sort an array in ascending or descending order.
Dijkstra’s shortest path algorithm: A popular graph algorithm that uses a priority queue to find the shortest path between two vertices.
Huffman coding: A lossless data compression algorithm that builds a binary tree from a frequency table and assigns codes to each symbol of the alphabet based on its frequency. It uses a priority queue to build the binary tree.
Lazy deletion: A technique used to remove elements from priority queues lazily (i.e., not actually removing them). This makes it possible to remove elements while maintaining the heap property.
Applications of priority queues: Priority queues are used in various real-world applications like job scheduling, network routing, and computer simulation.
Heap operations like heapify, sifting up and sifting down: Heapify generates the heap from an unordered array. Sifting up is used when inserting an element to the heap whereas sifting down is used for removing the head/root element of the heap.
Binomial heaps: Binomial heaps are a type of heap data structure made up of smaller trees called "binomial trees". They have some good properties such as faster insertions and merges than a binary heap.
Leftist heaps: Leftist heaps are another variation of the heap data structure which is used to optimize the merge operation.
Binary Heap: A binary heap is a complete binary tree where the value of each node is greater than or equal to its children, and the root node has the highest value. It is the most commonly used heap data structure.
Binomial Heap: A binomial heap is a collection of binomial trees. A binomial tree is a complete binary tree where the value of each node is greater than or equal to its children. It is efficient for implementing priority queues.
Fibonacci Heap: A Fibonacci heap is a collection of trees with minimum-heap property. It provides faster amortized time complexity for decrease key and merge operations than a binary heap, but slower for extract-min.
Pairing Heap: A pairing heap is a tree-based heap data structure, where each node has an arbitrarily large number of children. It is usually faster than binary heap for insert and merge operations, but slower for extract-min and decrease-key operations.
D-ary Heap: A D-ary heap is a generalization of binary heap where each node has D children, instead of 2 children. The value of each node is greater than or equal to its children, and the root node has the highest value.
Leftist Heap: A leftist heap is a binary tree-based heap where the value of each node is greater than or equal to its children. It has a special property where the right child has a smaller rank than the left child, making it suitable for merge operations.
Skew Heap: A skew heap is a binary tree-based heap with the same heap property as a binary heap, but with no order in the right subtrees. It has the same time complexity as binary heap for most operations, but faster for merge operations.
Rank-Pairing Heap: A rank-pairing heap is a tree-based heap where each node has a rank (size of its subtree) and a priority. It provides efficient O(log n) time complexity for all priority queue operations.
Multiway Heap: A multiway heap is a tree-based heap where each node has an arbitrary number of children. It is often used for external storage where the heap may need to be paged in and out of memory.
Bucket Heap: A bucket heap is a type of heap that is used when the range of the priority values is known in advance. The priority values are divided into several buckets, and a linked list of elements is stored in each bucket. It is used when the range of keys is small and known in advance.
"Each element in a priority queue has an associated priority. In a priority queue, elements with high priority are served before elements with low priority."
"In some implementations, if two elements have the same priority, they are served in the same order in which they were enqueued."
"In other implementations, the order of elements with the same priority is undefined."
"While priority queues are often implemented using heaps, they are conceptually distinct from heaps."
"A priority queue is an abstract data structure like a list or a map."
"Just as a list can be implemented with a linked list or with an array..."
"A priority queue can be implemented with a heap or another method such as an unordered array."
"Elements with high priority are served before elements with low priority."
"Elements in a regular queue are served in the order they were enqueued, while in a priority queue, elements are served based on their priority."
"The priority of each element in a priority queue is associated with the element and can be predefined or modified."
"If a priority queue is empty, there are no elements to be served."
"When a new element is enqueued in a priority queue, it is placed in the appropriate position based on its priority."
"In a priority queue, elements are served based on their priority, not their position in the queue."
"Yes, a priority queue can contain duplicate elements with the same priority."
"The order of elements with the same priority is undefined in some implementations."
"A priority queue allows for efficient retrieval of elements with the highest priority, ensuring they are served first."
"While priority queues have applications in computer science, they can also be used in various other fields, such as scheduling tasks in real-time systems."
"While heaps are commonly used to implement priority queues, other methods such as an unordered array can also be used, each with their own advantages and limitations."
"The choice of implementation, such as using a heap or an unordered array, can affect the time complexity of priority queue operations, influencing factors like insertion time and retrieval efficiency."