A priority queue can efficiently implemented using which of the following data structures? Assume that the number of insert and peek (operation to see the current highest priority item) and extraction (remove the highest priority item) operations are almost same.a)Arrayb)Linked Listc)Heap Data Structures like Binary Heap, Fibonacci Heapd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Priority Queue Implementation using Data Structures

A priority queue is a data structure that stores a collection of elements and each element has a priority associated with it. The priority determines the order in which the elements are retrieved from the queue. To efficiently implement a priority queue, we need a data structure that supports fast insertion, extraction, and peek operations.

Data Structures for Priority Queue Implementation

The following data structures can be used for implementing a priority queue:

1. Array: An array can be used to implement a simple priority queue. However, inserting and extracting elements from the array can be slow, especially if the array is large. Also, maintaining the order of elements in the array can be complicated.

2. Linked List: A linked list can be used to implement a priority queue. However, finding the element with the highest priority can be slow because we need to traverse the entire list. Also, inserting and deleting elements can be slow, especially if the list is long.

3. Heap Data Structures: A heap data structure like a Binary Heap or Fibonacci Heap is the most efficient way to implement a priority queue. Both of these data structures support fast insertion, extraction, and peek operations.

Binary Heap:

- A binary heap is a binary tree with the property that the value of each node is greater than or equal to the values of its children.
- A binary heap can be implemented using an array. The root of the tree is stored at index 0, and the children of node i are stored at indices 2i+1 and 2i+2.
- Insertion and extraction operations can be performed in O(log n) time, where n is the number of elements in the heap.

Fibonacci Heap:

- A Fibonacci heap is a collection of trees with the same shape property as a binary heap but with a different ordering property.
- A Fibonacci heap supports fast insertion, extraction, and peek operations, and has the added advantage of faster amortized time complexity for some operations.
- However, Fibonacci heaps have a higher overhead than binary heaps, and their implementation is more complex.

Conclusion

In conclusion, a heap data structure like a Binary Heap or Fibonacci Heap is the most efficient way to implement a priority queue. Both of these data structures support fast insertion, extraction, and peek operations. Binary heap is simple to implement and has a lower overhead, while Fibonacci heap has faster amortized time complexity for some operations.

Answer

Heap Data Structures like binary heap, fibonacciheap

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