Priority Queue is an extension of the queue with the following properties:
- Every item has a priority associated with it.
- An element with high priority is dequeued before an element with low priority.
- If two elements have the same priority, they are served according to their order in the queue.
A Binary Heap is a Binary Tree with the following properties:
- It is a Complete Tree. This property of Binary Heap makes them suitable to be stored in an array.
- A Binary Heap is either Min Heap or Max Heap.
- In a Min Binary Heap, the key at the root must be minimum among all keys present in Binary Heap. The same property must be recursively true for all nodes in Binary Tree.
- Similarly, in a Max Binary Heap, the key at the root must be maximum among all keys present in Binary Heap. The same property must be recursively true for all nodes in Binary Tree.
Operation on Binary Heap
- insert(p): Inserts a new element with priority p.
- extractMax(): Extracts an element with maximum priority.
- remove(i): Removes an element pointed by an iterator i.
- getMax(): Returns an element with maximum priority.
- changePriority(i, p): Changes the priority of an element pointed by i to p.
Example of A Binary Max Heap
- Suppose below is the given Binary Heap that follows all the properties of Binary Max Heap.
- Now a node with value 32 need to be insert in the above heap: To insert an element, attach the new element to any leaf. For Example A node with priority 32 can be added to the leaf of the node 7. But this violates the heap property. To maintain the heap property, shift up the new node 32.
- Shift Up Operation get node with 32 at the correct position: Swap the incorrectly placed node with its parent until the heap property is satisfied. For Example: As node 7 is less than node 32 so, swap node 7 and node 32. Then, swap node 31 and node 32.
- ExtractMax: The maximum value is stored at the root of the tree. But the root of the tree cannot be directly removed. First, it is replaced with any one of the leaves and then removed. For Example: To remove Node 45, it is first replaced with node 7. But this violates the heap property, so move the replaced node down. For that, use shift-down operation.
- ShiftDown operation: Swap the incorrectly placed node with a larger child until the heap property is satisfied. For Example Node 7 is swapped with node 32 then, last it is swapped with node 31.
- ChangePriority: Let the changed element shift up or down depending on whether its priority decreased or increased. For Example: Change the priority of nodes 11 to 35, due to this change the node has to shift up the node in order to maintain the heap property.
- Remove: To remove an element, change its priority to a value larger than the current maximum, then shift it up, and then extract it using extract max. Find the current maximum using getMax.
- GetMax: The max value is stored at the root of the tree. To getmax, just return the value at the root of the tree.
Array Representation of Binary Heap
Since the heap is maintained in form of a complete binary tree, because of this fact the heap can be represented in the form of an array. To keep the tree complete and shallow, while inserting a new element insert it in the leftmost vacant position in the last level i.e., at the end of our array. Similarly, while extracting maximum replace the root with the last leaf at the last level i.e., the last element of the array. Below is the illustration of the same:
Below is the program to implement Priority Queue using Binary Heap:
C++
// C++ code to implement priority-queue// using array implementation of// binary heap#include <bits/stdc++.h>using namespace std;int H[50];int size = -1;// Function to return the index of the// parent node of a given nodeint parent(int i){ return (i - 1) / 2;}// Function to return the index of the// left child of the given nodeint leftChild(int i){ return ((2 * i) + 1);}// Function to return the index of the// right child of the given nodeint rightChild(int i){ return ((2 * i) + 2);}// Function to shift up the node in order// to maintain the heap propertyvoid shiftUp(int i){ while (i > 0 && H[parent(i)] < H[i]) { // Swap parent and current node swap(H[parent(i)], H[i]); // Update i to parent of i i = parent(i); }}// Function to shift down the node in// order to maintain the heap propertyvoid shiftDown(int i){ int maxIndex = i; // Left Child int l = leftChild(i); if (l <= size && H[l] > H[maxIndex]) { maxIndex = l; } // Right Child int r = rightChild(i); if (r <= size && H[r] > H[maxIndex]) { maxIndex = r; } // If i not same as maxIndex if (i != maxIndex) { swap(H[i], H[maxIndex]); shiftDown(maxIndex); }}// Function to insert a new element// in the Binary Heapvoid insert(int p){ size = size + 1; H[size] = p; // Shift Up to maintain heap property shiftUp(size);}// Function to extract the element with// maximum priorityint extractMax(){ int result = H[0]; // Replace the value at the root // with the last leaf H[0] = H[size]; size = size - 1; // Shift down the replaced element // to maintain the heap property shiftDown(0); return result;}// Function to change the priority// of an elementvoid changePriority(int i, int p){ int oldp = H[i]; H[i] = p; if (p > oldp) { shiftUp(i); } else { shiftDown(i); }}// Function to get value of the current// maximum elementint getMax(){ return H[0];}// Function to remove the element// located at given indexvoid remove(int i){ H[i] = getMax() + 1; // Shift the node to the root // of the heap shiftUp(i); // Extract the node extractMax();}// Driver Codeint main(){ /* 45 / \ 31 14 / \ / \ 13 20 7 11 / \ 12 7 Create a priority queue shown in example in a binary max heap form. Queue will be represented in the form of array as: 45 31 14 13 20 7 11 12 7 */ // Insert the element to the // priority queue insert(45); insert(20); insert(14); insert(12); insert(31); insert(7); insert(11); insert(13); insert(7); int i = 0; // Priority queue before extracting max cout << "Priority Queue : "; while (i <= size) { cout << H[i] << " "; i++; } cout << "\n"; // Node with maximum priority cout << "Node with maximum priority : " << extractMax() << "\n"; // Priority queue after extracting max cout << "Priority queue after " << "extracting maximum : "; int j = 0; while (j <= size) { cout << H[j] << " "; j++; } cout << "\n"; // Change the priority of element // present at index 2 to 49 changePriority(2, 49); cout << "Priority queue after " << "priority change : "; int k = 0; while (k <= size) { cout << H[k] << " "; k++; } cout << "\n"; // Remove element at index 3 remove(3); cout << "Priority queue after " << "removing the element : "; int l = 0; while (l <= size) { cout << H[l] << " "; l++; } return 0;} |
Java
// Java code to implement // priority-queue using // array implementation of// binary heapimport java.util.*;class GFG{static int []H = new int[50];static int size = -1;// Function to return the index of the// parent node of a given nodestatic int parent(int i){ return (i - 1) / 2;}// Function to return the index of the// left child of the given nodestatic int leftChild(int i){ return ((2 * i) + 1);}// Function to return the index of the// right child of the given nodestatic int rightChild(int i){ return ((2 * i) + 2);}// Function to shift up the // node in order to maintain // the heap propertystatic void shiftUp(int i){ while (i > 0 && H[parent(i)] < H[i]) { // Swap parent and current node swap(parent(i), i); // Update i to parent of i i = parent(i); }}// Function to shift down the node in// order to maintain the heap propertystatic void shiftDown(int i){ int maxIndex = i; // Left Child int l = leftChild(i); if (l <= size && H[l] > H[maxIndex]) { maxIndex = l; } // Right Child int r = rightChild(i); if (r <= size && H[r] > H[maxIndex]) { maxIndex = r; } // If i not same as maxIndex if (i != maxIndex) { swap(i, maxIndex); shiftDown(maxIndex); }}// Function to insert a // new element in // the Binary Heapstatic void insert(int p){ size = size + 1; H[size] = p; // Shift Up to maintain // heap property shiftUp(size);}// Function to extract // the element with// maximum prioritystatic int extractMax(){ int result = H[0]; // Replace the value // at the root with // the last leaf H[0] = H[size]; size = size - 1; // Shift down the replaced // element to maintain the // heap property shiftDown(0); return result;}// Function to change the priority// of an elementstatic void changePriority(int i, int p){ int oldp = H[i]; H[i] = p; if (p > oldp) { shiftUp(i); } else { shiftDown(i); }}// Function to get value of // the current maximum elementstatic int getMax(){ return H[0];}// Function to remove the element// located at given indexstatic void remove(int i){ H[i] = getMax() + 1; // Shift the node to the root // of the heap shiftUp(i); // Extract the node extractMax();} static void swap(int i, int j){ int temp= H[i]; H[i] = H[j]; H[j] = temp;}// Driver Codepublic static void main(String[] args){ /* 45 / \ 31 14 / \ / \ 13 20 7 11 / \ 12 7 Create a priority queue shown in example in a binary max heap form. Queue will be represented in the form of array as: 45 31 14 13 20 7 11 12 7 */ // Insert the element to the // priority queue insert(45); insert(20); insert(14); insert(12); insert(31); insert(7); insert(11); insert(13); insert(7); int i = 0; // Priority queue before extracting max System.out.print("Priority Queue : "); while (i <= size) { System.out.print(H[i] + " "); i++; } System.out.print("\n"); // Node with maximum priority System.out.print("Node with maximum priority : " + extractMax() + "\n"); // Priority queue after extracting max System.out.print("Priority queue after " + "extracting maximum : "); int j = 0; while (j <= size) { System.out.print(H[j] + " "); j++; } System.out.print("\n"); // Change the priority of element // present at index 2 to 49 changePriority(2, 49); System.out.print("Priority queue after " + "priority change : "); int k = 0; while (k <= size) { System.out.print(H[k] + " "); k++; } System.out.print("\n"); // Remove element at index 3 remove(3); System.out.print("Priority queue after " + "removing the element : "); int l = 0; while (l <= size) { System.out.print(H[l] + " "); l++; }}}// This code is contributed by 29AjayKumar |
Python3
# Python3 code to implement priority-queue # using array implementation of # binary heapH = [0]*50size = -1 # Function to return the index of the # parent node of a given node def parent(i) : return (i - 1) // 2 # Function to return the index of the # left child of the given node def leftChild(i) : return ((2 * i) + 1) # Function to return the index of the # right child of the given node def rightChild(i) : return ((2 * i) + 2) # Function to shift up the # node in order to maintain # the heap property def shiftUp(i) : while (i > 0 and H[parent(i)] < H[i]) : # Swap parent and current node swap(parent(i), i) # Update i to parent of i i = parent(i) # Function to shift down the node in # order to maintain the heap property def shiftDown(i) : maxIndex = i # Left Child l = leftChild(i) if (l <= size and H[l] > H[maxIndex]) : maxIndex = l # Right Child r = rightChild(i) if (r <= size and H[r] > H[maxIndex]) : maxIndex = r # If i not same as maxIndex if (i != maxIndex) : swap(i, maxIndex) shiftDown(maxIndex) # Function to insert a # new element in # the Binary Heap def insert(p) : global size size = size + 1 H[size] = p # Shift Up to maintain # heap property shiftUp(size) # Function to extract # the element with # maximum priority def extractMax() : global size result = H[0] # Replace the value # at the root with # the last leaf H[0] = H[size] size = size - 1 # Shift down the replaced # element to maintain the # heap property shiftDown(0) return result # Function to change the priority # of an element def changePriority(i,p) : oldp = H[i] H[i] = p if (p > oldp) : shiftUp(i) else : shiftDown(i) # Function to get value of # the current maximum element def getMax() : return H[0] # Function to remove the element # located at given index def Remove(i) : H[i] = getMax() + 1 # Shift the node to the root # of the heap shiftUp(i) # Extract the node extractMax() def swap(i, j) : temp = H[i] H[i] = H[j] H[j] = temp # Insert the element to the # priority queue insert(45) insert(20) insert(14) insert(12) insert(31) insert(7) insert(11) insert(13) insert(7) i = 0 # Priority queue before extracting max print("Priority Queue : ", end = "") while (i <= size) : print(H[i], end = " ") i += 1 print() # Node with maximum priority print("Node with maximum priority :" , extractMax()) # Priority queue after extracting max print("Priority queue after extracting maximum : ", end = "") j = 0while (j <= size) : print(H[j], end = " ") j += 1 print() # Change the priority of element # present at index 2 to 49 changePriority(2, 49) print("Priority queue after priority change : ", end = "") k = 0while (k <= size) : print(H[k], end = " ") k += 1 print() # Remove element at index 3 Remove(3)print("Priority queue after removing the element : ", end = "") l = 0while (l <= size) : print(H[l], end = " ") l += 1 # This code is contributed by divyeshrabadiya07. |
C#
// C# code to implement priority-queue// using array implementation of// binary heapusing System;class GFG{static int []H = new int[50];static int size = -1;// Function to return the index of the// parent node of a given nodestatic int parent(int i){ return (i - 1) / 2;}// Function to return the index of the// left child of the given nodestatic int leftChild(int i){ return ((2 * i) + 1);}// Function to return the index of the// right child of the given nodestatic int rightChild(int i){ return ((2 * i) + 2);}// Function to shift up the // node in order to maintain // the heap propertystatic void shiftUp(int i){ while (i > 0 && H[parent(i)] < H[i]) { // Swap parent and current node swap(parent(i), i); // Update i to parent of i i = parent(i); }}// Function to shift down the node in// order to maintain the heap propertystatic void shiftDown(int i){ int maxIndex = i; // Left Child int l = leftChild(i); if (l <= size && H[l] > H[maxIndex]) { maxIndex = l; } // Right Child int r = rightChild(i); if (r <= size && H[r] > H[maxIndex]) { maxIndex = r; } // If i not same as maxIndex if (i != maxIndex) { swap(i, maxIndex); shiftDown(maxIndex); }}// Function to insert a // new element in // the Binary Heapstatic void insert(int p){ size = size + 1; H[size] = p; // Shift Up to maintain // heap property shiftUp(size);}// Function to extract // the element with// maximum prioritystatic int extractMax(){ int result = H[0]; // Replace the value // at the root with // the last leaf H[0] = H[size]; size = size - 1; // Shift down the replaced // element to maintain the // heap property shiftDown(0); return result;}// Function to change the priority// of an elementstatic void changePriority(int i, int p){ int oldp = H[i]; H[i] = p; if (p > oldp) { shiftUp(i); } else { shiftDown(i); }}// Function to get value of // the current maximum elementstatic int getMax(){ return H[0];}// Function to remove the element// located at given indexstatic void Remove(int i){ H[i] = getMax() + 1; // Shift the node to the root // of the heap shiftUp(i); // Extract the node extractMax();}static void swap(int i, int j){ int temp = H[i]; H[i] = H[j]; H[j] = temp;}// Driver Codepublic static void Main(String[] args){/* 45 / \ 31 14 / \ / \ 13 20 7 11 / \ 12 7 Create a priority queue shown in example in a binary max heap form. Queue will be represented in the form of array as: 45 31 14 13 20 7 11 12 7 */ // Insert the element to the // priority queue insert(45); insert(20); insert(14); insert(12); insert(31); insert(7); insert(11); insert(13); insert(7); int i = 0; // Priority queue before extracting max Console.Write("Priority Queue : "); while (i <= size) { Console.Write(H[i] + " "); i++; } Console.Write("\n"); // Node with maximum priority Console.Write("Node with maximum priority : " + extractMax() + "\n"); // Priority queue after extracting max Console.Write("Priority queue after " + "extracting maximum : "); int j = 0; while (j <= size) { Console.Write(H[j] + " "); j++; } Console.Write("\n"); // Change the priority of element // present at index 2 to 49 changePriority(2, 49); Console.Write("Priority queue after " + "priority change : "); int k = 0; while (k <= size) { Console.Write(H[k] + " "); k++; } Console.Write("\n"); // Remove element at index 3 Remove(3); Console.Write("Priority queue after " + "removing the element : "); int l = 0; while (l <= size) { Console.Write(H[l] + " "); l++; }}}// This code is contributed by Amit Katiyar |
Javascript
<script>// Javascript code to implement priority-queue// using array implementation of// binary heapvar H = Array(50).fill(0);var size = -1;// Function to return the index of the// parent node of a given nodefunction parent(i){ return parseInt((i - 1) / 2);}// Function to return the index of the// left child of the given nodefunction leftChild(i){ return parseInt((2 * i) + 1);}// Function to return the index of the// right child of the given nodefunction rightChild(i){ return parseInt((2 * i) + 2);}// Function to shift up the node in order// to maintain the heap propertyfunction shiftUp( i){ while (i > 0 && H[parent(i)] < H[i]) { // Swap parent and current node swap(parent(i), i); // Update i to parent of i i = parent(i); }}function swap(i, j){ var temp = H[i]; H[i] = H[j]; H[j] = temp;}// Function to shift down the node in// order to maintain the heap propertyfunction shiftDown( i){ var maxIndex = i; // Left Child var l = leftChild(i); if (l <= size && H[l] > H[maxIndex]) { maxIndex = l; } // Right Child var r = rightChild(i); if (r <= size && H[r] > H[maxIndex]) { maxIndex = r; } // If i not same as maxIndex if (i != maxIndex) { swap(i, maxIndex); shiftDown(maxIndex); }}// Function to insert a new element// in the Binary Heapfunction insert( p){ size = size + 1; H[size] = p; // Shift Up to maintain heap property shiftUp(size);}// Function to extract the element with// maximum priorityfunction extractMax(){ var result = H[0]; // Replace the value at the root // with the last leaf H[0] = H[size]; size = size - 1; // Shift down the replaced element // to maintain the heap property shiftDown(0); return result;}// Function to change the priority// of an elementfunction changePriority(i, p){ var oldp = H[i]; H[i] = p; if (p > oldp) { shiftUp(i); } else { shiftDown(i); }}// Function to get value of the current// maximum elementfunction getMax(){ return H[0];}// Function to remove the element// located at given indexfunction remove(i){ H[i] = getMax() + 1; // Shift the node to the root // of the heap shiftUp(i); // Extract the node extractMax();}// Driver Code/* 45 / \ 31 14 / \ / \ 13 20 7 11 / \ 12 7Create a priority queue shown in example in a binary max heap form.Queue will be represented in theform of array as:45 31 14 13 20 7 11 12 7 */// Insert the element to the// priority queueinsert(45);insert(20);insert(14);insert(12);insert(31);insert(7);insert(11);insert(13);insert(7);var i = 0;// Priority queue before extracting maxdocument.write( "Priority Queue : ");while (i <= size) { document.write( H[i] + " "); i++;}document.write( "<br>");// Node with maximum prioritydocument.write( "Node with maximum priority : " + extractMax() + "<br>");// Priority queue after extracting maxdocument.write( "Priority queue after " + "extracting maximum : ");var j = 0;while (j <= size) { document.write( H[j] + " "); j++;}document.write( "<br>");// Change the priority of element// present at index 2 to 49changePriority(2, 49);document.write( "Priority queue after " + "priority change : ");var k = 0;while (k <= size) { document.write( H[k] + " "); k++;}document.write( "<br>");// Remove element at index 3remove(3);document.write( "Priority queue after " + "removing the element : ");var l = 0;while (l <= size) { document.write( H[l] + " "); l++;}// This code is contributed by noob2000.</script> |
Output
Priority Queue : 45 31 14 13 20 7 11 12 7 Node with maximum priority : 45 Priority queue after extracting maximum : 31 20 14 13 7 7 11 12 Priority queue after priority change : 49 20 31 13 7 7 11 12 Priority queue after removing the element : 49 20 31 12 7 7 11
Time Complexity: The time complexity of all the operation is O(log N) except for GetMax() which has time complexity of O(1).
Auxiliary Space: O(N)
Method – 2
below is also a valid method to implement this priority queue using a max heap. this code is a generic method to implement a priority queue using a class-based structure. here in the implementation part, we are using a generic template (not a specific data type) so this implementation works for all data types.
C++
#include <iostream>#include <vector>using namespace std;// Priority queue implementation in C++template<typename T>class PriorityQueue { private: vector<T> data; public: // Implementing Priority Queue using inbuilt available vector in C++ PriorityQueue() {} // Element Inserting function void Enqueue(T item) { // item Insertion data.push_back(item); int ci = data.size() - 1; // Re-structure heap(Max Heap) so that after // addition max element will lie on top of pq while (ci > 0) { int pi = (ci - 1) / 2; if (data[ci] <= data[pi]) break; T tmp = data[ci]; data[ci] = data[pi]; data[pi] = tmp; ci = pi; } } T Dequeue() { // deleting top element of pq int li = data.size() - 1; T frontItem = data[0]; data[0] = data[li]; data.pop_back(); --li; int pi = 0; // Re-structure heap(Max Heap) so that after // deletion max element will lie on top of pq while (true) { int ci = pi * 2 + 1; if (ci > li) break; int rc = ci + 1; if (rc <= li && data[rc] < data[ci]) ci = rc; if (data[pi] >= data[ci]) break; T tmp = data[pi]; data[pi] = data[ci]; data[ci] = tmp; pi = ci; } return frontItem; } // Function which returns peek element T Peek() { T frontItem = data[0]; return frontItem; } int Count() { return data.size(); }};// Driver codeint main(){ // Basic functionality sample of Priority Queue // Creating priority queue which contains int in it PriorityQueue<int> pq; // Insert element 1 in pq pq.Enqueue(1); cout << "Size of pq is : " << pq.Count() << " and Peek Element is : " << pq.Peek() << endl; // Insert element 10 and -8 in pq pq.Enqueue(10); pq.Enqueue(-8); cout << "Size of pq is : " << pq.Count() << " and Peek Element is : " << pq.Peek() << endl; // Delete element from pq pq.Dequeue(); cout << "Size of pq is : " << pq.Count() << " and Peek Element is : " << pq.Peek() << endl; // Delete element from pq pq.Dequeue(); cout << "Size of pq is : " << pq.Count() << " and Peek Element is : " << pq.Peek() << endl; // Insert element 25 in pq pq.Enqueue(25); cout << "Size of pq is : " << pq.Count() << " and Peek Element is : " << pq.Peek() << endl; return 0;} |
Java
import java.util.ArrayList;import java.util.List;public class GFG { // Priority queue implementation in Javastatic class PriorityQueue<T extends Comparable<T>> { private List<T> data; // Implementing Priority Queue using inbuilt available List in Java public PriorityQueue() { this.data = new ArrayList<T>(); } // Element Inserting function public void Enqueue(T item) { // item Insertion data.add(item); int ci = data.size() - 1; // Re-structure heap(Max Heap) so that after addition max element will lie on top of pq while (ci > 0) { int pi = (ci - 1) / 2; if (data.get(ci).compareTo(data.get(pi)) <= 0) break; T tmp = data.get(ci); data.set(ci, data.get(pi)); data.set(pi, tmp); ci = pi; } } public T Dequeue() { // deleting top element of pq int li = data.size() - 1; T frontItem = data.get(0); data.set(0, data.get(li)); data.remove(li); --li; int pi = 0; // Re-structure heap(Max Heap) so that after deletion max element will lie on top of pq while (true) { int ci = pi * 2 + 1; if (ci > li) break; int rc = ci + 1; if (rc <= li && data.get(rc).compareTo(data.get(ci)) < 0) ci = rc; if (data.get(pi).compareTo(data.get(ci)) >= 0) break; T tmp = data.get(pi); data.set(pi, data.get(ci)); data.set(ci, tmp); pi = ci; } return frontItem; } // Function which returns peek element public T Peek() { T frontItem = data.get(0); return frontItem; } public int Count() { return data.size(); }}// Driver codepublic static void main(String[] args) { // Basic functionality sample of Priority Queue // Creating priority queue which contains int in it PriorityQueue<Integer> pq = new PriorityQueue<Integer>(); // Insert element 1 in pq pq.Enqueue(1); System.out.println("Size of pq is : " + pq.Count() + " and Peek Element is : " + pq.Peek()); // Insert element 10 and -8 in pq pq.Enqueue(10); pq.Enqueue(-8); System.out.println("Size of pq is : " + pq.Count() + " and Peek Element is : " + pq.Peek()); // Delete element from pq pq.Dequeue(); System.out.println("Size of pq is : " + pq.Count() + " and Peek Element is : " + pq.Peek()); // Delete element from pq pq.Dequeue(); System.out.println("Size of pq is : " + pq.Count() + " and Peek Element is : " + pq.Peek()); // Insert element 25 in pq pq.Enqueue(25); System.out.println("Size of pq is : " + pq.Count() + " and Peek Element is : " + pq.Peek());}} |
Python3
import heapqclass PriorityQueue: def __init__(self): self._queue = [] self._index = 0 def enqueue(self, item, priority): heapq.heappush(self._queue, (priority, self._index, item)) self._index += 1 def dequeue(self): return heapq.heappop(self._queue)[-1] def peek(self): return self._queue[0][-1] def count(self): return len(self._queue) # Driver codeif __name__ == "__main__": # Basic functionality sample of Priority Queue # Creating priority queue which contains int in it pq = PriorityQueue() # Insert element 1 in pq pq.enqueue(1, 1) print("Size of pq is : ", pq.count(), " and Peek Element is : ", pq.peek()) # Insert element 10 and -8 in pq pq.enqueue(10, 2) pq.enqueue(-8, 3) print("Size of pq is : ", pq.count(), " and Peek Element is : ", pq.peek()) # Delete element from pq pq.dequeue() print("Size of pq is : ", pq.count(), " and Peek Element is : ", pq.peek()) # Delete element from pq pq.dequeue() print("Size of pq is : ", pq.count(), " and Peek Element is : ", pq.peek()) # Insert element 25 in pq pq.enqueue(25, 4) print("Size of pq is : ", pq.count(), " and Peek Element is : ", pq.peek()) |
C#
using System;using System.Collections.Generic;class GFG { // Priority queue implementation in C# class PriorityQueue<T> where T : IComparable<T> { private List<T> data; // Implemeting Priority Queue using inbuilt available List in C# public PriorityQueue() { this.data = new List<T>(); } // Element Inserting function public void Enqueue(T item) { // item Insertion data.Add(item); int ci = data.Count - 1; // re-structure heap(Max Heap) so that after addition max element will lie on top of pq while (ci > 0) { int pi = (ci - 1) / 2; if (data[ci].CompareTo(data[pi]) <= 0) break; T tmp = data[ci]; data[ci] = data[pi]; data[pi] = tmp; ci = pi; } } public T Dequeue() { // deleting top element of pq int li = data.Count - 1; T frontItem = data[0]; data[0] = data[li]; data.RemoveAt(li); --li; int pi = 0; // re-structure heap(Max Heap) so that after deletion max element will lie on top of pq while (true) { int ci = pi * 2 + 1; if (ci > li) break; int rc = ci + 1; if (rc <= li && data[rc].CompareTo(data[ci]) < 0) ci = rc; if (data[pi].CompareTo(data[ci]) >= 0) break; T tmp = data[pi]; data[pi] = data[ci]; data[ci] = tmp; pi = ci; } return frontItem; } // function which returns peek element public T Peek() { T frontItem = data[0]; return frontItem; } public int Count() { return data.Count; } } // Driver code public static void Main(string[] args) { // basic functionality sample of Priority Queue // creating priority queue which contains int in it var pq = new PriorityQueue<int>(); // Insert element 1 in pq pq.Enqueue(1); Console.WriteLine("Size of pq is : " + pq.Count() + " and Peek Element is : " + pq.Peek()); // Insert element 10 and -8 in pq pq.Enqueue(10); pq.Enqueue(-8); Console.WriteLine("Size of pq is : " + pq.Count() + " and Peek Element is : " + pq.Peek()); // Delete element from pq pq.Dequeue(); Console.WriteLine("Size of pq is : " + pq.Count() + " and Peek Element is : " + pq.Peek()); // Delete element from pq pq.Dequeue(); Console.WriteLine("Size of pq is : " + pq.Count() + " and Peek Element is : " + pq.Peek()); // Insert element 25 in pq pq.Enqueue(25); Console.WriteLine("Size of pq is : " + pq.Count() + " and Peek Element is : " + pq.Peek()); }} |
Javascript
// Priority queue implementation in JavaScriptclass PriorityQueue { constructor() { this.data = []; } // Element Inserting function enqueue(item) { // item Insertion this.data.push(item); let ci = this.data.length - 1; // Re-structure heap(Max Heap) so that after // addition max element will lie on top of pq while (ci > 0) { let pi = Math.floor((ci - 1) / 2); if (this.data[ci] <= this.data[pi]) break; let tmp = this.data[ci]; this.data[ci] = this.data[pi]; this.data[pi] = tmp; ci = pi; } } dequeue() { // deleting top element of pq let li = this.data.length - 1; let frontItem = this.data[0]; this.data[0] = this.data[li]; this.data.pop(); --li; let pi = 0; // Re-structure heap(Max Heap) so that after // deletion max element will lie on top of pq while (true) { let ci = pi * 2 + 1; if (ci > li) break; let rc = ci + 1; if (rc <= li && this.data[rc] < this.data[ci]) ci = rc; if (this.data[pi] >= this.data[ci]) break; let tmp = this.data[pi]; this.data[pi] = this.data[ci]; this.data[ci] = tmp; pi = ci; } return frontItem; } // Function which returns peek element peek() { let frontItem = this.data[0]; return frontItem; } count() { return this.data.length; }}// Driver codelet pq = new PriorityQueue();// Basic functionality sample of Priority Queue// Insert element 1 in pqpq.enqueue(1);console.log(`Size of pq is: ${pq.count()} and Peek Element is: ${pq.peek()}`);// Insert element 10 and -8 in pqpq.enqueue(10);pq.enqueue(-8);console.log(`Size of pq is: ${pq.count()} and Peek Element is: ${pq.peek()}`);// Delete element from pqpq.dequeue();console.log(`Size of pq is: ${pq.count()} and Peek Element is: ${pq.peek()}`);// Delete element from pqpq.dequeue();console.log(`Size of pq is: ${pq.count()} and Peek Element is: ${pq.peek()}`);// Insert element 25 in pqpq.enqueue(25);console.log(`Size of pq is: ${pq.count()} and Peek Element is: ${pq.peek()}`); |
Output
Size of pq is : 1 and Peek Element is : 1 Size of pq is : 3 and Peek Element is : 10 Size of pq is : 2 and Peek Element is : 1 Size of pq is : 1 and Peek Element is : -8 Size of pq is : 2 and Peek Element is : 25
Time Complexity: O(log(n)) for EnQueue operation and O(log(n)) for Dequeue operation
Space complexity: O(n) (as we need n size array for implementation)
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