A priority queue is a data structure that stores elements with associated priorities. In a priority queue, elements are dequeued in order of their priority, with the highest priority elements being removed first. It is commonly used in algorithms like Dijkstra's for shortest path and in real-time scheduling tasks. Priority queues can be implemented using arrays, heaps, or linked lists.

Examples:

Input: Values = 4 (priority = 1), 5 (priority = 2), 6 (priority = 3), 7 (priority = 0)
Output: 7 4 5 6 (In descending order of priority, starting from the highest priority).
Explanation: The elements are stored in an array sorted by priority.
When you perform a dequeue(), the highest priority element (7 with priority 0) is removed first.
The next highest priority element (4 with priority 1) is then at the front of the array, followed by the others.

Input: Values = 10 (priority = 3), 3 (priority = 1), 8 (priority = 2), 1 (priority = 0)
Output: 1 3 8 10 (In descending order of priority)
Explanation: The array will be sorted by priority: 1 (highest priority) comes first, followed by 3, 8, and 10. After calling dequeue(), the element with the highest priority, 1, is removed first, then 3, followed by 8, and finally 10.

Priority Queue using Array

A priority queue stores elements where each element has a priority associated with it. In an array-based priority queue, elements are ordered so that the highest priority element is always at the front of the array. The array is sorted according to the priority values, with the element with the lowest priority value (highest priority) placed at the front.

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Operations:

1. enqueue(value, priority): This function inserts a new element into the queue by adding it to the end of the array. The element is appended without any sorting. The queue remains unsorted until the peek() or dequeue() function is called, which scans the entire array to find and handle the element with the highest priority based on the lowest priority value.

2. dequeue(): This function removes and returns the element with the highest priority (i.e., the element with the lowest priority value). It locates the element with the highest priority using the peek() function, then removes it by shifting the remaining elements.

3. peek(): This function returns the element with the highest priority (the element with the smallest priority value) without removing it from the queue. It scans the array to find the element with the lowest priority value and returns its index.

#include <bits/stdc++.h>
using namespace std;

struct Item {
    int val, priority;
};

// To store priority queue items 
vector<Item> pq;

// Function to insert element in priority queue
void enqueue(int val, int priority) {
    pq.push_back({val, priority});
}

// Function to get index of element with
// highest priority
int peek() {
    int ind = -1, maxPriority = INT_MIN;
    for (int i = 0; i < pq.size(); i++) {
        
        // Update index if a higher priority 
        // is found
        if (pq[i].priority > maxPriority || 
           (pq[i].priority == maxPriority && pq[i].val > pq[ind].val)) {
            maxPriority = pq[i].priority;
            ind = i;
        }
    }
    return ind;
}

// Function to remove the element with highest priority
void dequeue() {
    int ind = peek(); // Get index of highest priority element
    if (ind != -1) pq.erase(pq.begin() + ind);
}

int main() {
    enqueue(10, 2);
    enqueue(14, 4);
    enqueue(16, 4);
    enqueue(12, 3);

    cout << pq[peek()].val << endl; 
    dequeue();

    cout << pq[peek()].val << endl; 
    dequeue();

    cout << pq[peek()].val << endl;
    return 0;
}

#include <stdio.h>
#include <limits.h>

struct item {
    int value, priority;
};

struct item pr[100000];
int size = -1;

// Function to insert element in priority queue
void enqueue(int value, int priority) {
    pr[++size] = (struct item){value, priority};
}

// Function to get index of element with highest priority
int peek() {
    int highestPriority = INT_MIN, ind = -1;
    for (int i = 0; i <= size; i++) {
        if (pr[i].priority > highestPriority || 
           (pr[i].priority == highestPriority && pr[i].value > pr[ind].value)) {
            highestPriority = pr[i].priority;
            ind = i;
        }
    }
    return ind;
}

// Function to remove the element with highest priority
void dequeue() {
    int ind = peek();
    for (int i = ind; i < size; i++) {
        pr[i] = pr[i + 1];
    }
    size--;
}

int main() {
    enqueue(10, 2);
    enqueue(14, 4);
    enqueue(16, 4);
    enqueue(12, 3);

    printf("%d\n", pr[peek()].value);
    dequeue();

    printf("%d\n", pr[peek()].value);
    dequeue();

    printf("%d\n", pr[peek()].value);
    return 0;
}

class Item {
    int val, priority;

    Item(int val, int priority) {
        this.val = val;
        this.priority = priority;
    }
}

class PriorityQueue {
    Item[] pq;
    int size;

    PriorityQueue(int capacity) {
        pq = new Item[capacity];
        size = 0;
    }

    // Function to insert element in priority queue
    void enqueue(int val, int priority) {
        pq[size++] = new Item(val, priority);
    }

    // Function to get index of element with highest priority
    int peek() {
        int ind = -1, maxPriority = Integer.MIN_VALUE;
        for (int i = 0; i < size; i++) {
            
            // Update index if a higher priority is found
            if (pq[i].priority > maxPriority || 
               (pq[i].priority == maxPriority && pq[i].val > pq[ind].val)) {
                maxPriority = pq[i].priority;
                ind = i;
            }
        }
        return ind;
    }

    // Function to remove the element with highest priority
    void dequeue() {
        // Get index of highest priority element
        int ind = peek(); 
        if (ind != -1) {
            pq[ind] = pq[size - 1];
            size--;
        }
    }

    public static void main(String[] args) {
        PriorityQueue pq = new PriorityQueue(10);
        pq.enqueue(10, 2);
        pq.enqueue(14, 4);
        pq.enqueue(16, 4);
        pq.enqueue(12, 3);

        System.out.println(pq.pq[pq.peek()].val);
        pq.dequeue();

        System.out.println(pq.pq[pq.peek()].val);
        pq.dequeue();

        System.out.println(pq.pq[pq.peek()].val);
    }
}

class Item:
    def __init__(self, val, priority):
        self.val = val
        self.priority = priority

# To store priority queue items 
pq = []

# Function to insert element in priority queue
def enqueue(val, priority):
    pq.append(Item(val, priority))

# Function to get index of element with
# highest priority
def peek():
    ind = -1
    maxPriority = float('-inf')
    for i in range(len(pq)):
        # Update index if a higher priority 
        # is found
        if pq[i].priority > maxPriority or (
           pq[i].priority == maxPriority and pq[i].val > pq[ind].val):
            maxPriority = pq[i].priority
            ind = i
    return ind

# Function to remove the element with highest priority
def dequeue():
    
    # Get index of highest priority element
    ind = peek() 
    if ind != -1:
        pq.pop(ind)

if __name__ == '__main__':
    enqueue(10, 2)
    enqueue(14, 4)
    enqueue(16, 4)
    enqueue(12, 3)

    print(pq[peek()].val)
    dequeue()

    print(pq[peek()].val)
    dequeue()

    print(pq[peek()].val)

using System;
using System.Collections.Generic;

class Item {
    public int val, priority;

    public Item(int val, int priority) {
        this.val = val;
        this.priority = priority;
    }
}

// To store priority queue items 
List<Item> pq = new List<Item>();

// Function to insert element in priority queue
void enqueue(int val, int priority) {
    pq.Add(new Item(val, priority));
}

// Function to get index of element with
// highest priority
int peek() {
    int ind = -1;
    int maxPriority = int.MinValue;
    for (int i = 0; i < pq.Count; i++) {
        
        // Update index if a higher priority 
        // is found
        if (pq[i].priority > maxPriority || 
           (pq[i].priority == maxPriority && pq[i].val > pq[ind].val)) {
            maxPriority = pq[i].priority;
            ind = i;
        }
    }
    return ind;
}

// Function to remove the element with highest priority
void dequeue() {
    
    // Get index of highest priority element
    int ind = peek();
    if (ind != -1) pq.RemoveAt(ind);
}

class GfG {
    static void Main() {
        enqueue(10, 2);
        enqueue(14, 4);
        enqueue(16, 4);
        enqueue(12, 3);

        Console.WriteLine(pq[peek()].val);
        dequeue();

        Console.WriteLine(pq[peek()].val);
        dequeue();

        Console.WriteLine(pq[peek()].val);
    }
}

class Item {
    constructor(val, priority) {
        this.val = val;
        this.priority = priority;
    }
}

// To store priority queue items 
let pq = [];

// Function to insert element in priority queue
function enqueue(val, priority) {
    pq.push(new Item(val, priority));
}

// Function to get index of element with
// highest priority
function peek() {
    let ind = -1;
    let maxPriority = Number.NEGATIVE_INFINITY;
    for (let i = 0; i < pq.length; i++) {
        // Update index if a higher priority 
        // is found
        if (pq[i].priority > maxPriority || 
           (pq[i].priority === maxPriority && pq[i].val > pq[ind].val)) {
            maxPriority = pq[i].priority;
            ind = i;
        }
    }
    return ind;
}

// Function to remove the element with highest priority
function dequeue() {
    
    // Get index of highest priority element
    let ind = peek(); 
    
    if (ind !== -1) pq.splice(ind, 1);
}

enqueue(10, 2);
enqueue(14, 4);
enqueue(16, 4);
enqueue(12, 3);

console.log(pq[peek()].val);
dequeue();

console.log(pq[peek()].val);
dequeue();

console.log(pq[peek()].val);

16
14
12

Time Complexity:

• enqueue(value, priority): O(1) (since it's just an insertion).
• peek(): O(n) (iterating through the entire array).
• dequeue(): O(n) (finding the highest-priority element and shifting elements).

Auxiliary Space: The auxiliary space complexity for this program is O(1)

Related Articles:

What is Priority Queue | Introduction to Priority Queue
Priority Queue using Linked List
Priority Queue using Binary Heap
Why is Binary Heap Preferred over BST for Priority Queue ?