Implement Priority Queue using Linked Lists. The Linked List should be so created so that the highest priority ( priority is assigned from 0 to n-1 where n is the number of elements, where 0 means the highest priority and n-1 being the least ) element is always at the head of the list. The list is arranged in descending order of elements based on their priority. The Priority Queue should have the below functions

• push(): This function is used to insert a new data into the queue.
• pop(): This function removes the element with the highest priority from the queue.
• peek() / top(): This function is used to get the highest priority element in the queue without removing it from the queue.

Examples:

Input: Values = 4 (priority = 1), 5 (priority = 2), 6 (priority = 3), 7 (priority = 0)
Output: 7 4 5 6
Explanation: Values get peeked and popped according to their priority in descending order.

This approach manages a priority queue using a linked list. The PUSH operation inserts nodes in order of priority, ensuring the highest priority node is always at the head. The POP operation removes the highest priority node, while PEEK returns the data of the highest priority node without removing it.

Follow these steps to solve the problem

PUSH(HEAD, DATA, PRIORITY):

• Step 1: Create new node with DATA and PRIORITY 
• Step 2: Check if HEAD has lower priority. If true follow Steps 3-4 and end. Else goto Step 5. 
• Step 3: NEW -> NEXT = HEAD 
• Step 4: HEAD = NEW 
• Step 5: Set TEMP to head of the list 
• Step 6: While TEMP -> NEXT != NULL and TEMP -> NEXT -> PRIORITY > PRIORITY 
• Step 7: TEMP = TEMP -> NEXT 
  [END OF LOOP] 
• Step 8: NEW -> NEXT = TEMP -> NEXT 
• Step 9: TEMP -> NEXT = NEW 
• Step 10: End

POP(HEAD):

• Step 1: Set the head of the list to the next node in the list. HEAD = HEAD -> NEXT. 
• Step 2: Free the node at the head of the list 
• Step 3: End

PEEK(HEAD): 

• Step 1: Return HEAD -> DATA 
• Step 2: End

// C++ code to implement Priority Queue 
// using Linked List

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

struct Node {
    int data;
    int priority;
    Node* next;
  
    Node(int x, int p) {
        data = x;
        priority = p;
        next = NULL;
    }
};

// Return the value at head
int peek(Node* head) {

    // Return the data of the node at the head of the list
    return head->data;
}

// Removes the element with the highest priority from the list
Node* pop(Node* head) {

    // Store the current head node in a temporary variable
    Node* temp = head;

    // Move the head to the next node in the list
    head = head->next;

    // Free the memory of the removed head node
    delete temp;

    // Return the new head of the list
    return head;
}

// Function to push according to priority
Node* push(Node* head, int d, int p) {
    Node* start = head;

    // Create new Node with the given data and priority
    Node* temp = new Node(d, p);

    // Special Case: Insert the new node before the head
    // if the list is empty or the head has lower priority
    if (head == NULL || head->priority > p) {

        // Insert the new node before the head
        temp->next = head;
        head = temp;
    }
    else {

        // Traverse the list to find the correct position
        // to insert the new node based on priority
        while (start->next != NULL &&
               start->next->priority < p) {
            start = start->next;
        }

        // Insert the new node at the found position
        temp->next = start->next;
        start->next = temp;
    }
    return head;
}

// Function to check if the list is empty
int isEmpty(Node* head) {
    return (head == NULL);
}

// Driver code
int main() {

    Node* pq = new Node(4, 1);

    pq = push(pq, 5, 2);
    pq = push(pq, 6, 3);
    pq = push(pq, 7, 0);

    while (!isEmpty(pq)) {
        cout << " " << peek(pq);
        pq = pop(pq);
    }
    return 0;
}

// C++ code to implement Priority Queue 

// using Linked List

​

#include <bits/stdc++.h>

using namespace std;

​

struct Node {

    int data;

    int priority;

    Node* next;

    Node(int x, int p) {

        data = x;

        priority = p;

        next = NULL;

    }

};

​

// Return the value at head

int peek(Node* head) {

​

    // Return the data of the node at the head of the list

    return head->data;

}

​

// Removes the element with the highest priority from the list

Node* pop(Node* head) {

​

    // Store the current head node in a temporary variable

    Node* temp = head;

​

    // Move the head to the next node in the list

    head = head->next;

​

    // Free the memory of the removed head node

    delete temp;

​

    // Return the new head of the list

    return head;

}

​

// Function to push according to priority

Node* push(Node* head, int d, int p) {

    Node* start = head;

​

    // Create new Node with the given data and priority

    Node* temp = new Node(d, p);

​

    // Special Case: Insert the new node before the head

    // if the list is empty or the head has lower priority

    if (head == NULL || head->priority > p) {

​

        // Insert the new node before the head

        temp->next = head;

        head = temp;

    }

    else {

​

        // Traverse the list to find the correct position

        // to insert the new node based on priority

        while (start->next != NULL &&

               start->next->priority < p) {

            start = start->next;

        }

​

        // Insert the new node at the found position

        temp->next = start->next;

        start->next = temp;

    }

    return head;

}

​

// Function to check if the list is empty

int isEmpty(Node* head) {

    return (head == NULL);

}

​

// Driver code

int main() {

​

    Node* pq = new Node(4, 1);

​

    pq = push(pq, 5, 2);

    pq = push(pq, 6, 3);

    pq = push(pq, 7, 0);

​

    while (!isEmpty(pq)) {

        cout << " " << peek(pq);

        pq = pop(pq);

    }

    return 0;

}

// C code to implement Priority Queue 
// using Linked List 
#include <stdio.h> 
#include <stdlib.h> 

typedef struct node { 
    int data; 

    int priority; 

    struct node* next; 
} Node; 


Node* newNode(int d, int p) { 
  
    Node* temp = (Node*)malloc(sizeof(Node)); 
    temp->data = d; 
    temp->priority = p; 
    temp->next = NULL; 

    return temp; 
} 

// Return the value at head 
int peek(Node* head) {

    // Return the data of the node at the head of the list
    return head->data; 
} 

// Removes the element with the highest priority from the list 
Node* pop(Node* head) {

    // Store the current head node in a temporary variable
    Node* temp = head; 
    
    // Move the head to the next node in the list
    head = head->next; 
    
    // Free the memory of the removed head node
    free(temp); 
    
    // Return the new head of the list
    return head; 
} 

// Function to push according to priority 
Node* push(Node* head, int d, int p) { 
    Node* start = head; 

    // Create new Node with the given data and priority
    Node* temp = newNode(d, p); 

    // Special Case: Insert the new node before the head
    // if the list is empty or the head has lower priority
    if (head->priority > p) { 

        // Insert the new node before the head
        temp->next = head; 
        head = temp; 
    } 
    else { 

        // Traverse the list to find the correct position
        // to insert the new node based on priority
        while (start->next != NULL && 
               start->next->priority < p) { 
            start = start->next; 
        } 

        // Insert the new node at the found position
        temp->next = start->next; 
        start->next = temp; 
    } 
    return head; 
} 

// Function to check if the list is empty 
int isEmpty(Node* head) { 
    return (head == NULL); 
} 

// Driver code 
int main() { 
 
    Node* pq = newNode(4, 1); 
    pq = push(pq, 5, 2); 
    pq = push(pq, 6, 3); 
    pq = push(pq, 7, 0); 

    while (!isEmpty(pq)) { 
        printf("%d ", peek(pq)); 
        pq = pop(pq); 
    } 

    return 0; 
} 

// Java code to implement Priority Queue 
// using Linked List 
import java.util.* ; 

class GfG { 
    
static class Node { 
    int data; 
    
    int priority; 
    
    Node next; 
    
} 

static Node node = new Node(); 
    
// Function to Create A New Node 
static Node newNode(int d, int p) { 
    Node temp = new Node(); 
    temp.data = d; 
    temp.priority = p; 
    temp.next = null; 
    
    return temp; 
} 
    
// Return the value at head 
static int peek(Node head) { 
    return (head).data; 
} 
    
// Removes the element with the 
// highest priority from the list 
static Node pop(Node head) { 
    (head) = (head).next; 
    return head; 
} 
    
// Function to push according to priority 
static Node push(Node head, int d, int p) { 
  
    Node start = (head); 
    
    // Create new Node 
    Node temp = newNode(d, p); 
    
    // Special Case: The head of list has lesser 
    // priority than new node. So insert new 
    // node before head node and change head node. 
    if ((head).priority > p) { 
    
        // Insert New Node before head 
        temp.next = head; 
        (head) = temp; 
    } 
    else { 
    
        // Traverse the list and find a 
        // position to insert new node 
        while (start.next != null && 
            start.next.priority <= p) { 
            start = start.next; 
        } 
    
        // Either at the ends of the list 
        // or at required position 
        temp.next = start.next; 
        start.next = temp; 
    } 
    return head; 
} 
    
// Function to check is list is empty 
static int isEmpty(Node head) { 
    return ((head) == null)?1:0; 
} 
    
// Driver code 
public static void main(String args[]) { 
    Node pq = newNode(4, 1); 
    pq =push(pq, 5, 2); 
    pq =push(pq, 6, 3); 
    pq =push(pq, 7, 0); 
    
    while (isEmpty(pq)==0) { 
        System.out.printf("%d ", peek(pq)); 
        pq=pop(pq); 
    } 
    
} 
} 

# Python3 code to implement Priority Queue 
# using Singly Linked List

class PriorityQueueNode:
    
    def __init__(self, value, pr):
        self.data = value
        self.priority = pr
        self.next = None

# Global variable for the front of the queue
front = None

# Method to check Priority Queue is Empty 
def isEmpty():
    return front is None

# Method to add items in Priority Queue 
# According to their priority value
def push(value, priority):
    global front
    
    # Condition check for checking Priority
    # Queue is empty or not
    if isEmpty():
        front = PriorityQueueNode(value, priority)
        return 1
    else:
        # Special condition check to see that
        # first node priority value
        if front.priority > priority:
            newNode = PriorityQueueNode(value, priority)
            newNode.next = front
            front = newNode
            return 1
        else:
            temp = front
            while temp.next:
                if priority <= temp.next.priority:
                    break
                temp = temp.next
            
            newNode = PriorityQueueNode(value, priority)
            newNode.next = temp.next
            temp.next = newNode
            return 1

# Method to remove high priority item
# from the Priority Queue
def pop():
    global front
    
    if isEmpty():
        return
    else:
        front = front.next
        return 1

# Method to return high priority node 
# value without removing it
def peek():
    if isEmpty():
        return
    else:
        return front.data

# Method to traverse the Priority Queue
def traverse():
    if isEmpty():
        return "Queue is Empty!"
    else:
        temp = front
        while temp:
            print(temp.data, end=" ")
            temp = temp.next

# Driver code
if __name__ == "__main__":
    push(4, 1)
    push(5, 2)
    push(6, 3)
    push(7, 0)
    
    traverse()
    pop()

// C# code to implement Priority Queue 
// using Linked List 
using System; 

public class GfG { 

public class Node { 
    public int data; 

    public int priority; 

    public Node next; 
} 

public static Node node = new Node(); 

static Node newNode(int d, int p) { 
    Node temp = new Node(); 
    temp.data = d; 
    temp.priority = p; 
    temp.next = null; 

    return temp; 
} 

// Return the value at head 
static int peek(Node head) { 
    return (head).data; 
} 

// Removes the element with the 
// highest priority from the list 
static Node pop(Node head) { 
    (head) = (head).next; 
    return head; 
} 

// Function to push according to priority 
static Node push(Node head, 
                        int d, int p) { 
    Node start = (head); 

    // Create new Node 
    Node temp = newNode(d, p); 

    // Special Case: The head of list 
    // has lesser priority than new node. 
    // So insert new node before head node 
    // and change head node. 
    if ((head).priority > p) { 

        // Insert New Node before head 
        temp.next = head; 
        (head) = temp; 
    } 
    else { 

        // Traverse the list and find a 
        // position to insert new node 
        while (start.next != null && 
            start.next.priority <= p) 
        { 
            start = start.next; 
        } 

        // Either at the ends of the list 
        // or at required position 
        temp.next = start.next; 
        start.next = temp; 
    } 
  
    return head; 
} 

// Function to check is list is empty 
static int isEmpty(Node head) { 
    return ((head) == null) ? 1 : 0; 
} 

// Driver code 
public static void Main(string[] args) { 

    Node pq = newNode(4, 1); 
    pq = push(pq, 5, 2); 
    pq = push(pq, 6, 3); 
    pq = push(pq, 7, 0); 

    while (isEmpty(pq) == 0) { 
        Console.Write("{0:D} ", peek(pq)); 
        pq = pop(pq); 
    } 
} 
} 

// JavaScript code to implement Priority Queue
// using Linked List

class Node {
  
    constructor() {
        this.data = 0;
        this.priority = 0;
        this.next = null;
    }
}

var node = new Node();

function newNode(d, p) {
    var temp = new Node();
    temp.data = d;
    temp.priority = p;
    temp.next = null;

    return temp;
}

// Return the value at head
function peek(head) {

    // Return the data of the node at the head of the list
    return head.data;
}

// Removes the element with the highest priority from the list
function pop(head) {

    // Store the current head node in a temporary variable
    var temp = head;

    // Move the head to the next node in the list
    head = head.next;

    // Return the new head of the list
    return head;
}

// Function to push according to priority
function push(head, d, p) {
    var start = head;

    // Create new Node with the given data and priority
    var temp = newNode(d, p);

    // Special Case: Insert the new node before the head
    // if the list is empty or the head has lower priority
    if (head.priority > p) {
      
        // Insert New Node before head
        temp.next = head;
        head = temp;
    } 
    else {
      
        // Traverse the list to find the correct position
        // to insert the new node based on priority
        while (start.next != null && start.next.priority <= p) {
            start = start.next;
        }

        // Insert the new node at the found position
        temp.next = start.next;
        start.next = temp;
    }
    return head;
}

// Function to check if the list is empty
function isEmpty(head) {
    return head == null ? 1 : 0;
}

// Driver code
var pq = newNode(4, 1);
pq = push(pq, 5, 2);
pq = push(pq, 6, 3);
pq = push(pq, 7, 0);

while (isEmpty(pq) == 0) {
    console.log(peek(pq) + " ");
    pq = pop(pq);
}


      
       

7 4 5 6

Time Complexity: push() -> O(n) , To insert an element we must traverse the list and find the proper position to insert the node . This makes the push() operation takes O(n) time.

pop -> O(1), as it is performed in constant time.

peek -> O(1), as it is performed in constant time.

Space Complexity: O(n), as we are making a List of size n