Priority Queue using Linked List

Implement Priority Queue using Linked Lists. 

• 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.

Priority Queues can be implemented using common data structures like arrays, linked-lists, heaps and binary trees.

Prerequisites :
Linked Lists, Priority Queues

The list is so created so that the highest priority element is always at the head of the list. The list is arranged in descending order of elements based on their priority. This allow us to remove the highest priority element in O(1) time. To insert an element we must traverse the list and find the proper position to insert the node so that the overall order of the priority queue is maintained. This makes the push() operation takes O(N) time. The pop() and peek() operations are performed in constant time.

Algorithm :

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

Below is the implementation of the algorithm : 

C++

// C++ code to implement Priority Queue
// using Linked List
#include <bits/stdc++.h>
using namespace std;

// Node
typedef struct node
{
    int data;

    // Lower values indicate
    // higher priority
    int priority;

    struct node* next;

} Node;

// Function to create a new 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 (*head)->data;
}

// Removes the element with the
// highest priority from the list
void pop(Node** head)
{
    Node* temp = *head;
    (*head) = (*head)->next;
    free(temp);
}

// Function to push according to priority
void 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 newnode 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;
    }
}

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

// Driver code
int main()
{

    // Create a Priority Queue
    // 7->4->5->6
    Node* pq = newNode(4, 1);
    push(&pq, 5, 2);
    push(&pq, 6, 3);
    push(&pq, 7, 0);

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

// This code is contributed by shivanisinghss2110

C

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

// Node
typedef struct node {
    int data;

    // Lower values indicate higher priority
    int priority;

    struct node* next;

} Node;

// Function to Create A New 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 (*head)->data;
}

// Removes the element with the
// highest priority from the list
void pop(Node** head)
{
    Node* temp = *head;
    (*head) = (*head)->next;
    free(temp);
}

// Function to push according to priority
void 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;
    }
}

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

// Driver code
int main()
{
    // Create a Priority Queue
    // 7->4->5->6
    Node* pq = newNode(4, 1);
    push(&pq, 5, 2);
    push(&pq, 6, 3);
    push(&pq, 7, 0);

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

    return 0;
}

Java

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

class Solution
{


// Node
static class Node {
    int data;

    // Lower values indicate higher priority
    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)
{
    Node temp = 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[])
{
    // Create a Priority Queue
    // 7.4.5.6
    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);
    }

}
}

// This code is contributed
// by Arnab Kundu

Python3

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

# Class to create new node which includes
# Node Data, and Node Priority
class PriorityQueueNode:

  def __init__(self, value, pr):

    self.data = value
    self.priority = pr
    self.next = None

# Implementation of Priority Queue
class PriorityQueue:

    def __init__(self):

        self.front = None

    # Method to check Priority Queue is Empty
    # or not if Empty then it will return True
    # Otherwise False
    def isEmpty(self):

        return True if self.front == None else False

    # Method to add items in Priority Queue
    # According to their priority value
    def push(self, value, priority):

        # Condition check for checking Priority
        # Queue is empty or not
        if self.isEmpty() == True:

            # Creating a new node and assigning
            # it to class variable
            self.front = PriorityQueueNode(value,
                                           priority)

            # Returning 1 for successful execution
            return 1

        else:

            # Special condition check to see that
            # first node priority value
            if self.front.priority > priority:

                # Creating a new node
                newNode = PriorityQueueNode(value,
                                            priority)

                # Updating the new node next value
                newNode.next = self.front

                # Assigning it to self.front
                self.front = newNode

                # Returning 1 for successful execution
                return 1

            else:

                # Traversing through Queue until it
                # finds the next smaller priority node
                temp = self.front

                while temp.next:

                    # If same priority node found then current
                    # node will come after previous node
                    if priority <= temp.next.priority:
                        break

                    temp = temp.next

                newNode = PriorityQueueNode(value,
                                            priority)
                newNode.next = temp.next
                temp.next = newNode

                # Returning 1 for successful execution
                return 1

    # Method to remove high priority item
    # from the Priority Queue
    def pop(self):

        # Condition check for checking
        # Priority Queue is empty or not
        if self.isEmpty() == True:
            return

        else:

            # Removing high priority node from
            # Priority Queue, and updating front
            # with next node
            self.front = self.front.next
            return 1

    # Method to return high priority node
    # value Not removing it
    def peek(self):

        # Condition check for checking Priority
        # Queue is empty or not
        if self.isEmpty() == True:
            return
        else:
            return self.front.data

    # Method to Traverse through Priority
    # Queue
    def traverse(self):

        # Condition check for checking Priority
        # Queue is empty or not
        if self.isEmpty() == True:
            return "Queue is Empty!"
        else:
            temp = self.front
            while temp:
                print(temp.data, end = " ")
                temp = temp.next

# Driver code
if __name__ == "__main__":

    # Creating an instance of Priority
    # Queue, and adding values
    # 7 -> 4 -> 5 -> 6
    pq = PriorityQueue()
    pq.push(4, 1)
    pq.push(5, 2)
    pq.push(6, 3)
    pq.push(7, 0)

    # Traversing through Priority Queue
    pq.traverse()

    # Removing highest Priority item
    # for priority queue
    pq.pop()

# This code is contributed by himanshu kanojiya

C#

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

class GFG
{
// Node
public class Node
{
    public int data;

    // Lower values indicate
    // higher priority
    public int priority;

    public Node next;
}

public static Node node = new Node();

// Function to Create A New Node
public 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
public static int peek(Node head)
{
    return (head).data;
}

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

// Function to push according to priority
public 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
public static int isEmpty(Node head)
{
    return ((head) == null) ? 1 : 0;
}

// Driver code
public static void Main(string[] args)
{
    // Create a Priority Queue
    // 7.4.5.6
    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);
    }
}
}

// This code is contributed by Shrikant13

Javascript

<script>
      // JavaScript code to implement Priority Queue
      // using Linked List
      // Node
      class Node
      {

        // Lower values indicate
        // higher priority
        constructor() {
          this.data = 0;
          this.priority = 0;
          this.next = null;
        }
      }

      var node = new Node();

      // Function to Create A 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 head.data;
      }

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

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

        // Create new Node
        var 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
      function isEmpty(head) {
        return head == null ? 1 : 0;
      }

      // Driver code
      // Create a Priority Queue
      // 7.4.5.6
      var pq = newNode(4, 1);
      pq = push(pq, 5, 2);
      pq = push(pq, 6, 3);
      pq = push(pq, 7, 0);

      while (isEmpty(pq) == 0) {
        document.write(peek(pq) + " ");
        pq = pop(pq);
      }

      // This code is contributed by rdtank.
    </script>

Output:

7 4 5 6

Time Complexities and Comparison with Binary Heap: 

               peek()    push()    pop()
-----------------------------------------
Linked List |   O(1)      O(n)      O(1)
            |
Binary Heap |   O(1)    O(Log n)   O(Log n)