Implement Priority Queue using Linked Lists.
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Operations on Priority Queue :
- push(): This function is used to insert a new data into the queue.
- pop(): This function removes the element with the highest priority form 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 2: Set the head of the list to the next node in the list. HEAD = HEAD -> NEXT.
Step 3: Free the node at the head of the list
Step 4: 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 <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 form 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 form 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 |
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 form 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 |
7 4 5 6
Time Complexities and Comparison with Binary Heap:
peek() push() pop()
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Linked List | O(1) O(n) O(1)
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Binary Heap | O(1) O(Log n) O(Log n)
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