# Priority Queue using Linked List

Implement Priority Queue using Linked Lists.

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 :

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 :
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 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

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

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 ` `#include ` ` `  `// 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 `

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)```