# Delete all Prime Nodes from a Circular Singly Linked List

• Difficulty Level : Medium
• Last Updated : 06 Sep, 2022

Given a circular singly linked list containing N nodes. The task is to delete all nodes from the list which are prime. Examples:

Input : 9->11->32->6->13->20
Output : 9 32 6 20

Input : 6->11->16->21->17->10
Output : 6 16 21 10

Approach: The idea is to traverse the nodes of the circular singly linked list one by one and get the pointer of the nodes which are prime. Delete those nodes by following the approach used in the post: Delete a node from circular Linked List.

Below is the implementation of the above idea:

## C++

 `// CPP program to delete all prime``// node from a Circular singly linked list` `#include ``using` `namespace` `std;` `// Structure for a node``struct` `Node {``    ``int` `data;``    ``struct` `Node* next;``};` `// Function to insert a node at the beginning``// of a Circular linked list``void` `push(``struct` `Node** head_ref, ``int` `data)``{``    ``struct` `Node* ptr1``        ``= (``struct` `Node*)``malloc``(``sizeof``(``struct` `Node));``    ``struct` `Node* temp = *head_ref;``    ``ptr1->data = data;``    ``ptr1->next = *head_ref;` `    ``// If linked list is not NULL then``    ``// set the next of last node``    ``if` `(*head_ref != NULL) {``        ``while` `(temp->next != *head_ref)``            ``temp = temp->next;``        ``temp->next = ptr1;``    ``}``    ``else``        ``ptr1->next = ptr1; ``// For the first node` `    ``*head_ref = ptr1;``}` `// Delete the node if it is prime``void` `deleteNode(Node* head_ref, Node* del)``{``    ``struct` `Node *temp = head_ref, *temp2 = head_ref;``    ``// traverse list till not found``    ``// delete node``    ``while` `(temp->next != del) {``        ``temp = temp->next;``    ``}` `    ``// copy address of node``    ``temp->next = del->next;` `    ``// Finally, free the memory``    ``// occupied by del``    ``free``(del);` `    ``return``;``}` `// Function to check if a number is prime``bool` `isPrime(``int` `n)``{``    ``// Corner cases``    ``if` `(n <= 1)``        ``return` `false``;` `    ``if` `(n <= 3)``        ``return` `true``;` `    ``// This is checked so that we can skip``    ``// middle five numbers in below loop``    ``if` `(n % 2 == 0 || n % 3 == 0)``        ``return` `false``;` `    ``for` `(``int` `i = 5; i * i <= n; i = i + 6)``        ``if` `(n % i == 0 || n % (i + 2) == 0)``            ``return` `false``;` `    ``return` `true``;``}` `// Function to delete all prime nodes``// from the singly circular linked list``Node* deletePrimeNodes(Node* head)``{``   ``if` `(head == NULL)``        ``return` `NULL;``    ``struct` `Node* ptr = head;` `    ``struct` `Node* temp;` `    ``// setting up the head node to the first non prime node``    ``while` `(isPrime(ptr->data)) {``        ``ptr = ptr->next;``        ``if` `(ptr == head) {``            ``return` `NULL;``        ``}``    ``}``    ``temp = ptr;``    ``Node* temp2 = ptr;``    ``ptr = ptr->next;``    ``// setting up the last node next to the first non prime``    ``// node``    ``while` `(ptr != head) {``        ``temp2 = ptr;``        ``ptr = ptr->next;``    ``}``    ``temp2->next = temp;``    ``head = temp;``    ``ptr = head;``    ``// traverse list till the endl``    ``// if node is prime then delete it``    ``do` `{``        ``temp = ptr->next;``        ``// if node is prime``        ``if` `(isPrime(ptr->data))``            ``deleteNode(head, ptr);``        ``ptr = temp;` `    ``} ``while` `(ptr != head);``    ``return` `head;``}` `// Function to print nodes in a``// given singly linked list``void` `printList(``struct` `Node* head)``{``    ``if` `(!head) {``        ``printf``(``"NULL"``);``    ``}``    ``struct` `Node* temp = head;``    ``if` `(head != NULL) {``        ``do` `{``            ``printf``(``"%d "``, temp->data);``            ``temp = temp->next;``        ``} ``while` `(temp != head);``    ``}``}` `// Driver code``int` `main()``{``    ``// Initialize lists as empty``    ``struct` `Node* head = NULL;` `    ``// Created linked list will be``    ``// 9->11->32->6->13->20``    ``push(&head, 20);``    ``push(&head, 13);``    ``push(&head, 6);``    ``push(&head, 32);``    ``push(&head, 11);``    ``push(&head, 9);` `    ``cout << ``"Given List : "``;``    ``printList(head);` `    ``cout << ``"\nList After deleting prime nodes : "``;``    ``head = deletePrimeNodes(head);``    ``printList(head);` `    ``return` `0;``}`

## Java

 `// Java program to delete all prime``// node from a Circular singly linked list``class` `GFG``{``    ` `// Structure for a node``static` `class` `Node``{``    ``int` `data;``    ``Node next;``};` `// Function to insert a node at the beginning``// of a Circular linked list``static` `Node push(Node head_ref, ``int` `data)``{``    ``Node ptr1 = ``new` `Node();``    ``Node temp = head_ref;``    ``ptr1.data = data;``    ``ptr1.next = head_ref;` `    ``// If linked list is not null then``    ``// set the next of last node``    ``if` `(head_ref != ``null``)``    ``{``        ``while` `(temp.next != head_ref)``            ``temp = temp.next;``        ``temp.next = ptr1;``    ``}``    ``else``        ``ptr1.next = ptr1; ``// For the first node` `    ``head_ref = ptr1;``    ``return` `head_ref;``}` `// Delete the node if it is prime``static` `Node deleteNode(Node head_ref, Node del)``{``    ``Node temp = head_ref;` `    ``// If node to be deleted is head node``    ``if` `(head_ref == del)``        ``head_ref = del.next;` `    ``// traverse list till not found``    ``// delete node``    ``while` `(temp.next != del)``    ``{``        ``temp = temp.next;``    ``}` `    ``// copy address of node``    ``temp.next = del.next;``    ``return` `head_ref;``}` `// Function to check if a number is prime``static` `boolean` `isPrime(``int` `n)``{``    ``// Corner cases``    ``if` `(n <= ``1``)``        ``return` `false``;` `    ``if` `(n <= ``3``)``        ``return` `true``;` `    ``// This is checked so that we can skip``    ``// middle five numbers in below loop``    ``if` `(n % ``2` `== ``0` `|| n % ``3` `== ``0``)``        ``return` `false``;` `    ``for` `(``int` `i = ``5``; i * i <= n; i = i + ``6``)``        ``if` `(n % i == ``0` `|| n % (i + ``2``) == ``0``)``            ``return` `false``;` `    ``return` `true``;``}` `// Function to delete all prime nodes``// from the singly circular linked list``static` `Node deletePrimeNodes(Node head)``{``    ``Node ptr = head;` `    ``Node next;` `    ``// traverse list till the endl``    ``// if node is prime then delete it``    ``do``    ``{``        ``// if node is prime``        ``if` `(isPrime(ptr.data))``            ``deleteNode(head, ptr);` `        ``// point to next node``        ``next = ptr.next;``        ``ptr = next;` `    ``}``    ``while` `(ptr != head);``        ``return` `head;``}` `// Function to print nodes in a``// given singly linked list``static` `void` `printList(Node head)``{``    ``Node temp = head;``    ``if` `(head != ``null``)``    ``{``        ``do``        ``{``            ``System.out.printf(``"%d "``, temp.data);``            ``temp = temp.next;``        ``}``        ``while` `(temp != head);``    ``}``}` `// Driver code``public` `static` `void` `main(String args[])``{``    ``// Initialize lists as empty``    ``Node head = ``null``;` `    ``// Created linked list will be``    ``// 9.11.32.6.13.20``    ``head=push(head, ``20``);``    ``head=push(head, ``13``);``    ``head=push(head, ``6``);``    ``head=push(head, ``32``);``    ``head=push(head, ``11``);``    ``head=push(head, ``9``);` `    ``System.out.println(``"Given List : "``);``    ``printList(head);` `    ``System.out.println( ``"\nList After deleting prime nodes : "``);``    ``head=deletePrimeNodes(head);``    ``printList(head);``}``}` `// This code is contributed by Arnab Kundu`

## Python3

 `# Python3 program to delete all prime``# node from a Circular singly linked list``import` `math` `# Structure for a node``class` `Node:``    ``def` `__init__(``self``, data):``        ``self``.data ``=` `data``        ``self``.``next` `=` `None` `# Function to insert a node at the``# beginning of a Circular linked list``def` `push(head_ref, data):``    ``ptr1 ``=` `Node(data)``    ``temp ``=` `head_ref``    ``ptr1.data ``=` `data``    ``ptr1.``next` `=` `head_ref` `    ``# If linked list is not None then``    ``# set the next of last node``    ``if` `(head_ref !``=` `None``) :``        ``while` `(temp.``next` `!``=` `head_ref):``            ``temp ``=` `temp.``next``        ``temp.``next` `=` `ptr1``    ` `    ``else``:``        ``ptr1.``next` `=` `ptr1 ``# For the first node` `    ``head_ref ``=` `ptr1``    ``return` `head_ref` `# Delete the node if it is prime``def` `deleteNode(head_ref, delete):``    ``temp ``=` `head_ref``    ` `    ``# If node to be deleted is head node``    ``if` `(head_ref ``=``=` `delete):``        ``head_ref ``=` `delete.``next` `    ``# traverse list till not found``    ``# delete node``    ``while` `(temp.``next` `!``=` `delete):``        ``temp ``=` `temp.``next``    ` `    ``# copy address of node``    ``temp.``next` `=` `delete.``next` `    ``# Finally, free the memory``    ``# occupied by delete``    ``# free(delete)``    ``return` `head_ref` `# Function to check if a number is prime``def` `isPrime(n):``    ` `    ``# Corner cases``    ``if` `(n <``=` `1``):``        ``return` `False` `    ``if` `(n <``=` `3``):``        ``return` `True` `    ``# This is checked so that we can skip``    ``# middle five numbers in below loop``    ``if` `(n ``%` `2` `=``=` `0` `or` `n ``%` `3` `=``=` `0``):``        ``return` `False` `    ``for` `i ``in` `range``(``5``, n ``+` `1``, ``6``):``        ``if` `(i ``*` `i < n ``+` `2` `and``               ``(n ``%` `i ``=``=` `0` `or``                ``n ``%` `(i ``+` `2``) ``=``=` `0``)):``            ``return` `False` `    ``return` `True` `# Function to delete all prime nodes``# from the singly circular linked list``def` `deletePrimeNodes( head):``    ``ptr ``=` `head` `    ``#next` `    ``# traverse list till the endl``    ``# if node is prime then delete it``    ``# if (isPrime(ptr.data)!=True):``    ``# deleteNode(head, ptr)` `    ``# point to next node``    ``next` `=` `ptr.``next``    ``ptr ``=` `next``    ``while` `(ptr !``=` `head):``        ` `        ``# if node is prime``        ``if` `(isPrime(ptr.data) ``=``=` `True``):``            ``deleteNode(head, ptr)` `        ``# point to next node``        ``next` `=` `ptr.``next``        ``ptr ``=` `next` `    ``return` `head` `# Function to print nodes in a``# given singly linked list``def` `printList(head):``    ``temp ``=` `head``    ``if` `(head !``=` `None``) :``        ``print``(temp.data, end ``=` `" "``)``        ``temp ``=` `temp.``next``        ``while` `(temp !``=` `head):``            ``print``(temp.data, end ``=` `" "``)``            ``temp ``=` `temp.``next``    ` `# Driver code``if` `__name__``=``=``'__main__'``:` `    ``# Initialize lists as empty``    ``head ``=` `None` `    ``# Created linked list will be``    ``# 9.11.32.6.13.20``    ``head ``=` `push(head, ``20``)``    ``head ``=` `push(head, ``13``)``    ``head ``=` `push(head, ``6``)``    ``head ``=` `push(head, ``32``)``    ``head ``=` `push(head, ``11``)``    ``head ``=` `push(head, ``9``)` `    ``print``(``"Given List : "``, end ``=` `"")``    ``printList(head)` `    ``print``( ``"\nList After deleting"``,``           ``"prime nodes : "``, end ``=` `"")``    ``head ``=` `deletePrimeNodes(head)``    ``printList(head)` `# This code is contributed by Srathore`

## C#

 `// C# program to delete all prime``// node from a Circular singly linked list``using` `System;` `class` `GFG``{``    ` `// Structure for a node``public` `class` `Node``{``    ``public` `int` `data;``    ``public` `Node next;``};` `// Function to insert a node at the beginning``// of a Circular linked list``static` `Node push(Node head_ref, ``int` `data)``{``    ``Node ptr1 = ``new` `Node();``    ``Node temp = head_ref;``    ``ptr1.data = data;``    ``ptr1.next = head_ref;` `    ``// If linked list is not null then``    ``// set the next of last node``    ``if` `(head_ref != ``null``)``    ``{``        ``while` `(temp.next != head_ref)``            ``temp = temp.next;``        ``temp.next = ptr1;``    ``}``    ``else``        ``ptr1.next = ptr1; ``// For the first node` `    ``head_ref = ptr1;``    ``return` `head_ref;``}` `// Delete the node if it is prime``static` `Node deleteNode(Node head_ref, Node del)``{``    ``Node temp = head_ref;` `    ``// If node to be deleted is head node``    ``if` `(head_ref == del)``        ``head_ref = del.next;` `    ``// traverse list till not found``    ``// delete node``    ``while` `(temp.next != del)``    ``{``        ``temp = temp.next;``    ``}` `    ``// copy address of node``    ``temp.next = del.next;``    ``return` `head_ref;``}` `// Function to check if a number is prime``static` `bool` `isPrime(``int` `n)``{``    ``// Corner cases``    ``if` `(n <= 1)``        ``return` `false``;` `    ``if` `(n <= 3)``        ``return` `true``;` `    ``// This is checked so that we can skip``    ``// middle five numbers in below loop``    ``if` `(n % 2 == 0 || n % 3 == 0)``        ``return` `false``;` `    ``for` `(``int` `i = 5; i * i <= n; i = i + 6)``        ``if` `(n % i == 0 || n % (i + 2) == 0)``            ``return` `false``;` `    ``return` `true``;``}` `// Function to delete all prime nodes``// from the singly circular linked list``static` `Node deletePrimeNodes(Node head)``{``    ``Node ptr = head;` `    ``Node next;` `    ``// traverse list till the endl``    ``// if node is prime then delete it``    ``do``    ``{``        ``// if node is prime``        ``if` `(isPrime(ptr.data))``            ``deleteNode(head, ptr);` `        ``// point to next node``        ``next = ptr.next;``        ``ptr = next;` `    ``}``    ``while` `(ptr != head);``        ``return` `head;``}` `// Function to print nodes in a``// given singly linked list``static` `void` `printList(Node head)``{``    ``Node temp = head;``    ``if` `(head != ``null``)``    ``{``        ``do``        ``{``            ``Console.Write(``"{0} "``, temp.data);``            ``temp = temp.next;``        ``}``        ``while` `(temp != head);``    ``}``}` `// Driver code``public` `static` `void` `Main()``{``    ``// Initialize lists as empty``    ``Node head = ``null``;` `    ``// Created linked list will be``    ``// 9.11.32.6.13.20``    ``head=push(head, 20);``    ``head=push(head, 13);``    ``head=push(head, 6);``    ``head=push(head, 32);``    ``head=push(head, 11);``    ``head=push(head, 9);` `    ``Console.WriteLine(``"Given List : "``);``    ``printList(head);` `    ``Console.WriteLine( ``"\nList After deleting prime nodes : "``);``    ``head=deletePrimeNodes(head);``    ``printList(head);``}``}` `/* This code contributed by PrinciRaj1992 */`

## Javascript

 ``

Output

```Given List : 9 11 32 6 13 20
List After deleting prime nodes : 9 32 6 20 ```

Complexity Analysis:

• Time Complexity: O(N * sqrt(N))
• Auxiliary Space: O(1)

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