# Delete all Prime Nodes from a Doubly Linked List

Given a doubly linked list containing N nodes, the task is to delete all nodes from the list which are prime.

Examples:

Input: List = 15 <=> 16 <=> 6 <=> 7 <=> 17
Output: Final List = 15 <=> 16 <=> 6

Input: List = 5 <=> 3 <=> 4 <=> 2 <=> 9
Output: Final List = 5 <=> 4 <=> 9

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The idea is to traverse the nodes of the doubly linked list one by one and get the pointer of the nodes which are prime. Delete those nodes by following the approach used in this post.

Below is the implementation of above idea:

## C++

 `// C++ implementation to delete all ` `// prime nodes from the doubly ` `// linked list ` `#include ` ` `  `using` `namespace` `std; ` ` `  `// Node of the doubly linked list ` `struct` `Node { ` `    ``int` `data; ` `    ``Node *prev, *next; ` `}; ` ` `  `// function to insert a node at the beginning ` `// of the Doubly Linked List ` `void` `push(Node** head_ref, ``int` `new_data) ` `{ ` `    ``// allocate node ` `    ``Node* new_node = (Node*)``malloc``(``sizeof``(``struct` `Node)); ` ` `  `    ``// put in the data ` `    ``new_node->data = new_data; ` ` `  `    ``// since we are adding at the beginning, ` `    ``// prev is always NULL ` `    ``new_node->prev = NULL; ` ` `  `    ``// link the old list off the new node ` `    ``new_node->next = (*head_ref); ` ` `  `    ``// change prev of head node to new node ` `    ``if` `((*head_ref) != NULL) ` `        ``(*head_ref)->prev = new_node; ` ` `  `    ``// move the head to point to the new node ` `    ``(*head_ref) = new_node; ` `} ` ` `  `// 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 a node in a Doubly Linked List. ` `// head_ref --> pointer to head node pointer. ` `// del --> pointer to node to be deleted ` `void` `deleteNode(Node** head_ref, Node* del) ` `{ ` `    ``// base case ` `    ``if` `(*head_ref == NULL || del == NULL) ` `        ``return``; ` ` `  `    ``// If node to be deleted is head node ` `    ``if` `(*head_ref == del) ` `        ``*head_ref = del->next; ` ` `  `    ``// Change next only if node to be ` `    ``// deleted is NOT the last node ` `    ``if` `(del->next != NULL) ` `        ``del->next->prev = del->prev; ` ` `  `    ``// Change prev only if node to be ` `    ``// deleted is NOT the first node ` `    ``if` `(del->prev != NULL) ` `        ``del->prev->next = del->next; ` ` `  `    ``// Finally, free the memory occupied by del ` `    ``free``(del); ` ` `  `    ``return``; ` `} ` ` `  `// function to delete all prime nodes ` `// from the doubly linked list ` `void` `deletePrimeNodes(Node** head_ref) ` `{ ` `    ``Node* ptr = *head_ref; ` `    ``Node* next; ` ` `  `    ``while` `(ptr != NULL) { ` `        ``next = ptr->next; ` `        ``// if true, delete node 'ptr' ` `        ``if` `(isPrime(ptr->data)) ` `            ``deleteNode(head_ref, ptr); ` `        ``ptr = next; ` `    ``} ` `} ` ` `  `// function to print nodes in a ` `// given doubly linked list ` `void` `printList(Node* head) ` `{ ` `    ``while` `(head != NULL) { ` `        ``cout << head->data << ``" "``; ` `        ``head = head->next; ` `    ``} ` `} ` ` `  `// Driver program ` `int` `main() ` `{ ` `    ``// start with the empty list ` `    ``Node* head = NULL; ` ` `  `    ``// create the doubly linked list ` `    ``// 15 <-> 16 <-> 7 <-> 6 <-> 17 ` `    ``push(&head, 17); ` `    ``push(&head, 6); ` `    ``push(&head, 7); ` `    ``push(&head, 16); ` `    ``push(&head, 15); ` ` `  `    ``cout << ``"Original List: "``; ` `    ``printList(head); ` ` `  `    ``deletePrimeNodes(&head); ` ` `  `    ``cout << ``"\nModified List: "``; ` `    ``printList(head); ` `} `

## Java

 `// Java implementation to delete all  ` `// prime nodes from the doubly  ` `// linked list  ` `class` `GFG ` `{ ` `     `  ` `  `// Node of the doubly linked list  ` `static` `class` `Node ` `{  ` `    ``int` `data;  ` `    ``Node prev, next;  ` `};  ` ` `  `// function to insert a node at the beginning  ` `// of the Doubly Linked List  ` `static` `Node push(Node head_ref, ``int` `new_data)  ` `{  ` `    ``// allocate node  ` `    ``Node new_node = ``new` `Node();  ` ` `  `    ``// put in the data  ` `    ``new_node.data = new_data;  ` ` `  `    ``// since we are adding at the beginning,  ` `    ``// prev is always null  ` `    ``new_node.prev = ``null``;  ` ` `  `    ``// link the old list off the new node  ` `    ``new_node.next = (head_ref);  ` ` `  `    ``// change prev of head node to new node  ` `    ``if` `((head_ref) != ``null``)  ` `        ``(head_ref).prev = new_node;  ` ` `  `    ``// move the head to point to the new node  ` `    ``(head_ref) = new_node;  ` `     `  `    ``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 a node in a Doubly Linked List.  ` `// head_ref -. pointer to head node pointer.  ` `// del -. pointer to node to be deleted  ` `static` `Node deleteNode(Node head_ref, Node del)  ` `{  ` `    ``// base case  ` `    ``if` `(head_ref == ``null` `|| del == ``null``)  ` `        ``return` `null``;  ` ` `  `    ``// If node to be deleted is head node  ` `    ``if` `(head_ref == del)  ` `        ``head_ref = del.next;  ` ` `  `    ``// Change next only if node to be  ` `    ``// deleted is NOT the last node  ` `    ``if` `(del.next != ``null``)  ` `        ``del.next.prev = del.prev;  ` ` `  `    ``// Change prev only if node to be  ` `    ``// deleted is NOT the first node  ` `    ``if` `(del.prev != ``null``)  ` `        ``del.prev.next = del.next;  ` ` `  `    ``return` `head_ref; ` `}  ` ` `  `// function to delete all prime nodes  ` `// from the doubly linked list  ` `static` `Node deletePrimeNodes(Node head_ref)  ` `{  ` `    ``Node ptr = head_ref;  ` `    ``Node next;  ` ` `  `    ``while` `(ptr != ``null``) ` `    ``{  ` `        ``next = ptr.next;  ` `         `  `        ``// if true, delete node 'ptr'  ` `        ``if` `(isPrime(ptr.data))  ` `            ``deleteNode(head_ref, ptr);  ` `        ``ptr = next;  ` `    ``}  ` `    ``return` `head_ref; ` `}  ` ` `  `// function to print nodes in a  ` `// given doubly linked list  ` `static` `void` `printList(Node head)  ` `{  ` `    ``while` `(head != ``null``) ` `    ``{  ` `        ``System.out.print( head.data + ``" "``);  ` `        ``head = head.next;  ` `    ``}  ` `}  ` ` `  `// Driver program  ` `public` `static` `void` `main(String args[]) ` `{  ` `    ``// start with the empty list  ` `    ``Node head = ``null``;  ` ` `  `    ``// create the doubly linked list  ` `    ``// 15 <. 16 <. 7 <. 6 <. 17  ` `    ``head = push(head, ``17``);  ` `    ``head = push(head, ``6``);  ` `    ``head = push(head, ``7``);  ` `    ``head = push(head, ``16``);  ` `    ``head = push(head, ``15``);  ` ` `  `    ``System.out.print( ``"Original List: "``);  ` `    ``printList(head);  ` ` `  `    ``head = deletePrimeNodes(head);  ` ` `  `    ``System.out.print(``"\nModified List: "``);  ` `    ``printList(head);  ` `}  ` `} ` ` `  `// This code is contributed by Arnab Kundu `

## Python3

 `# Python3 implementation to delete all ` `# prime nodes from the doubly ` `# linked list ` `import` `math ` ` `  `# Node of the doubly linked list ` `class` `Node:  ` `    ``def` `__init__(``self``, data):  ` `        ``self``.data ``=` `data  ` `        ``self``.``next` `=` `None` `         `  `# function to insert a node at the beginning ` `# of the Doubly Linked List ` `def` `push(head_ref, new_data): ` `     `  `    ``# allocate node ` `    ``new_node ``=` `Node(new_data) ` ` `  `    ``# put in the data ` `    ``new_node.data ``=` `new_data ` ` `  `    ``# since we are adding at the beginning, ` `    ``# prev is always None ` `    ``new_node.prev ``=` `None` ` `  `    ``# link the old list off the new node ` `    ``new_node.``next` `=` `head_ref ` ` `  `    ``# change prev of head node to new node ` `    ``if` `(head_ref !``=` `None``): ` `        ``head_ref.prev ``=` `new_node ` ` `  `    ``# move the head to point to the new node ` `    ``head_ref ``=` `new_node ` `    ``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 a node in a Doubly Linked List. ` `# head_ref --> pointer to head node pointer. ` `# del --> pointer to node to be deleted ` `def` `deleteNode(head_ref, delete): ` `     `  `    ``# base case ` `    ``if` `(head_ref ``=``=` `None` `or` `delete ``=``=` `None``): ` `        ``return` `None` ` `  `    ``# If node to be deleted is head node ` `    ``if` `(head_ref ``=``=` `delete): ` `        ``head_ref ``=` `delete.``next` ` `  `    ``# Change next only if node to be ` `    ``# deleted is NOT the last node ` `    ``if` `(delete.``next` `!``=` `None``): ` `        ``delete.``next``.prev ``=` `delete.prev ` ` `  `    ``# Change prev only if node to be ` `    ``# deleted is NOT the first node ` `    ``if` `(delete.prev !``=` `None``): ` `        ``delete.prev.``next` `=` `delete.``next` ` `  `    ``# Finally, free the memory occupied by del ` `    ``return` `head_ref ` ` `  `# function to delete all prime nodes ` `# from the doubly linked list ` `def` `deletePrimeNodes(head_ref): ` `    ``ptr ``=` `head_ref ` `    ``#next ` ` `  `    ``while` `(ptr !``=` `None``): ` `        ``next` `=` `ptr.``next` `         `  `        ``# if true, delete node 'ptr' ` `        ``if` `(isPrime(ptr.data)): ` `            ``deleteNode(head_ref, ptr) ` `        ``ptr ``=` `next` `     `  `    ``return` `head_ref ` ` `  `# function to print nodes in a ` `# given doubly linked list ` `def` `printList(head): ` `    ``while` `(head !``=` `None``) : ` `        ``print``(head.data, end ``=` `" "``) ` `        ``head ``=` `head.``next` ` `  `# Driver Code ` `if` `__name__``=``=``'__main__'``:  ` `     `  `    ``# start with the empty list ` `    ``head ``=` `None` ` `  `    ``# create the doubly linked list ` `    ``# 15 <-> 16 <-> 7 <-> 6 <-> 17 ` `    ``head ``=` `push(head, ``17``) ` `    ``head ``=` `push(head, ``6``) ` `    ``head ``=` `push(head, ``7``) ` `    ``head ``=` `push(head, ``16``) ` `    ``head ``=` `push(head, ``15``) ` ` `  `    ``print``(``"Original List: "``, end ``=` `"") ` `    ``printList(head) ` ` `  `    ``deletePrimeNodes(head) ` ` `  `    ``print``(``"\nModified List: "``, end ``=` `"") ` `    ``printList(head) ` ` `  `# This code is contributed by AbhiThakur `

## C#

 `// C# implementation to delete all  ` `// prime nodes from the doubly  ` `// linked list  ` `using` `System; ` ` `  `class` `GFG  ` `{  ` `     `  `// Node of the doubly linked list  ` `public` `class` `Node  ` `{  ` `    ``public` `int` `data;  ` `    ``public` `Node prev, next;  ` `};  ` ` `  `// function to insert a node at the beginning  ` `// of the Doubly Linked List  ` `static` `Node push(Node head_ref, ``int` `new_data)  ` `{  ` `    ``// allocate node  ` `    ``Node new_node = ``new` `Node();  ` ` `  `    ``// put in the data  ` `    ``new_node.data = new_data;  ` ` `  `    ``// since we are adding at the beginning,  ` `    ``// prev is always null  ` `    ``new_node.prev = ``null``;  ` ` `  `    ``// link the old list off the new node  ` `    ``new_node.next = (head_ref);  ` ` `  `    ``// change prev of head node to new node  ` `    ``if` `((head_ref) != ``null``)  ` `        ``(head_ref).prev = new_node;  ` ` `  `    ``// move the head to point to the new node  ` `    ``(head_ref) = new_node;  ` `     `  `    ``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 a node in a Doubly Linked List.  ` `// head_ref -. pointer to head node pointer.  ` `// del -. pointer to node to be deleted  ` `static` `Node deleteNode(Node head_ref, Node del)  ` `{  ` `    ``// base case  ` `    ``if` `(head_ref == ``null` `|| del == ``null``)  ` `        ``return` `null``;  ` ` `  `    ``// If node to be deleted is head node  ` `    ``if` `(head_ref == del)  ` `        ``head_ref = del.next;  ` ` `  `    ``// Change next only if node to be  ` `    ``// deleted is NOT the last node  ` `    ``if` `(del.next != ``null``)  ` `        ``del.next.prev = del.prev;  ` ` `  `    ``// Change prev only if node to be  ` `    ``// deleted is NOT the first node  ` `    ``if` `(del.prev != ``null``)  ` `        ``del.prev.next = del.next;  ` ` `  `    ``return` `head_ref;  ` `}  ` ` `  `// function to delete all prime nodes  ` `// from the doubly linked list  ` `static` `Node deletePrimeNodes(Node head_ref)  ` `{  ` `    ``Node ptr = head_ref;  ` `    ``Node next;  ` ` `  `    ``while` `(ptr != ``null``)  ` `    ``{  ` `        ``next = ptr.next;  ` `         `  `        ``// if true, delete node 'ptr'  ` `        ``if` `(isPrime(ptr.data))  ` `            ``deleteNode(head_ref, ptr);  ` `        ``ptr = next;  ` `    ``}  ` `    ``return` `head_ref;  ` `}  ` ` `  `// function to print nodes in a  ` `// given doubly linked list  ` `static` `void` `printList(Node head)  ` `{  ` `    ``while` `(head != ``null``)  ` `    ``{  ` `        ``Console.Write(head.data + ``" "``);  ` `        ``head = head.next;  ` `    ``}  ` `}  ` ` `  `// Driver program  ` `public` `static` `void` `Main()  ` `{  ` `    ``// start with the empty list  ` `    ``Node head = ``null``;  ` ` `  `    ``// create the doubly linked list  ` `    ``// 15 <. 16 <. 7 <. 6 <. 17  ` `    ``head = push(head, 17);  ` `    ``head = push(head, 6);  ` `    ``head = push(head, 7);  ` `    ``head = push(head, 16);  ` `    ``head = push(head, 15);  ` ` `  `    ``Console.Write( ``"Original List: "``);  ` `    ``printList(head);  ` ` `  `    ``head = deletePrimeNodes(head);  ` ` `  `    ``Console.Write(``"\nModified List: "``);  ` `    ``printList(head);  ` `}  ` `}  ` ` `  `// This code is contributed by Rajput-Ji `

Output:

```Original List: 15 16 7 6 17
Modified List: 15 16 6
```

Time Complexity: O(N), where N is the total number of nodes.

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