# Product of all prime nodes in a Doubly Linked List

Given a doubly linked list containing N nodes. The task is to find the product of all prime nodes.

Example:

Input: List = 15 <=> 16 <=> 6 <=> 7 <=> 17
Output: Product of Prime Nodes: 119

Input: List = 5 <=> 3 <=> 4 <=> 2 <=> 9
Output: Product of Prime Nodes: 30

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

Approach:

• Initialize a pointer temp with the head of the linked list and a product variable with 1.
• Start traversing the linked list using a loop until all the nodes get traversed.
• If node value is prime then multiply the value of the current node to the product i.e. product *= current_node-> data.
• Increment the pointer to the next node of linked list i.e. temp = temp -> next.
• Return the product.

Below is the implementation of the above approach:

## C++

 `// C++ implementation to product 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 product all prime nodes ` `// from the doubly linked list ` `int` `prodOfPrime(Node** head_ref) ` `{ ` `    ``Node* ptr = *head_ref; ` `    ``Node* next; ` `    ``// variable prod = 1 for multiplying nodes value ` `    ``int` `prod = 1; ` `    ``// travese list till last node ` `    ``while` `(ptr != NULL) { ` `        ``next = ptr->next; ` `        ``// if number is prime then ` `        ``// multiply to product ` `        ``if` `(isPrime(ptr->data)) ` `            ``prod = prod * ptr->data; ` `        ``ptr = next; ` `    ``} ` ` `  `    ``// return product ` `    ``return` `prod; ` `} ` ` `  `// 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); ` `    ``int` `prod = prodOfPrime(&head); ` ` `  `    ``cout << ``"Product of Prime Nodes : "` `<< prod; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation to product all ` `// prime nodes from the doubly ` `// linked list ` ` `  `// Node of the doubly linked list ` `class` `Node ` `{ ` `    ``int` `data; ` `    ``Node next, prev; ` ` `  `    ``Node(``int` `d) ` `    ``{ ` `        ``data = d; ` `        ``next = ``null``; ` `        ``prev = ``null``; ` `    ``} ` `} ` ` `  `class` `DLL  ` `{ ` `    ``// function to insert a node at the beginning ` `    ``// of the Doubly Linked List ` `    ``static` `Node push(Node head, ``int` `data) ` `    ``{ ` `        ``Node newNode = ``new` `Node(data); ` `        ``newNode.next = head; ` `        ``newNode.prev = ``null``; ` `        ``if` `(head != ``null``) ` `            ``head.prev = newNode; ` `        ``head = newNode; ` ` `  `        ``return` `head; ` `    ``} ` ` `  `    ``// 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 product all prime nodes ` `    ``// from the doubly linked list ` `    ``static` `int` `prodOfPrime(Node node) ` `    ``{ ` `        ``// variable prod = 1 for multiplying nodes value ` `        ``int` `prod = ``1``; ` `         `  `        ``// travese list till last node ` `        ``while` `(node != ``null``) ` `        ``{ ` `            ``// check is node value is Prime ` `            ``// if true then multiply to prod ` `            ``if` `(isPrime(node.data)) ` `                ``prod *= node.data; ` `            ``node = node.next; ` `        ``} ` `        ``// return product ` `        ``return` `prod; ` `    ``} ` ` `  `    ``// Driver Program ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``// Start with empty list ` `        ``Node head = ``null``; ` ` `  `        ``// create the doubly linked list ` `        ``// 15 <-> 16 <-> 7 <-> 6 <-> 17 ` `        ``head = push(head, ``17``); ` `        ``head = push(head, ``7``); ` `        ``head = push(head, ``6``); ` `        ``head = push(head, ``9``); ` `        ``head = push(head, ``10``); ` `        ``head = push(head, ``16``); ` `        ``head = push(head, ``15``); ` ` `  `        ``int` `prod = prodOfPrime(head); ` `        ``System.out.println(``"Product of Prime Nodes: "` `+ prod); ` `    ``} ` `} ` ` `  `// This code is contributed by Vivekkumar Singh `

## Python3

 `# Python3 implementation to product all ` `# prime nodes from the doubly ` `# linked list ` ` `  `# Node of the doubly linked list  ` `class` `Node:  ` `     `  `    ``def` `__init__(``self``, data):  ` `        ``self``.data ``=` `data  ` `        ``self``.prev ``=` `None` `        ``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(``0``) ` ` `  `    ``# put in the data ` `    ``new_node.data ``=` `new_data ` ` `  `    ``# since we are multiplying 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` `    ``i ``=` `5` `    ``while` `( i ``*` `i <``=` `n ): ` `        ``if` `(n ``%` `i ``=``=` `0` `or` `n ``%` `(i ``+` `2``) ``=``=` `0``): ` `            ``return` `False` `        ``i ``+``=` `6``; ` ` `  `    ``return` `True` ` `  `# function to product all prime nodes ` `# from the doubly linked list ` `def` `prodOfPrime(head_ref): ` ` `  `    ``ptr ``=` `head_ref ` `    ``next` `=` `None` `     `  `    ``# variable prod = 1 for multiplying nodes value ` `    ``prod ``=` `1` `     `  `    ``# travese list till last node ` `    ``while` `(ptr !``=` `None``):  ` `        ``next` `=` `ptr.``next` `         `  `        ``# if number is prime then ` `        ``# multiply to product ` `        ``if` `(isPrime(ptr.data)): ` `            ``prod ``=` `prod ``*` `ptr.data ` `        ``ptr ``=` `next` ` `  `    ``# return product ` `    ``return` `prod ` ` `  `# 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``) ` `    ``prod ``=` `prodOfPrime(head) ` ` `  `    ``print``(``"Product of Prime Nodes : "``, prod) ` ` `  `# This code is contributed by Arnab Kundu `

## C#

 `// C# implementation to product all  ` `// prime nodes from the doubly  ` `// linked list  ` `using` `System; ` ` `  `// Node of the doubly linked list  ` `public` `class` `Node  ` `{  ` `    ``public` `int` `data;  ` `    ``public` `Node next, prev;  ` ` `  `    ``public` `Node(``int` `d)  ` `    ``{  ` `        ``data = d;  ` `        ``next = ``null``;  ` `        ``prev = ``null``;  ` `    ``}  ` `}  ` ` `  `class` `DLL  ` `{  ` `    ``// function to insert a node at the beginning  ` `    ``// of the Doubly Linked List  ` `    ``static` `Node push(Node head, ``int` `data)  ` `    ``{  ` `        ``Node newNode = ``new` `Node(data);  ` `        ``newNode.next = head;  ` `        ``newNode.prev = ``null``;  ` `        ``if` `(head != ``null``)  ` `            ``head.prev = newNode;  ` `        ``head = newNode;  ` ` `  `        ``return` `head;  ` `    ``}  ` ` `  `    ``// 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 product all prime nodes  ` `    ``// from the doubly linked list  ` `    ``static` `int` `prodOfPrime(Node node)  ` `    ``{  ` `        ``// variable prod = 1 for multiplying nodes value  ` `        ``int` `prod = 1;  ` `         `  `        ``// travese list till last node  ` `        ``while` `(node != ``null``)  ` `        ``{  ` `            ``// check is node value is Prime  ` `            ``// if true then multiply to prod  ` `            ``if` `(isPrime(node.data))  ` `                ``prod *= node.data;  ` `            ``node = node.next;  ` `        ``}  ` `        ``// return product  ` `        ``return` `prod;  ` `    ``}  ` ` `  `    ``// Driver code  ` `    ``public` `static` `void` `Main(String []args)  ` `    ``{  ` `        ``// Start with empty list  ` `        ``Node head = ``null``;  ` ` `  `        ``// create the doubly linked list  ` `        ``// 15 <-> 16 <-> 7 <-> 6 <-> 17  ` `        ``head = push(head, 17);  ` `        ``head = push(head, 7);  ` `        ``head = push(head, 6);  ` `        ``head = push(head, 9);  ` `        ``head = push(head, 10);  ` `        ``head = push(head, 16);  ` `        ``head = push(head, 15);  ` ` `  `        ``int` `prod = prodOfPrime(head);  ` `        ``Console.WriteLine(``"Product of Prime Nodes: "` `+ prod);  ` `    ``}  ` `}  ` ` `  `// This code is contributed by Arnab Kundu `

Output:

```Product of Prime Nodes : 119
```

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

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