# Sum of factorials of Prime numbers in a Linked list

Given a Linked list of N integers, the task is to find the sum of factorials of each prime element in the list.

Examples:

Input: L1 = 4 -> 6 -> 2 -> 12 -> 3
Output: 8
Explanation:
Prime numbers are 2 and 3, hence 2! + 3! = 2 + 6 = 8.

Input: L1 = 7 -> 4 -> 5
Output: 5160
Explanation:
Prime numbers are 7 and 5, hence 7! + 5! = 5160.

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

Approach: To solve the problem mentioned above follow the steps given below:

• Implement a function factorial(n) that finds the factorial of N .
• Initialize a variable sum = 0. Now, traverse the given list and for each node check whether node is prime or not.
• If node is prime then update sum = sum + factorial(node) otherwise else move the node to next.
• Print the calculated sum in the end.

Below is the implementation of the above approach:

## C++

 `// C++ implementation to fine Sum of ` `// prime factorials in a Linked list ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Node of the singly linked list ` `struct` `Node { ` `    ``int` `data; ` `    ``Node* next; ` `}; ` ` `  `// Function to insert a node ` `// at the beginning ` `// of the singly 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; ` ` `  `    ``// link the old list ` `    ``// off the new node ` `    ``new_node->next = (*head_ref); ` ` `  `    ``// move the head to point ` `    ``// to the new node ` `    ``(*head_ref) = new_node; ` `} ` ` `  `// Function to return the factorial of N ` `int` `factorial(``int` `n) ` `{ ` `    ``int` `f = 1; ` `    ``for` `(``int` `i = 1; i <= n; i++) { ` `        ``f *= i; ` `    ``} ` `    ``return` `f; ` `} ` ` `  `// Function to check if number is prime ` `bool` `isPrime(``int` `n) ` `{ ` `    ``if` `(n <= 1) ` `        ``return` `false``; ` `    ``if` `(n <= 3) ` `        ``return` `true``; ` ` `  `    ``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 return the sum of ` `// factorials of the LL elements ` `int` `sumFactorial(Node* head_1) ` `{ ` ` `  `    ``// To store the required sum ` `    ``Node* ptr = head_1; ` `    ``int` `s = 0; ` `    ``while` `(ptr != NULL) { ` ` `  `        ``// Add factorial of all the elements ` `        ``if` `(isPrime(ptr->data)) { ` `            ``s += factorial(ptr->data); ` `            ``ptr = ptr->next; ` `        ``} ` `        ``else` `            ``ptr = ptr->next; ` `    ``} ` `    ``return` `s; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``Node* head1 = NULL; ` ` `  `    ``push(&head1, 4); ` `    ``push(&head1, 6); ` `    ``push(&head1, 2); ` `    ``push(&head1, 12); ` `    ``push(&head1, 3); ` ` `  `    ``cout << sumFactorial(head1); ` `    ``return` `0; ` `} `

## Java

 `// Java implementation to find Sum of ` `// prime factorials in a Linked list ` ` `  `import` `java.util.*; ` ` `  `class` `GFG { ` ` `  `    ``// Node of the singly linked list ` `    ``static` `class` `Node { ` `        ``int` `data; ` `        ``Node next; ` `    ``}; ` ` `  `    ``// Function to insert a ` `    ``// node at the beginning ` `    ``// of the singly 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; ` ` `  `        ``// link the old list ` `        ``// off the new node ` `        ``new_node.next = (head_ref); ` ` `  `        ``// move the head to point ` `        ``// to the new node ` `        ``(head_ref) = new_node; ` `        ``return` `head_ref; ` `    ``} ` ` `  `    ``// Function to return ` `    ``// the factorial of n ` `    ``static` `int` `factorial(``int` `n) ` `    ``{ ` `        ``int` `f = ``1``; ` `        ``for` `(``int` `i = ``1``; i <= n; i++) { ` `            ``f *= i; ` `        ``} ` `        ``return` `f; ` `    ``} ` ` `  `    ``// Function to check if number is prime ` `    ``static` `boolean` `isPrime(``int` `n) ` `    ``{ ` `        ``// Corner cases ` `        ``if` `(n <= ``1``) ` `            ``return` `false``; ` `        ``if` `(n <= ``3``) ` `            ``return` `true``; ` ` `  `        ``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 return the sum of ` `    ``// factorials of the LL elements ` `    ``static` `int` `sumFactorial(Node head_1) ` `    ``{ ` `        ``Node ptr = head_1; ` `        ``// To store the required sum ` `        ``int` `s = ``0``; ` `        ``while` `(ptr != ``null``) { ` ` `  `            ``// Add factorial of ` `            ``// all the elements ` `            ``if` `(isPrime(ptr.data)) { ` `                ``s += factorial(ptr.data); ` `                ``ptr = ptr.next; ` `            ``} ` `            ``else` `{ ` `                ``ptr = ptr.next; ` `            ``} ` `        ``} ` `        ``return` `s; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` ` `  `        ``Node head1 = ``null``; ` ` `  `        ``head1 = push(head1, ``4``); ` `        ``head1 = push(head1, ``6``); ` `        ``head1 = push(head1, ``2``); ` `        ``head1 = push(head1, ``12``); ` `        ``head1 = push(head1, ``3``); ` `        ``int` `ans = sumFactorial(head1); ` ` `  `        ``System.out.println(ans); ` `    ``} ` `} `

## Python3

 `# Python implementation of the approach  ` `class` `Node:   ` `          `  `    ``def` `__init__(``self``, data):   ` `        ``self``.data ``=` `data   ` `        ``self``.``next` `=` `next` `              `  `# Function to insert a ` `# node at the beginning   ` `# of the singly Linked List   ` `def` `push( head_ref, new_data) :  ` `      `  `    ``# allocate node   ` `    ``new_node ``=` `Node(``0``)   ` `      `  `    ``# put in the data   ` `    ``new_node.data ``=` `new_data   ` `      `  `    ``# link the old list ` `    ``# off the new node   ` `    ``new_node.``next` `=` `(head_ref)   ` `      `  `    ``# move the head to ` `    ``# point to the new node   ` `    ``(head_ref) ``=` `new_node  ` `    ``return` `head_ref ` `     `  `def` `factorial(n):  ` `    ``f ``=` `1``;  ` `    ``for` `i ``in` `range``(``1``, n ``+` `1``):  ` `        ``f ``*``=` `i;  ` `    ``return` `f;  ` `  ``# prime for def   ` `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 return the sum of  ` `# factorials of the LL elements  ` `def` `sumFactorial(head_ref1):  ` `   `  `    ``# To store the required sum  ` `    ``s ``=` `0``;  ` `    ``ptr1 ``=` `head_ref1 ` `    ``while` `(ptr1 !``=` `None``) :  ` `   `  `        ``# Add factorial of all the elements ` `        ``if``(isPrime(ptr1.data)): ` `            ``s ``+``=` `factorial(ptr1.data); ` `            ``ptr1 ``=` `ptr1.``next` `        ``else``: ` `            ``ptr1 ``=` `ptr1.``next` `    ``return` `s;  ` `# Driver code   ` `# start with the empty list   ` `head1 ``=` `None` `# create the linked list   ` `head1 ``=` `push(head1, ``4``)   ` `head1 ``=` `push(head1, ``6``)   ` `head1 ``=` `push(head1, ``2``)   ` `head1 ``=` `push(head1, ``12``)   ` `head1 ``=` `push(head1, ``3``) ` `ans ``=` `sumFactorial(head1) ` `print``(ans) `

## C#

 `// C# implementation to find Sum of ` `// prime factorials in a Linked list ` `using` `System; ` ` `  `class` `GFG{ ` ` `  `// Node of the singly linked list ` `class` `Node ` `{ ` `    ``public` `int` `data; ` `    ``public` `Node next; ` `}; ` ` `  `// Function to insert a node  ` `// at the beginning of the  ` `// singly 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; ` ` `  `    ``// Link the old list ` `    ``// off the new node ` `    ``new_node.next = (head_ref); ` ` `  `    ``// Move the head to point ` `    ``// to the new node ` `    ``(head_ref) = new_node; ` `    ``return` `head_ref; ` `} ` ` `  `// Function to return ` `// the factorial of n ` `static` `int` `factorial(``int` `n) ` `{ ` `    ``int` `f = 1; ` `    ``for``(``int` `i = 1; i <= n; i++) ` `    ``{ ` `       ``f *= i; ` `    ``} ` `    ``return` `f; ` `} ` ` `  `// Function to check if number ` `// is prime ` `static` `bool` `isPrime(``int` `n) ` `{ ` `     `  `    ``// Corner cases ` `    ``if` `(n <= 1) ` `        ``return` `false``; ` `    ``if` `(n <= 3) ` `        ``return` `true``; ` ` `  `    ``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 return the sum of ` `// factorials of the LL elements ` `static` `int` `sumFactorial(Node head_1) ` `{ ` `    ``Node ptr = head_1; ` `     `  `    ``// To store the required sum ` `    ``int` `s = 0; ` `    ``while` `(ptr != ``null``)  ` `    ``{ ` ` `  `        ``// Add factorial of ` `        ``// all the elements ` `        ``if` `(isPrime(ptr.data)) ` `        ``{ ` `            ``s += factorial(ptr.data); ` `            ``ptr = ptr.next; ` `        ``} ` `        ``else` `        ``{ ` `            ``ptr = ptr.next; ` `        ``} ` `    ``} ` `    ``return` `s; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(String []args) ` `{ ` `    ``Node head1 = ``null``; ` ` `  `    ``head1 = push(head1, 4); ` `    ``head1 = push(head1, 6); ` `    ``head1 = push(head1, 2); ` `    ``head1 = push(head1, 12); ` `    ``head1 = push(head1, 3); ` `     `  `    ``int` `ans = sumFactorial(head1); ` ` `  `    ``Console.WriteLine(ans); ` `} ` `} ` ` `  `// This code is contributed by Amit Katiyar `

Output:

```8
```

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : amit143katiyar