# Sum and Product of all Prime Nodes of a Singly Linked List

Last Updated : 30 Nov, 2023

Given a singly linked list containing N nodes, the task is to find the sum and product of all nodes from the list which are prime.

Examples

```Input : List = 15 -> 16 -> 6 -> 7 -> 17
Output : Product = 119, Sum = 24
Prime nodes are 7, 17.
Input : List = 15 -> 3 -> 4 -> 2 -> 9
Output : Product = 6, Sum = 5

```

Approach: The idea is to traverse the nodes of the singly linked list one by one and check if the current node is prime or not. Find the sum and product of the data of the nodes which are prime.

Below is the implementation of above idea:

## C++

 `// C++ implementation to find sum and` `// product of all of prime nodes of` `// the singly 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 of the new node` `    ``new_node->next = (*head_ref);`   `    ``// 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 find sum and product of all` `// prime nodes of the singly linked list` `void` `sumAndProduct(Node* head_ref)` `{` `    ``int` `prod = 1;` `    ``int` `sum = 0;`   `    ``Node* ptr = head_ref;`   `    ``// Traverse the linked list` `    ``while` `(ptr != NULL) {` `        ``// if current node is prime,` `        ``// Find sum and product` `        ``if` `(isPrime(ptr->data)) {` `            ``prod *= ptr->data;` `            ``sum += ptr->data;` `        ``}`   `        ``ptr = ptr->next;` `    ``}`   `    ``cout << ``"Sum = "` `<< sum << endl;` `    ``cout << ``"Product = "` `<< prod;` `}`   `// Driver program` `int` `main()` `{` `    ``// start with the empty list` `    ``Node* head = NULL;`   `    ``// create the linked list` `    ``// 15 -> 16 -> 7 -> 6 -> 17` `    ``push(&head, 17);` `    ``push(&head, 7);` `    ``push(&head, 6);` `    ``push(&head, 16);` `    ``push(&head, 15);`   `    ``sumAndProduct(head);`   `    ``return` `0;` `}`

## Java

 `// Java implementation to find sum and ` `// product of all of prime nodes of ` `// the singly linked list ` `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 of 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 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 find sum and product of all ` `// prime nodes of the singly linked list ` `static` `void` `sumAndProduct(Node head_ref) ` `{ ` `    ``int` `prod = ``1``; ` `    ``int` `sum = ``0``; `   `    ``Node ptr = head_ref; `   `    ``// Traverse the linked list ` `    ``while` `(ptr != ``null``)` `    ``{ ` `        ``// if current node is prime, ` `        ``// Find sum and product ` `        ``if` `(isPrime(ptr.data))` `        ``{ ` `            ``prod *= ptr.data; ` `            ``sum += ptr.data; ` `        ``} `   `        ``ptr = ptr.next; ` `    ``} `   `    ``System.out.println(``"Sum = "` `+ sum ); ` `    ``System.out.println( ``"Product = "` `+ prod); ` `} `   `// Driver code ` `public` `static` `void` `main(String args[])` `{ ` `    ``// start with the empty list ` `    ``Node head = ``null``; `   `    ``// create the linked list ` `    ``// 15 . 16 . 7 . 6 . 17 ` `    ``head=push(head, ``17``); ` `    ``head=push(head, ``7``); ` `    ``head=push(head, ``6``); ` `    ``head=push(head, ``16``); ` `    ``head=push(head, ``15``); `   `    ``sumAndProduct(head); `   `}` `}`   `// This code is contributed by Arnab Kundu`

## Python

 `# Python implementation to find sum and ` `# product of all of prime nodes of ` `# the singly linked list `   `# Link list node ` `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 of 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 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 ``=` `i ``+` `6` `    ``return` `True`   `# Function to find sum and product of all ` `# prime nodes of the singly linked list ` `def` `sumAndProduct(head_ref) :`   `    ``prod ``=` `1` `    ``sum` `=` `0`   `    ``ptr ``=` `head_ref `   `    ``# Traverse the linked list ` `    ``while` `(ptr !``=` `None``):` `    `  `        ``# if current node is prime, ` `        ``# Find sum and product ` `        ``if` `(isPrime(ptr.data)):` `        `  `            ``prod ``*``=` `ptr.data ` `            ``sum` `+``=` `ptr.data ` `        `  `        ``ptr ``=` `ptr.``next` `    `  `    ``print``(``"Sum = "` `, ``sum` `) ` `    ``print``( ``"Product = "` `, prod) `   `# Driver code `   `# start with the empty list ` `head ``=` `None`   `# create the linked list ` `# 15 . 16 . 7 . 6 . 17 ` `head ``=` `push(head, ``17``) ` `head ``=` `push(head, ``7``) ` `head ``=` `push(head, ``6``) ` `head ``=` `push(head, ``16``) ` `head ``=` `push(head, ``15``) `   `sumAndProduct(head) `     `# This code is contributed by Arnab Kundu`

## C#

 `// C# implementation to find sum and ` `// product of all of prime nodes of ` `// the singly linked list ` `using` `System;` `    `  `class` `GFG ` `{ `   `// Node of the singly linked list ` `public` `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 of 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 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 find sum and product of all ` `// prime nodes of the singly linked list ` `static` `void` `sumAndProduct(Node head_ref) ` `{ ` `    ``int` `prod = 1; ` `    ``int` `sum = 0; `   `    ``Node ptr = head_ref; `   `    ``// Traverse the linked list ` `    ``while` `(ptr != ``null``) ` `    ``{ ` `        ``// if current node is prime, ` `        ``// Find sum and product ` `        ``if` `(isPrime(ptr.data)) ` `        ``{ ` `            ``prod *= ptr.data; ` `            ``sum += ptr.data; ` `        ``} `   `        ``ptr = ptr.next; ` `    ``} `   `    ``Console.WriteLine(``"Sum = "` `+ sum); ` `    ``Console.WriteLine( ``"Product = "` `+ prod); ` `} `   `// Driver code ` `public` `static` `void` `Main(String []args) ` `{ ` `    ``// start with the empty list ` `    ``Node head = ``null``; `   `    ``// create the linked list ` `    ``// 15 . 16 . 7 . 6 . 17 ` `    ``head = push(head, 17); ` `    ``head = push(head, 7); ` `    ``head = push(head, 6); ` `    ``head = push(head, 16); ` `    ``head = push(head, 15); `   `    ``sumAndProduct(head); ` `} ` `} `   `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output

```Sum = 24
Product = 119

```

complexity Analysis:

• Time Complexity: O(N), where N is the number of nodes in the linked list.
• Auxiliary Space: O(1) because it is using constant space

Approach (Recursive):

We can traverse the linked list recursively and for each node, check if it is prime or not. If it is prime, we add its value to the sum and multiply its value to the product. Then we call the same function recursively for the next node until we reach the end of the list.

• Create a recursive function that takes a pointer to the head of the linked list, a pointer to an integer variable that will hold the sum of prime nodes, and a pointer to an integer variable that will hold the product of prime nodes.
• Check if the head pointer is NULL. If it is, return from the function.
• If the data of the current node is prime, add it to the sum and multiply it to the product.
• Recursively call the function with the next node in the linked list and the updated sum and product variables.
• In the calling function, print the final values of the sum and product variables.

Below is the implementation of the above approach:

## C++

 `#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 = ``new` `Node;`   `    ``// put in the data` `    ``new_node->data = new_data;`   `    ``// link the old list of the new node` `    ``new_node->next = (*head_ref);`   `    ``// 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 find sum and product of all` `// prime nodes of the singly linked list` `void` `sumAndProductUtil(Node* node, ``int``& prod, ``int``& sum)` `{` `    ``if` `(node == NULL)` `        ``return``;`   `    ``// Check if the current node is prime` `    ``if` `(isPrime(node->data)) {` `        ``prod *= node->data;` `        ``sum += node->data;` `    ``}`   `    ``// Recursively call the function for the next node` `    ``sumAndProductUtil(node->next, prod, sum);` `}`   `// Wrapper function for the sumAndProductUtil function` `void` `sumAndProduct(Node* head)` `{` `    ``int` `prod = 1;` `    ``int` `sum = 0;` `    ``sumAndProductUtil(head, prod, sum);` `    ``cout << ``"Sum = "` `<< sum << endl;` `    ``cout << ``"Product = "` `<< prod;` `}`   `// Driver program` `int` `main()` `{` `    ``// start with the empty list` `    ``Node* head = NULL;`   `    ``// create the linked list` `    ``// 15 -> 16 -> 7 -> 6 -> 17` `    ``push(&head, 17);` `    ``push(&head, 7);` `    ``push(&head, 6);` `    ``push(&head, 16);` `    ``push(&head, 15);`   `    ``sumAndProduct(head);`   `    ``return` `0;` `}`

## Java

 `// Java program to implement the above approach`   `// Node of the singly linked list` `class` `Node {` `    ``int` `data;` `    ``Node next;`   `    ``Node(``int` `data)` `    ``{` `        ``this``.data = data;` `        ``this``.next = ``null``;` `    ``}` `}`   `public` `class` `GFG {`   `    ``// Function to insert a node at the beginning` `    ``// of the singly Linked List` `    ``static` `Node push(Node head, ``int` `new_data)` `    ``{` `        ``// allocate node` `        ``Node new_node = ``new` `Node(new_data);`   `        ``// link the old list of the new node` `        ``new_node.next = head;`   `        ``// move the head to point to the new node` `        ``head = new_node;`   `        ``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 find sum and product of all` `    ``// prime nodes of the singly linked list` `    ``static` `void` `sumAndProduct(Node node)` `    ``{` `        ``int` `prod = ``1``;` `        ``int` `sum = ``0``;`   `        ``// Traverse the linked list` `        ``while` `(node != ``null``) {` `            ``// Check if the current node is prime` `            ``if` `(isPrime(node.data)) {` `                ``prod *= node.data;` `                ``sum += node.data;` `            ``}` `            ``node = node.next;` `        ``}`   `        ``System.out.println(``"Sum = "` `+ sum);` `        ``System.out.println(``"Product = "` `+ prod);` `    ``}`   `    ``// Driver program` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``// Start with an empty list` `        ``Node head = ``null``;`   `        ``// Create the linked list` `        ``// 15 -> 16 -> 7 -> 6 -> 17` `        ``head = push(head, ``17``);` `        ``head = push(head, ``7``);` `        ``head = push(head, ``6``);` `        ``head = push(head, ``16``);` `        ``head = push(head, ``15``);`   `        ``// Calculate and print sum and product of prime` `        ``// nodes` `        ``sumAndProduct(head);` `    ``}` `}`   `// This code is contributed by Susobhan Akhuli`

## Python3

 `# Python program to implement the above approach` `class` `Node:` `    ``def` `__init__(``self``, data):` `        ``self``.data ``=` `data` `        ``self``.``next` `=` `None`   `# Function to insert a node at the beginning of the singly Linked List` `def` `push(head_ref, new_data):` `    ``# allocate node` `    ``new_node ``=` `Node(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 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 find sum and product of all prime nodes of the singly linked list` `def` `sumAndProductUtil(node, prod, ``sum``):` `    ``if` `node ``is` `None``:` `        ``return` `sum``, prod`   `    ``# Check if the current node is prime` `    ``if` `isPrime(node.data):` `        ``prod ``*``=` `node.data` `        ``sum` `+``=` `node.data`   `    ``# Recursively call the function for the next node` `    ``return` `sumAndProductUtil(node.``next``, prod, ``sum``)`   `# Wrapper function for the sumAndProductUtil function` `def` `sumAndProduct(head):` `    ``prod ``=` `1` `    ``sum` `=` `0` `    ``sum``, prod ``=` `sumAndProductUtil(head, prod, ``sum``)` `    ``print``(``"Sum ="``, ``sum``)` `    ``print``(``"Product ="``, prod)`   `# Driver program` `if` `__name__ ``=``=` `'__main__'``:` `    ``# start with the empty list` `    ``head ``=` `None`   `    ``# create the linked list` `    ``# 15 -> 16 -> 7 -> 6 -> 17` `    ``head ``=` `push(head, ``17``)` `    ``head ``=` `push(head, ``7``)` `    ``head ``=` `push(head, ``6``)` `    ``head ``=` `push(head, ``16``)` `    ``head ``=` `push(head, ``15``)`   `    ``sumAndProduct(head)`   `# This code is contributed by Susobhan Akhuli`

## C#

 `using` `System;`   `public` `class` `Node {` `    ``public` `int` `data;` `    ``public` `Node next;`   `    ``public` `Node(``int` `data)` `    ``{` `        ``this``.data = data;` `        ``this``.next = ``null``;` `    ``}` `}`   `public` `class` `LinkedList {` `    ``public` `Node head;`   `    ``// Function to insert a node at the beginning of the` `    ``// singly Linked List` `    ``public` `void` `Push(``int` `new_data)` `    ``{` `        ``// Allocate a new node` `        ``Node new_node = ``new` `Node(new_data);`   `        ``// Link the old list off the new node` `        ``new_node.next = head;`   `        ``// Move the head to point to the new node` `        ``head = new_node;` `    ``}` `}`   `public` `class` `Program {` `    ``// Function to check if a number is prime` `    ``public` `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 the below loop` `        ``if` `(n % 2 == 0 || n % 3 == 0)` `            ``return` `false``;`   `        ``int` `i = 5;` `        ``while` `(i * i <= n) {` `            ``if` `(n % i == 0 || n % (i + 2) == 0)` `                ``return` `false``;` `            ``i += 6;` `        ``}` `        ``return` `true``;` `    ``}`   `    ``// Function to find sum and product of all prime nodes` `    ``// of the singly linked list` `    ``public` `static` `void` `    ``SumAndProductUtil(Node node, ``ref` `int` `prod, ``ref` `int` `sum)` `    ``{` `        ``if` `(node == ``null``)` `            ``return``;`   `        ``// Check if the current node is prime` `        ``if` `(IsPrime(node.data)) {` `            ``prod *= node.data;` `            ``sum += node.data;` `        ``}`   `        ``// Recursively call the function for the next node` `        ``SumAndProductUtil(node.next, ``ref` `prod, ``ref` `sum);` `    ``}`   `    ``// Wrapper function for the SumAndProductUtil function` `    ``public` `static` `void` `SumAndProduct(LinkedList list)` `    ``{` `        ``int` `prod = 1;` `        ``int` `sum = 0;` `        ``SumAndProductUtil(list.head, ``ref` `prod, ``ref` `sum);` `        ``Console.WriteLine(``"Sum = "` `+ sum);` `        ``Console.WriteLine(``"Product = "` `+ prod);` `    ``}`   `    ``public` `static` `void` `Main(``string``[] args)` `    ``{` `        ``// Start with an empty list` `        ``LinkedList list = ``new` `LinkedList();`   `        ``// Create the linked list: 15 -> 16 -> 7 -> 6 -> 17` `        ``list.Push(17);` `        ``list.Push(7);` `        ``list.Push(6);` `        ``list.Push(16);` `        ``list.Push(15);`   `        ``SumAndProduct(list);` `    ``}` `}`

## Javascript

 ``

Output:

```      Sum = 24
Product = 119

```

Time Complexity: O(n), where n is the number of nodes in the linked list.
Auxiliary Space: O(p), where p is the number of prime nodes in the linked list.