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

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 <bits/stdc++.h>

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

<script>
// javascript implementation to find sum and
// product of all of prime nodes of
// the singly linked list     // Node of the singly linked list
class Node {
    constructor() {
        this.data = 0;
        this.next = null;
    }
}

    // Function to insert a node at the beginning
    // of the singly Linked List
    function push(head_ref , new_data) {
        // allocate node
var 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
    function 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 || n % 3 == 0)
            return false;

        for (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
    function sumAndProduct(head_ref) {
        var prod = 1;
        var sum = 0;

var 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;
        }

        document.write("Sum = " + sum);
        document.write("<br/>Product = " + prod);
    }

    // Driver code

        // start with the empty list
var 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 contributed by umadevi9616
</script>

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 <bits/stdc++.h>
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

<script>
// JavaScript program to implement the above approach

// Node of the singly linked list
class Node {
    constructor(data) {
        this.data = data;
        this.next = null;
    }
}

// Function to insert a node at the beginning
// of the singly Linked List
function push(headRef, newData) {
    // Allocate node
    const newNode = new Node(newData);

    // Link the old list to the new node
    newNode.next = headRef;

    // Move the head to point to the new node
    headRef = newNode;
    return headRef;
}

// Function to check if a number is prime
function isPrime(n) {
    // Corner cases
    if (n <= 1) return false;
    if (n <= 3) return true;

    // Check if n is divisible by 2 or 3
    if (n % 2 === 0 || n % 3 === 0) return false;

    // Check for prime numbers using 6k +/- 1 rule
    for (let 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
function sumAndProductUtil(node, sol) {
    if (node === null) return;

    // Check if the current node is prime
    if (isPrime(node.data)) {
        sol.prod *= node.data;
        sol.sum += node.data;
    }

    // Recursively call the function for the next node
    sumAndProductUtil(node.next, sol);
}

// Wrapper function for the sumAndProductUtil function
function sumAndProduct(head) {
    let sol = {
        prod: 1,
        sum: 0
    };
    sumAndProductUtil(head, sol);
    document.write("Sum = ", sol.sum);
    document.write("<br>");
    document.write("Product = ", sol.prod);
}

// Start with an empty list
let 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 Susobhan Akhuli
</script>

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.