Count of Prime Nodes of a Singly Linked List

Given a singly linked list containing N nodes, the task is to find the total count of prime numbers.

Examples:

Input: List = 15 -> 5 -> 6 -> 10 -> 17
Output: 2
5 and 17 are the prime nodes
Input: List = 29 -> 3 -> 4 -> 2 -> 9
Output: 3
2, 3 and 29 are the prime nodes

Approach: The idea is to traverse the linked list to the end and check if the current node is prime or not. If YES, increment the count by 1 and keep doing the same until all the nodes get traversed. 

Below is the implementation of above approach:  

C++

// C++ implementation to find count of prime numbers
// in 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)
{
    Node* new_node = new Node;
    new_node->data = new_data;
    new_node->next = (*head_ref);
    (*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 count of prime
// nodes in a linked list
int countPrime(Node** head_ref)
{
    int count = 0;
    Node* ptr = *head_ref;

    while (ptr != NULL) {
        // If current node is prime
        if (isPrime(ptr->data)) {
            // Update count
            count++;
        }
        ptr = ptr->next;
    }

    return count;
}

// Driver program
int main()
{
    // start with the empty list
    Node* head = NULL;

    // create the linked list
    // 15 -> 5 -> 6 -> 10 -> 17
    push(&head, 17);
    push(&head, 10);
    push(&head, 6);
    push(&head, 5);
    push(&head, 15);

    // Function call to print require answer
    cout << "Count of prime nodes = "
         << countPrime(&head);

    return 0;
}

Java

// Java implementation to find count of prime numbers
// in the singly linked list
class solution
{

// 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)
{
    Node  new_node = new Node();
    new_node.data = new_data;
    new_node.next = ( head_ref);
    ( 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 count of prime
// nodes in a linked list
static int countPrime(Node   head_ref)
{
    int count = 0;
    Node  ptr =  head_ref;

    while (ptr != null) {
        // If current node is prime
        if (isPrime(ptr.data)) {
            // Update count
            count++;
        }
        ptr = ptr.next;
    }

    return count;
}

// Driver program
public static void main(String args[])
{
    // start with the empty list
    Node  head = null;

    // create the linked list
    // 15 . 5 . 6 . 10 . 17
    head=push(head, 17);
    head=push(head, 10);
    head=push(head, 6);
    head=push(head, 5);
    head=push(head, 15);

    // Function call to print require answer
    System.out.print( "Count of prime nodes = "+ countPrime(head));

}
}

// This code is contributed by Arnab Kundu

Python3

# Python3 implementation to find count of
# prime numbers in the singly linked list

# 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

# Link list node
class Node:

    def __init__(self, data, next):
        self.data = data
        self.next = next

class LinkedList:

    def __init__(self):
        self.head = None

    # Push a new node on the front of the list.
    def push(self, new_data):
        new_node = Node(new_data, self.head)
        self.head = new_node

    # Function to find count of prime
    # nodes in a linked list
    def countPrime(self):

        count = 0
        ptr = self.head

        while ptr != None:

            # If current node is prime
            if isPrime(ptr.data):

                # Update count
                count += 1

            ptr = ptr.next

        return count

# Driver Code
if __name__ == "__main__":

    # Start with the empty list
    linkedlist = LinkedList()

    # create the linked list
    # 15 -> 5 -> 6 -> 10 -> 17
    linkedlist.push(17)
    linkedlist.push(10)
    linkedlist.push(6)
    linkedlist.push(5)
    linkedlist.push(15)

    # Function call to print require answer
    print("Count of prime nodes =",
           linkedlist.countPrime())

# This code is contributed by Rituraj Jain

C#

// C# implementation to find count of prime numbers
// in 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)
{
    Node new_node = new Node();
    new_node.data = new_data;
    new_node.next = ( head_ref);
    ( 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 count of prime
// nodes in a linked list
static int countPrime(Node head_ref)
{
    int count = 0;
    Node ptr = head_ref;

    while (ptr != null)
    {
        // If current node is prime
        if (isPrime(ptr.data))
        {
            // Update count
            count++;
        }
        ptr = ptr.next;
    }

    return count;
}

// Driver code
public static void Main(String []args)
{
    // start with the empty list
    Node head = null;

    // create the linked list
    // 15 . 5 . 6 . 10 . 17
    head=push(head, 17);
    head=push(head, 10);
    head=push(head, 6);
    head=push(head, 5);
    head=push(head, 15);

    // Function call to print require answer
    Console.Write( "Count of prime nodes = "+ countPrime(head));
}
}

// This code has been contributed by 29AjayKumar

Javascript

<script>

// Javascript implementation to find count
// of prime numbers in the singly linked list

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

// Function to insert a node at the beginning
// of the singly Linked List
function push(head_ref, new_data)
{
    var new_node = new Node();
    new_node.data = new_data;
    new_node.next = (head_ref);
    (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 count of prime
// nodes in a linked list
function countPrime(head_ref)
{

    var count = 0;
    var ptr = head_ref;

    while (ptr != null)
    {

        // If current node is prime
        if (isPrime(ptr.data))
        {

            // Update count
            count++;
        }
        ptr = ptr.next;
    }
    return count;
}

// Driver code

// Start with the empty list
var head = null;

// Create the linked list
// 15 . 5 . 6 . 10 . 17
head = push(head, 17);
head = push(head, 10);
head = push(head, 6);
head = push(head, 5);
head = push(head, 15);

// Function call to print require answer
document.write("Count of prime nodes = " +
               countPrime(head));

// This code is contributed by gauravrajput1

</script>

Output

Count of prime nodes = 2

Complexity Analysis:

• Time Complexity: O(N*sqrt(P)), where N is length of the LinkedList and P is the maximum element in the List
• Auxiliary Space: O(1)

Recursive Approach:

The base case of the recursion is when the head node is NULL, in which case the function returns 0. Otherwise, the function first calls itself recursively for the next node in the linked list, and obtains the count of prime nodes in the remaining linked list. If the data of the current node is prime, it adds 1 to the count and returns it, otherwise it simply returns the count obtained from the recursive call. The final result returned by the function is the count of prime nodes in the entire linked list.

• If the head node is NULL, return 0.
• Recursively call the function for the rest of the linked list by passing the next node.
• If the data of the current node is prime, add 1 to the count and return it.
• Otherwise, return the count obtained from the recursive call.

Below is the implementation of the above approach:

C++

#include <iostream>
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) {
    Node* new_node = new Node;
    new_node->data = new_data;
    new_node->next = (*head_ref);
    (*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 count prime nodes in a linked list
int countPrimeRecursive(Node* head) {
    if (head == NULL)
        return 0;

    int count = countPrimeRecursive(head->next);

    if (isPrime(head->data))
        count++;

    return count;
}

// Driver program
int main() {
    // start with the empty list
    Node* head = NULL;

    // create the linked list
    // 15 -> 5 -> 6 -> 10 -> 17
    push(&head, 17);
    push(&head, 10);
    push(&head, 6);
    push(&head, 5);
    push(&head, 15);

    // Function call to print required answer
    cout << "Count of prime nodes = " << countPrimeRecursive(head);

    return 0;
}

Java

// Java program of the above approach
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 newData)
    {
        Node newNode = new Node(newData);
        newNode.next = head;
        return newNode;
    }

    // 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 count prime nodes in a linked list
    static int countPrimeRecursive(Node head)
    {
        if (head == null)
            return 0;

        int count = countPrimeRecursive(head.next);

        if (isPrime(head.data))
            count++;

        return count;
    }

    // Driver program
    public static void main(String[] args)
    {
        // Start with an empty list
        Node head = null;

        // Create the linked list
        // 15 -> 5 -> 6 -> 10 -> 17
        head = push(head, 17);
        head = push(head, 10);
        head = push(head, 6);
        head = push(head, 5);
        head = push(head, 15);

        // Function call to print the required answer
        System.out.println("Count of prime nodes = "
                           + countPrimeRecursive(head));
    }
}

// This code is contributed by Susobhan Akhuli

Python

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, new_data):
    new_node = Node(new_data)
    new_node.next = head
    return new_node

# Function to check if a number is prime


def is_prime(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 count prime nodes in a linked list


def count_prime_recursive(head):
    if head is None:
        return 0

    count = count_prime_recursive(head.next)

    if is_prime(head.data):
        count += 1

    return count


# Driver program
if __name__ == "__main__":
    # Start with an empty list
    head = None

    # Create the linked list
    # 15 -> 5 -> 6 -> 10 -> 17
    head = push(head, 17)
    head = push(head, 10)
    head = push(head, 6)
    head = push(head, 5)
    head = push(head, 15)

    # Function call to print the required answer
    print("Count of prime nodes =", count_prime_recursive(head))

C#

using System;

// Node of the singly linked list
class Node
{
    public int data;
    public Node next;

    public 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 newData)
    {
        Node newNode = new Node(newData);
        newNode.next = head;
        return newNode;
    }

    // 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 the loop
        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (int i = 5; i * i <= n; i += 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;

        return true;
    }

    // Function to count prime nodes in a linked list
    static int CountPrimeRecursive(Node head)
    {
        if (head == null)
            return 0;

        int count = CountPrimeRecursive(head.next);

        if (IsPrime(head.data))
            count++;

        return count;
    }

    // Driver program
    public static void Main(string[] args)
    {
        // Start with an empty list
        Node head = null;

        // Create the linked list: 15 -> 5 -> 6 -> 10 -> 17
        head = Push(head, 17);
        head = Push(head, 10);
        head = Push(head, 6);
        head = Push(head, 5);
        head = Push(head, 15);

        // Function call to count prime nodes and print the result
        Console.WriteLine("Count of prime nodes = " + CountPrimeRecursive(head));
    }
}

Javascript

// 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(head, new_data) {
    let new_node = new Node(new_data);
    new_node.next = head;
    head = new_node;
    return head;
}

// 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 (let i = 5; i * i <= n; i = i + 6)
        if (n % i === 0 || n % (i + 2) === 0)
            return false;

    return true;
}

// Function to count prime nodes in a linked list
function countPrimeRecursive(head) {
    if (head === null)
        return 0;

    let count = countPrimeRecursive(head.next);

    if (isPrime(head.data))
        count++;

    return count;
}

// Driver program
let head = null;

// Create the linked list: 15 -> 5 -> 6 -> 10 -> 17
head = push(head, 17);
head = push(head, 10);
head = push(head, 6);
head = push(head, 5);
head = push(head, 15);

// Function call to print the required answer
console.log("Count of prime nodes =", countPrimeRecursive(head));

Output

Count of prime nodes = 2

Time Complexity: O(N), where N is the number of nodes in the linked list.
Space Complexity: O(N), where N is the number of nodes in the linked list. This is because we create a recursive call stack for each node.