Delete all Non-Prime Nodes from a Singly Linked List

Given a singly linked list containing N nodes, the task is to delete all nodes from the list which are not prime.

Examples:

Input : List = 15 -> 16 -> 6 -> 7 -> 17 
Output : Final List = 7 -> 17

Input : List = 15 -> 3 -> 4 -> 2 -> 9 
Output : Final List = 3 ->2 

Approach: The idea is to traverse the nodes of the singly linked list one by one and get the pointer of the nodes which are not prime. Delete those nodes by following the approach used in the post: Delete a node from Linked List.

Below is the implementation of above idea: 

C++

// C++ implementation to delete all
// non-prime nodes from 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 delete all non-prime nodes
// from the singly linked list
void deleteNonPrimeNodes(Node** head_ref)
{
    // Remove all composite nodes at the beginning
    Node* ptr = *head_ref;
    while (ptr != NULL && !isPrime(ptr->data)) {
        Node* temp = ptr;
        ptr = ptr->next;
        delete (temp);
    }
    *head_ref = ptr;
    if (ptr == NULL)
        return;

    // Remove remaining nodes
    Node* curr = ptr->next;
    while (curr != NULL) {

        if (!isPrime(curr->data)) {
            ptr->next = curr->next;
            delete (curr);
            curr = ptr->next;
        }
        else {
            ptr = curr;
            curr = curr->next;
        }
    }
}

// function to print nodes in a
// given singly linked list
void printList(Node* head)
{
    while (head != NULL) {
        cout << head->data << " ";
        head = head->next;
    }
}

// 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);

    cout << "Original List: ";
    printList(head);

    deleteNonPrimeNodes(&head);

    cout << "\nModified List: ";
    printList(head);
}

Java

// Java implementation to delete all
// prime nodes from the singly
// linked list

import java.util.*;

// Node of the singly linked list
class Node {
    int data;
    Node next;
}
class GFG {
    // function to insert a node at the beginning
    // of the singly Linked List
    static 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 off the new node
        new_node.next = head_ref[0];

        // move the head to point to the new node
        head_ref[0] = new_node;
    }

    // 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 delete a node in a singly Linked List.
    // head_ref --> pointer to head node pointer.
    // del --> pointer to node to be deleted
    static void deleteNode(Node head_ref[], Node del)
    {

        // base case
        if (head_ref[0] == null || del == null)
            return;

        // If node to be deleted is head node
        if (head_ref[0] == del) {
            head_ref[0] = del.next;
            return;
        }

        // traverse list till not found
        // delete node
        Node temp = head_ref[0];
        while (temp.next != del) {
            temp = temp.next;
        }
        // copy address of node
        temp.next = del.next;

        // Finally, free the memory occupied by del
        del = null;
    }

    // function to delete all prime nodes
    // from the singly linked list
    static void deletePrimeNodes(Node head_ref[])
    {
        Node ptr = head_ref[0];
        Node next;
        while (ptr != null) {
            next = ptr.next;

            // if true, delete node 'ptr'
            if (isPrime(ptr.data) == false)
                deleteNode(head_ref, ptr);
            ptr = next;
        }
    }

    // function to print nodes in a
    // given singly linked list
    static void printList(Node head)
    {
        while (head != null) {
            System.out.print(head.data + " ");
            head = head.next;
        }
    }

    // Driver Code
    public static void main(String[] args)
    {
        // start with the empty list
        Node[] head_ref = new Node[1];
        head_ref[0] = null;

        // create the linked list
        // 15 -> 16 -> 7 -> 6 -> 17
        push(head_ref, 17);
        push(head_ref, 7);
        push(head_ref, 6);
        push(head_ref, 16);
        push(head_ref, 15);

        System.out.print("Original List: ");
        printList(head_ref[0]);

        deletePrimeNodes(head_ref);

        System.out.print("\nModified List: ");
        printList(head_ref[0]);
    }
}

// this code is contributed by shubhamrajput6156

Python3

# Python3 implementation to delete all
# non-prime nodes from the singly
# linked list
import math

# Node of the singly linked list


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):
    new_node = Node(new_data)
    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


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
    for i in range(5, n + 1, 6):
        if (i * i < n + 2 and
                (n % i == 0 or n % (i + 2) == 0)):
            return False

    return True

# function to delete all non-prime nodes
# from the singly linked list


def deleteNonPrimeNodes(head_ref):

    # Remove all composite nodes at the beginning
    ptr = head_ref
    while (ptr != None and
           isPrime(ptr.data) != True):
        temp = ptr
        ptr = ptr.next
        # delete(temp)

    head_ref = ptr
    if (ptr == None):
        return None

    # Remove remaining nodes
    curr = ptr.next
    while (curr != None):

        if (isPrime(curr.data) != True):
            ptr.next = curr.next
            # delete(curr)
            curr = ptr.next

        else:
            ptr = curr
            curr = curr.next

        return head_ref

# function to print nodes in a
# given singly linked list


def printList(head):
    while (head != None):
        print(head.data, end=" ")
        head = head.next


# Driver Code
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)

    print("Original List: ")
    printList(head)

    head = deleteNonPrimeNodes(head)

    print("\nModified List: ")
    printList(head)

# This code is contributed by AbhiThakur

C#

// C# implementation to delete all
// non-prime nodes from 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 delete all non-prime nodes
    // from the singly linked list
    static Node deleteNonPrimeNodes(Node head_ref)
    {
        // Remove all composite nodes
        // at the beginning
        Node ptr = head_ref;
        while (ptr != null && !isPrime(ptr.data)) {
            Node temp = ptr;
            ptr = ptr.next;
        }
        head_ref = ptr;
        if (ptr == null) {
            return null;
        }

        // Remove remaining nodes
        Node curr = ptr.next;
        while (curr != null) {
            if (!isPrime(curr.data)) {
                ptr.next = curr.next;
                curr = ptr.next;
            }
            else {
                ptr = curr;
                curr = curr.next;
            }
        }
        return head_ref;
    }

    // function to print nodes in a
    // given singly linked list
    static void printList(Node head)
    {
        while (head != null) {
            Console.Write(head.data + " ");
            head = head.next;
        }
    }

    // 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);

        Console.Write("Original List: ");
        printList(head);

        head = deleteNonPrimeNodes(head);

        Console.Write("\nModified List: ");
        printList(head);
    }
}

// This code is contributed by 29AjayKumar

Javascript

<script>
// javascript implementation to delete all
// non-prime nodes from 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) {
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 delete all non-prime nodes
    // from the singly linked list
    function deleteNonPrimeNodes(head_ref) {
        // Remove all composite nodes at the beginning
var ptr = head_ref;
        while (ptr != null && !isPrime(ptr.data)) {
    var temp = ptr;
            ptr = ptr.next;
        }
        head_ref = ptr;
        if (ptr == null)
            return null;

        // Remove remaining nodes
var curr = ptr.next;
        while (curr != null) {

            if (!isPrime(curr.data)) {
                ptr.next = curr.next;
                curr = ptr.next;
            } else {
                ptr = curr;
                curr = curr.next;
            }
        }
        return head_ref;
    }

    // function to print nodes in a
    // given singly linked list
    function printList(head) {
        while (head != null) {
            document.write(head.data + " ");
            head = head.next;
        }
    }

    // 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);

        document.write("Original List: ");
        printList(head);

        head = deleteNonPrimeNodes(head);

        document.write("<br/>Modified List: ");
        printList(head);

// This code contributed by aashish1995
</script>

Output

Original List: 15 16 6 7 17 
Modified List: 7 17 

Complexity Analysis:

• Time Complexity: O(N * sqrt(MAX) ) where N is the total number of nodes in the linked list and MAX is the maximum element in the array.
• Auxiliary Space: O(1).

Recursive Approach:

• Define a function called deleteNonPrimeNodesRecursive that takes a pointer to a node as its argument.
• If the given node is NULL (i.e., the end of the list has been reached), return NULL.
• Recursively call deleteNonPrimeNodesRecursive with the next node in the list as the argument.
• If the next node is NULL, return NULL.
• If the data in the next node is prime, return the next node.
• Otherwise, delete the next node, set the next pointer of the current node to the node after the deleted node, and recursively call deleteNonPrimeNodesRecursive with the current node as the argument.

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 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 delete all non-prime nodes recursively
Node* deleteNonPrimeNodes(Node* head)
{
    if (head == NULL) {
        return NULL;
    }
    if (isPrime(head->data)) {
        head->next = deleteNonPrimeNodes(head->next);
        return head;
    }
    return deleteNonPrimeNodes(head->next);
}

// function to print nodes in a given singly linked list
void printList(Node* head)
{
    while (head != NULL) {
        cout << head->data << " ";
        head = head->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;
}

// 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, 6);
    push(&head, 7);
    push(&head, 16);
    push(&head, 15);

    cout << "Original List: ";
    printList(head);

    head = deleteNonPrimeNodes(head);

    cout << "\nModified List: ";
    printList(head);
    return 0;
}

Java

class Node {
    int data;
    Node next;
}

public class DeleteNonPrimeNodes {

    // Function to check if a number is prime
    static boolean 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 delete all non-prime nodes recursively
    static Node deleteNonPrimeNodes(Node head) {
        if (head == null) {
            return null;
        }
        if (isPrime(head.data)) {
            head.next = deleteNonPrimeNodes(head.next);
            return head;
        }
        return deleteNonPrimeNodes(head.next);
    }

    // Function to print nodes in a given singly linked list
    static void printList(Node head) {
        while (head != null) {
            System.out.print(head.data + " ");
            head = head.next;
        }
    }

    // Function to insert a node at the beginning
    // of the singly Linked List
    static Node push(Node head, int new_data) {
        Node new_node = new Node();
        new_node.data = new_data;
        new_node.next = head;
        head = new_node;
        return head;
    }

    // Driver program
    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, 6);
        head = push(head, 7);
        head = push(head, 16);
        head = push(head, 15);

        System.out.print("Original List: ");
        printList(head);

        head = deleteNonPrimeNodes(head);

        System.out.print("\nModified List: ");
        printList(head);
    }
}
// This code is contributed by akshitaguprzj3

Python3

# Node of the singly linked list
class Node:
    def __init__(self, data):
        self.data = data
        self.next = None

# 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 delete all non-prime nodes recursively
def delete_non_prime_nodes(head):
    if head is None:
        return None
    if is_prime(head.data):
        head.next = delete_non_prime_nodes(head.next)
        return head
    return delete_non_prime_nodes(head.next)

# Function to print nodes in a given singly linked list
def print_list(head):
    while head:
        print(head.data, end=" ")
        head = head.next
    print()

# Function to insert a node at the beginning
# of the singly Linked List
def push(head_ref, new_data):
    new_node = Node(new_data)
    new_node.next = head_ref
    head_ref = new_node
    return head_ref

# 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, 6)
    head = push(head, 7)
    head = push(head, 16)
    head = push(head, 15)

    print("Original List:", end=" ")
    print_list(head)

    head = delete_non_prime_nodes(head)

    print("Modified List:", end=" ")
    print_list(head)

C#

using System;

// node of the singly linked list
public class node {
    public int data;
    public node next;
}
public class linkedList {
    // 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 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 delete all non-prime nodes recursively
    public static node DeleteNonPrimeNodes(node head)
    {
        if (head == null) {
            return null;
        }
        if (IsPrime(head.data)) {
            head.next = DeleteNonPrimeNodes(head.next);
            return head;
        }
        return DeleteNonPrimeNodes(head.next);
    }
    // Function to print nodes in a given
    // singly linked list
    public static void PrintList(node head)
    {
        while (head != null) {
            Console.Write(head.data + " ");
            head = head.next;
        }
    }
    // Function to insert a node at the beginning
    // of the singly Linked List
    public static void Push(ref 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;
    }
    // Driver program
    public static void Main()
    {
        // start with the empty list
        node head = null;
        // create the linked list
        // 15 -> 16 -> 7 -> 6 -> 17
        Push(ref head, 17);
        Push(ref head, 6);
        Push(ref head, 7);
        Push(ref head, 16);
        Push(ref head, 15);
        Console.Write("Original List: ");
        PrintList(head);
        head = DeleteNonPrimeNodes(head);
        Console.Write("\nModified List: ");
        PrintList(head);
    }
}

Javascript

class Node {
    constructor(data) {
        this.data = data;
        this.next = null;
    }
}

// Function to check if a number is prime
function isPrime(n) {
    if (n <= 1) return false;
    if (n <= 3) return true;
    if (n % 2 === 0 || n % 3 === 0) return false;

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

    return true;
}

// Function to delete all non-prime nodes recursively
function deleteNonPrimeNodes(head) {
    if (head === null) {
        return null;
    }
    if (isPrime(head.data)) {
        head.next = deleteNonPrimeNodes(head.next);
        return head;
    }
    return deleteNonPrimeNodes(head.next);
}

// Function to print nodes in a given singly linked list
function printList(head) {
    let current = head;
    while (current !== null) {
        console.log(current.data + " ");
        current = current.next;
    }
}

// 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;
}

// Driver program
let head = null;

// Create the 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);

console.log("Original List: ");
printList(head);

head = deleteNonPrimeNodes(head);

console.log("\nModified List: ");
printList(head);

Output

Original List: 15 16 7 6 17 
Modified List: 7 17 

Time Complexity: O(n), where n is the length of the linked list.

Auxiliary Space:  O(n), so the maximum depth of the recursive call stack is equal to the length of the linked list.