Move the First Fibonacci Number to the End of a Linked List

Given a singly linked list, the task is to identify the first Fibonacci number in the list and move that node to the end of the linked list.

Examples:

Input: 10 -> 15 -> 8 -> 13 -> 21 -> 5 -> 2 -> NULL
Output: 10 -> 15 -> 13 -> 21 -> 5 -> 2 -> 8 -> NULL
Explanation: In the given list, the Fibonacci numbers are 8, 13, 21 and 2. The first Fibonacci number is 8, and we move the node containing 8 to the end.

Input: 3 -> 1 -> 4 -> 11 -> 6 -> 18 -> 24 -> NULL
Output: 1 -> 4 -> 11 -> 6 -> 18 -> 24 -> 3 -> NULL
Explanation: In the given list, the Fibonacci numbers are 3 and 1. The first Fibonacci number is 3, and we move the node containing 3 to the end.

Approach: To solve the problem follow the below idea:

The approach starts by traversing the linked list to identify the first Fibonacci number. It does this by iteratively checking if each number in the list is a Fibonacci number using the “isFibonacci” function. When the first Fibonacci number is found, it records both the node containing it and the previous node. Then, it adjusts the pointers to remove the first Fibonacci node from its current position and appends it to the end of the list. This approach efficiently handles various cases, ensuring that the first Fibonacci number is correctly moved to the list’s end while maintaining the order of other nodes.

Steps of the approach:

• Create a function, isFibonacci, to check if a given number is a Fibonacci number. This function iterates through Fibonacci numbers until it reaches or surpasses the given number.
• Implement the moveFirstFibonacciToEnd function to move the first Fibonacci number to the end of the linked list.
• Handle the edge cases: If the list is empty or has only one element, return the list as there’s no need to move any elements.
• Initialize pointers to traverse the list: prev, current, firstFibonacciPrev, and firstFibonacci.
• Traverse the list while checking each element. When you find the first Fibonacci number, store it in firstFibonacci and keep track of its previous node in firstFibonacciPrev.
• Remove the first Fibonacci node from the list by updating the next pointer of its previous node (or the head if it’s the first node).
• Traverse to the end of the list using the prev pointer and attach the firstFibonacci node to the end.
• Set the next pointer of the firstFibonacci node to nullptr to indicate it’s now the last element in the list.
• Return the updated head of the linked list.

Implementation of the above approach:

C++

// C++ code for the above approach:
#include <bits/stdc++.h>
using namespace std;

// Definition for singly-linked list
struct Node {
    int val;
    Node* next;
    Node(int x)
        : val(x)
        , next(nullptr)
    {
    }
};

// Function to check if a number
// is a Fibonacci number
bool isFibonacci(int num)
{
    if (num == 0 || num == 1) {
        return true;
    }
    int a = 0, b = 1;
    while (b < num) {
        int temp = b;
        b = a + b;
        a = temp;
    }
    return b == num;
}

// Function to move the first Fibonacci number
// to the end of the list
Node* moveFirstFibonacciToEnd(Node* head)
{

    // No need to move if the list has 0 or
    // 1 elements.
    if (!head || !head->next) {
        return head;
    }

    Node* prev = nullptr;
    Node* current = head;
    Node* firstFibonacciPrev = nullptr;
    Node* firstFibonacci = nullptr;

    // Find the first Fibonacci number
    while (current) {
        if (isFibonacci(current->val)) {
            firstFibonacciPrev = prev;
            firstFibonacci = current;
            break;
        }
        prev = current;
        current = current->next;
    }

    // No Fibonacci number found in the
    // list.
    if (!firstFibonacci) {
        return head;
    }

    // Remove the first Fibonacci node
    // from its position
    if (firstFibonacciPrev) {
        firstFibonacciPrev->next = firstFibonacci->next;
    }
    else {
        head = firstFibonacci->next;
    }

    // Move the first Fibonacci node to the end
    prev = current;
    while (prev->next) {
        prev = prev->next;
    }
    prev->next = firstFibonacci;
    firstFibonacci->next = nullptr;

    return head;
}

// Function to print the linked list
void printLinkedList(Node* head)
{
    while (head) {
        cout << head->val << " -> ";
        head = head->next;
    }
    cout << "NULL" << endl;
}

// Drivers code
int main()
{
    // Example 1:
    Node* head1 = new Node(10);
    head1->next = new Node(15);
    head1->next->next = new Node(8);
    head1->next->next->next = new Node(13);
    head1->next->next->next->next = new Node(21);
    head1->next->next->next->next->next = new Node(5);
    head1->next->next->next->next->next->next = new Node(2);

    cout << "Input: ";
    printLinkedList(head1);

    Node* newHead1 = moveFirstFibonacciToEnd(head1);

    cout << "Output: ";
    printLinkedList(newHead1);

    // Example 2:
    Node* head2 = new Node(3);
    head2->next = new Node(1);
    head2->next->next = new Node(4);
    head2->next->next->next = new Node(11);
    head2->next->next->next->next = new Node(6);
    head2->next->next->next->next->next = new Node(18);
    head2->next->next->next->next->next->next
        = new Node(24);

    cout << "Input: ";
    printLinkedList(head2);

    Node* newHead2 = moveFirstFibonacciToEnd(head2);

    cout << "Output: ";
    printLinkedList(newHead2);

    return 0;
}

Java

// Java code for moving the first Fibonacci number to the end of a linked list

class Node {
    int val;
    Node next;

    // Constructor for creating a new node with the given value
    public Node(int x) {
        val = x;
        next = null;
    }
}

public class MoveFibonacciToEnd {

    // Function to check if a number is a Fibonacci number
    static boolean isFibonacci(int num) {
        if (num == 0 || num == 1) {
            return true;
        }
        int a = 0, b = 1;
        while (b < num) {
            int temp = b;
            b = a + b;
            a = temp;
        }
        return b == num;
    }

    // Function to move the first Fibonacci number to the end of the list
    static Node moveFirstFibonacciToEnd(Node head) {
        // No need to move if the list has 0 or 1 elements
        if (head == null || head.next == null) {
            return head;
        }

        Node prev = null;
        Node current = head;
        Node firstFibonacciPrev = null;
        Node firstFibonacci = null;

        // Find the first Fibonacci number
        while (current != null) {
            if (isFibonacci(current.val)) {
                firstFibonacciPrev = prev;
                firstFibonacci = current;
                break;
            }
            prev = current;
            current = current.next;
        }

        // No Fibonacci number found in the list
        if (firstFibonacci == null) {
            return head;
        }

        // Remove the first Fibonacci node from its position
        if (firstFibonacciPrev != null) {
            firstFibonacciPrev.next = firstFibonacci.next;
        } else {
            head = firstFibonacci.next;
        }

        // Move the first Fibonacci node to the end
        prev = current;
        while (prev.next != null) {
            prev = prev.next;
        }
        prev.next = firstFibonacci;
        firstFibonacci.next = null;

        return head;
    }

    // Function to print the linked list
    static void printLinkedList(Node head) {
        while (head != null) {
            System.out.print(head.val + " -> ");
            head = head.next;
        }
        System.out.println("NULL");
    }

    // Driver's code
    public static void main(String[] args) {
        // Example 1:
        Node head1 = new Node(10);
        head1.next = new Node(15);
        head1.next.next = new Node(8);
        head1.next.next.next = new Node(13);
        head1.next.next.next.next = new Node(21);
        head1.next.next.next.next.next = new Node(5);
        head1.next.next.next.next.next.next = new Node(2);

        System.out.print("Input: ");
        printLinkedList(head1);

        Node newHead1 = moveFirstFibonacciToEnd(head1);

        System.out.print("Output: ");
        printLinkedList(newHead1);

        // Example 2:
        Node head2 = new Node(3);
        head2.next = new Node(1);
        head2.next.next = new Node(4);
        head2.next.next.next = new Node(11);
        head2.next.next.next.next = new Node(6);
        head2.next.next.next.next.next = new Node(18);
        head2.next.next.next.next.next.next = new Node(24);

        System.out.print("Input: ");
        printLinkedList(head2);

        Node newHead2 = moveFirstFibonacciToEnd(head2);

        System.out.print("Output: ");
        printLinkedList(newHead2);
    }
}

Python3

class Node:
    def __init__(self, x):
        self.val = x
        self.next = None


def is_fibonacci(num):
    if num == 0 or num == 1:
        return True
    a, b = 0, 1
    while b < num:
        temp = b
        b = a + b
        a = temp
    return b == num


def move_first_fibonacci_to_end(head):
    # No need to move if the list has 0 or 1 elements.
    if not head or not head.next:
        return head

    prev = None
    current = head
    first_fibonacci_prev = None
    first_fibonacci = None

    # Find the first Fibonacci number
    while current:
        if is_fibonacci(current.val):
            first_fibonacci_prev = prev
            first_fibonacci = current
            break
        prev = current
        current = current.next

    # No Fibonacci number found in the list.
    if not first_fibonacci:
        return head

    # Remove the first Fibonacci node from its position
    if first_fibonacci_prev:
        first_fibonacci_prev.next = first_fibonacci.next
    else:
        head = first_fibonacci.next

    # Move the first Fibonacci node to the end
    prev = current
    while prev.next:
        prev = prev.next
    prev.next = first_fibonacci
    first_fibonacci.next = None

    return head


def print_linked_list(head):
    while head:
        print(head.val, end=" -> ")
        head = head.next
    print("NULL")


# Driver Code
if __name__ == "__main__":
    # Example 1
    head1 = Node(10)
    head1.next = Node(15)
    head1.next.next = Node(8)
    head1.next.next.next = Node(13)
    head1.next.next.next.next = Node(21)
    head1.next.next.next.next.next = Node(5)
    head1.next.next.next.next.next.next = Node(2)

    print("Input:", end=" ")
    print_linked_list(head1)

    new_head1 = move_first_fibonacci_to_end(head1)

    print("Output:", end=" ")
    print_linked_list(new_head1)

    # Example 2
    head2 = Node(3)
    head2.next = Node(1)
    head2.next.next = Node(4)
    head2.next.next.next = Node(11)
    head2.next.next.next.next = Node(6)
    head2.next.next.next.next.next = Node(18)
    head2.next.next.next.next.next.next = Node(24)

    print("Input:", end=" ")
    print_linked_list(head2)

    new_head2 = move_first_fibonacci_to_end(head2)

    print("Output:", end=" ")
    print_linked_list(new_head2)

# This code is contributed by shivamgupta0987654321

C#

using System;

public class Node
{
    public int val;
    public Node next;

    public Node(int x)
    {
        val = x;
        next = null;
    }
}

public class LinkedListOperations
{
    public static bool IsFibonacci(int num)
    {
        if (num == 0 || num == 1)
            return true;

        int a = 0, b = 1;
        while (b < num)
        {
            int temp = b;
            b = a + b;
            a = temp;
        }
        return b == num;
    }

    public static Node MoveFirstFibonacciToEnd(Node head)
    {
        // No need to move if the list has 0 or 1 elements.
        if (head == null || head.next == null)
            return head;

        Node prev = null;
        Node current = head;
        Node firstFibonacciPrev = null;
        Node firstFibonacci = null;

        // Find the first Fibonacci number
        while (current != null)
        {
            if (IsFibonacci(current.val))
            {
                firstFibonacciPrev = prev;
                firstFibonacci = current;
                break;
            }
            prev = current;
            current = current.next;
        }

        // No Fibonacci number found in the list.
        if (firstFibonacci == null)
            return head;

        // Remove the first Fibonacci node from its position
        if (firstFibonacciPrev != null)
            firstFibonacciPrev.next = firstFibonacci.next;
        else
            head = firstFibonacci.next;

        // Move the first Fibonacci node to the end
        prev = current;
        while (prev.next != null)
            prev = prev.next;
        prev.next = firstFibonacci;
        firstFibonacci.next = null;

        return head;
    }

    public static void PrintLinkedList(Node head)
    {
        while (head != null)
        {
            Console.Write(head.val + " -> ");
            head = head.next;
        }
        Console.WriteLine("NULL");
    }

    // Driver Code
    public static void Main(string[] args)
    {
        // Example 1
        Node head1 = new Node(10);
        head1.next = new Node(15);
        head1.next.next = new Node(8);
        head1.next.next.next = new Node(13);
        head1.next.next.next.next = new Node(21);
        head1.next.next.next.next.next = new Node(5);
        head1.next.next.next.next.next.next = new Node(2);

        Console.Write("Input: ");
        PrintLinkedList(head1);

        Node newHead1 = MoveFirstFibonacciToEnd(head1);

        Console.Write("Output: ");
        PrintLinkedList(newHead1);

        // Example 2
        Node head2 = new Node(3);
        head2.next = new Node(1);
        head2.next.next = new Node(4);
        head2.next.next.next = new Node(11);
        head2.next.next.next.next = new Node(6);
        head2.next.next.next.next.next = new Node(18);
        head2.next.next.next.next.next.next = new Node(24);

        Console.Write("Input: ");
        PrintLinkedList(head2);

        Node newHead2 = MoveFirstFibonacciToEnd(head2);

        Console.Write("Output: ");
        PrintLinkedList(newHead2);
    }
}

Javascript

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

// Function to check if a number is a Fibonacci number
function isFibonacci(num) {
    if (num === 0 || num === 1) {
        return true;
    }
    let a = 0, b = 1;
    while (b < num) {
        const temp = b;
        b = a + b;
        a = temp;
    }
    return b === num;
}

// Function to move the first Fibonacci number to the end of the linked list
function moveFirstFibonacciToEnd(head) {
    if (!head || !head.next) {
        return head; // Return if the list has 0 or 1 elements
    }

    let prev = null;
    let current = head;
    let firstFibonacciPrev = null;
    let firstFibonacci = null;

    // Find the first Fibonacci number in the linked list
    while (current) {
        if (isFibonacci(current.val)) {
            firstFibonacciPrev = prev;
            firstFibonacci = current;
            break;
        }
        prev = current;
        current = current.next;
    }

    if (!firstFibonacci) {
        return head; // If no Fibonacci number found, return the original list
    }

    // Remove the first Fibonacci node from its position
    if (firstFibonacciPrev) {
        firstFibonacciPrev.next = firstFibonacci.next;
    } else {
        head = firstFibonacci.next;
    }

    // Move the first Fibonacci node to the end of the list
    prev = current;
    while (prev.next) {
        prev = prev.next;
    }
    prev.next = firstFibonacci;
    firstFibonacci.next = null;

    return head; // Return the updated head of the list
}

// Function to print the linked list
function printLinkedList(head) {
    while (head) {
        process.stdout.write(head.val + " -> ");
        head = head.next;
    }
    console.log("NULL");
}

// Driver Code
if (require.main === module) {
    // Example 1
    const head1 = new Node(10);
    head1.next = new Node(15);
    head1.next.next = new Node(8);
    head1.next.next.next = new Node(13);
    head1.next.next.next.next = new Node(21);
    head1.next.next.next.next.next = new Node(5);
    head1.next.next.next.next.next.next = new Node(2);

    process.stdout.write("Input: ");
    printLinkedList(head1);

    const newHead1 = moveFirstFibonacciToEnd(head1);

    process.stdout.write("Output: ");
    printLinkedList(newHead1);

    // Example 2
    const head2 = new Node(3);
    head2.next = new Node(1);
    head2.next.next = new Node(4);
    head2.next.next.next = new Node(11);
    head2.next.next.next.next = new Node(6);
    head2.next.next.next.next.next = new Node(18);
    head2.next.next.next.next.next.next = new Node(24);

    process.stdout.write("Input: ");
    printLinkedList(head2);

    const newHead2 = moveFirstFibonacciToEnd(head2);

    process.stdout.write("Output: ");
    printLinkedList(newHead2);
}

Output

Input: 10 -> 15 -> 8 -> 13 -> 21 -> 5 -> 2 -> NULL
Output: 10 -> 15 -> 13 -> 21 -> 5 -> 2 -> 8 -> NULL
Input: 3 -> 1 -> 4 -> 11 -> 6 -> 18 -> 24 -> NULL
Output: 1 -> 4 -> 11 -> 6 -> 18 -> 24 -> 3 -> N...

Time Complexity: O(n), where n is the number of nodes in the list.
Auxiliary Space: O(1) because it uses a constant amount of extra space.