Check linked list with a loop is palindrome or not

Given a linked list with a loop, the task is to find whether it is palindrome or not. You are not allowed to remove the loop.  

Examples:

Input : 1 -> 2 -> 3 -> 2
             /|\      \|/
               ------- 1  
Output: Palindrome
Linked list is 1 2 3 2 1 which is a 
palindrome.

Input : 1 -> 2 -> 3 -> 4
             /|\      \|/
               ------- 1  
Output: Not Palindrome
Linked list is 1 2 3 4 1 which is a 
not palindrome. 

Algorithm:

1. Detect the loop using the Floyd Cycle Detection Algorithm.
2. Then find the starting node of the loop as discussed in this
3. Check the linked list is palindrome or not as discussed in this

Below is the implementation. 

C++

// C++ program to check if a linked list with
// loop is palindrome or not.
#include<bits/stdc++.h>
using namespace std;

/* Link list node */
struct Node
{
    int data;
    struct Node * next;
};

/* Function to find loop starting node.
loop_node --> Pointer to one of the loop nodes
head --> Pointer to the start node of the linked list */
Node* getLoopstart(Node *loop_node, Node *head)
{
    Node *ptr1 = loop_node;
    Node *ptr2 = loop_node;

    // Count the number of nodes in loop
    unsigned int k = 1, i;
    while (ptr1->next != ptr2)
    {
        ptr1 = ptr1->next;
        k++;
    }

    // Fix one pointer to head
    ptr1 = head;

    // And the other pointer to k nodes after head
    ptr2 = head;
    for (i = 0; i < k; i++)
        ptr2 = ptr2->next;

    /* Move both pointers at the same pace,
    they will meet at loop starting node */
    while (ptr2 != ptr1)
    {
        ptr1 = ptr1->next;
        ptr2 = ptr2->next;
    }
    return ptr1;
}

/* This function detects and find loop starting
  node  in the list*/
Node* detectAndgetLoopstarting(Node *head)
{
    Node *slow_p = head, *fast_p = head,*loop_start;

    //Start traversing list and detect loop
    while (slow_p && fast_p && fast_p->next)
    {
        slow_p = slow_p->next;
        fast_p = fast_p->next->next;

        /* If slow_p and fast_p meet then find
           the loop starting node*/
        if (slow_p == fast_p)
        {
            loop_start = getLoopstart(slow_p, head);
            break;
        }
    }

    // Return starting node of loop
    return loop_start;
}

// Utility function to check if a linked list with loop
// is palindrome with given starting point.
bool isPalindromeUtil(Node *head, Node* loop_start)
{
    Node *ptr = head;
    stack<int> s;

    // Traverse linked list until last node is equal
    // to loop_start and store the elements till start
    // in a stack
    int count = 0;
    while (ptr != loop_start || count != 1)
    {
        s.push(ptr->data);
        if (ptr == loop_start)
            count = 1;
        ptr = ptr->next;
    }
    ptr = head;
    count = 0;

    // Traverse linked list until last node is
    // equal to loop_start second time
    while (ptr != loop_start || count != 1)
    {
        // Compare data of node with the top of stack
        // If equal then continue
        if (ptr->data == s.top())
            s.pop();

        // Else return false
        else
            return false;

        if (ptr == loop_start)
            count = 1;
        ptr = ptr->next;
    }

    // Return true if linked list is palindrome
    return true;
}

// Function to find if linked list is palindrome or not
bool isPalindrome(Node* head)
{
    // Find the loop starting node
    Node* loop_start = detectAndgetLoopstarting(head);

    // Check if linked list is palindrome
    return isPalindromeUtil(head, loop_start);
}

Node *newNode(int key)
{
    Node *temp = new Node;
    temp->data = key;
    temp->next = NULL;
    return temp;
}

/* Driver program to test above function*/
int main()
{
    Node *head = newNode(50);
    head->next = newNode(20);
    head->next->next = newNode(15);
    head->next->next->next = newNode(20);
    head->next->next->next->next = newNode(50);

    /* Create a loop for testing */
    head->next->next->next->next->next = head->next->next;

    isPalindrome(head)? cout << "\nPalindrome"
                     : cout << "\nNot Palindrome";

    return 0;
}

Java

// Java program to check if a linked list
// with loop is palindrome or not.
import java.util.*;

class GfG
{

/* Link list node */
static class Node
{
    int data;
    Node next;
}

/* Function to find loop starting node.
loop_node --> Pointer to one of
the loop nodes head --> Pointer to
the start node of the linked list */
static Node getLoopstart(Node loop_node,
                            Node head)
{
    Node ptr1 = loop_node;
    Node ptr2 = loop_node;

    // Count the number of nodes in loop
    int k = 1, i;
    while (ptr1.next != ptr2)
    {
        ptr1 = ptr1.next;
        k++;
    }

    // Fix one pointer to head
    ptr1 = head;

    // And the other pointer to k
    // nodes after head
    ptr2 = head;
    for (i = 0; i < k; i++)
        ptr2 = ptr2.next;

    /* Move both pointers at the same pace,
    they will meet at loop starting node */
    while (ptr2 != ptr1)
    {
        ptr1 = ptr1.next;
        ptr2 = ptr2.next;
    }
    return ptr1;
}

/* This function detects and find
loop starting node in the list*/
static Node detectAndgetLoopstarting(Node head)
{
    Node slow_p = head, fast_p = head,loop_start = null;

    //Start traversing list and detect loop
    while (slow_p != null && fast_p != null &&
            fast_p.next != null)
    {
        slow_p = slow_p.next;
        fast_p = fast_p.next.next;

        /* If slow_p and fast_p meet then find
        the loop starting node*/
        if (slow_p == fast_p)
        {
            loop_start = getLoopstart(slow_p, head);
            break;
        }
    }

    // Return starting node of loop
    return loop_start;
}

// Utility function to check if
// a linked list with loop is
// palindrome with given starting point.
static boolean isPalindromeUtil(Node head,
                            Node loop_start)
{
    Node ptr = head;
    Stack<Integer> s = new Stack<Integer> ();

    // Traverse linked list until last node
    // is equal to loop_start and store the
    // elements till start in a stack
    int count = 0;
    while (ptr != loop_start || count != 1)
    {
        s.push(ptr.data);
        if (ptr == loop_start)
            count = 1;
        ptr = ptr.next;
    }
    ptr = head;
    count = 0;

    // Traverse linked list until last node is
    // equal to loop_start second time
    while (ptr != loop_start || count != 1)
    {
        // Compare data of node with the top of stack
        // If equal then continue
        if (ptr.data == s.peek())
            s.pop();

        // Else return false
        else
            return false;

        if (ptr == loop_start)
            count = 1;
        ptr = ptr.next;
    }

    // Return true if linked list is palindrome
    return true;
}

// Function to find if linked list
// is palindrome or not
static boolean isPalindrome(Node head)
{
    // Find the loop starting node
    Node loop_start = detectAndgetLoopstarting(head);

    // Check if linked list is palindrome
    return isPalindromeUtil(head, loop_start);
}

static Node newNode(int key)
{
    Node temp = new Node();
    temp.data = key;
    temp.next = null;
    return temp;
}

/* Driver code*/
public static void main(String[] args)
{
    Node head = newNode(50);
    head.next = newNode(20);
    head.next.next = newNode(15);
    head.next.next.next = newNode(20);
    head.next.next.next.next = newNode(50);

    /* Create a loop for testing */
    head.next.next.next.next.next = head.next.next;

    if(isPalindrome(head) == true)
        System.out.println("Palindrome");
    else
        System.out.println("Not Palindrome");

}
}

// This code is contributed by prerna saini

Python

# Python3 program to check if a linked list
# with loop is palindrome or not.

# Node class
class Node:

    # Constructor to initialize the node object
    def __init__(self, data):
        self.data = data
        self.next = None

# Function to find loop starting node.
# loop_node -. Pointer to one of
# the loop nodes head -. Pointer to
# the start node of the linked list
def getLoopstart(loop_node,head):

    ptr1 = loop_node
    ptr2 = loop_node

    # Count the number of nodes in loop
    k = 1
    i = 0
    while (ptr1.next != ptr2):

        ptr1 = ptr1.next
        k = k + 1


    # Fix one pointer to head
    ptr1 = head

    # And the other pointer to k
    # nodes after head
    ptr2 = head
    i = 0
    while ( i < k ) :
        ptr2 = ptr2.next
        i = i + 1

    # Move both pointers at the same pace,
    #they will meet at loop starting node */
    while (ptr2 != ptr1):

        ptr1 = ptr1.next
        ptr2 = ptr2.next

    return ptr1

# This function detects and find
# loop starting node in the list
def detectAndgetLoopstarting(head):

    slow_p = head
    fast_p = head
    loop_start = None

    # Start traversing list and detect loop
    while (slow_p != None and fast_p != None and
            fast_p.next != None) :

        slow_p = slow_p.next
        fast_p = fast_p.next.next

        # If slow_p and fast_p meet then find
        # the loop starting node
        if (slow_p == fast_p) :

            loop_start = getLoopstart(slow_p, head)
            break

    # Return starting node of loop
    return loop_start

# Utility function to check if
# a linked list with loop is
# palindrome with given starting point.
def isPalindromeUtil(head, loop_start):

    ptr = head
    s = []

    # Traverse linked list until last node
    # is equal to loop_start and store the
    # elements till start in a stack
    count = 0
    while (ptr != loop_start or count != 1):

        s.append(ptr.data)
        if (ptr == loop_start) :
            count = 1
        ptr = ptr.next

    ptr = head
    count = 0

    # Traverse linked list until last node is
    # equal to loop_start second time
    while (ptr != loop_start or count != 1):

        # Compare data of node with the top of stack
        # If equal then continue
        if (ptr.data == s[-1]):
            s.pop()

        # Else return False
        else:
            return False

        if (ptr == loop_start) :
            count = 1
        ptr = ptr.next

    # Return True if linked list is palindrome
    return True

# Function to find if linked list
# is palindrome or not
def isPalindrome(head) :

    # Find the loop starting node
    loop_start = detectAndgetLoopstarting(head)

    # Check if linked list is palindrome
    return isPalindromeUtil(head, loop_start)

def newNode(key) :

    temp = Node(0)
    temp.data = key
    temp.next = None
    return temp

# Driver code
head = newNode(50)
head.next = newNode(20)
head.next.next = newNode(15)
head.next.next.next = newNode(20)
head.next.next.next.next = newNode(50)

# Create a loop for testing
head.next.next.next.next.next = head.next.next

if(isPalindrome(head) == True):
    print("Palindrome")
else:
    print("Not Palindrome")

# This code is contributed by Arnab Kundu

C#

// C# program to check if a linked list
// with loop is palindrome or not.
using System;
using System.Collections.Generic;

class GfG
{

/* Link list node */
class Node
{
    public int data;
    public Node next;
}

/* Function to find loop starting node.
loop_node --> Pointer to one of
the loop nodes head --> Pointer to
the start node of the linked list */
static Node getLoopstart(Node loop_node,
                            Node head)
{
    Node ptr1 = loop_node;
    Node ptr2 = loop_node;

    // Count the number of nodes in loop
    int k = 1, i;
    while (ptr1.next != ptr2)
    {
        ptr1 = ptr1.next;
        k++;
    }

    // Fix one pointer to head
    ptr1 = head;

    // And the other pointer to k
    // nodes after head
    ptr2 = head;
    for (i = 0; i < k; i++)
        ptr2 = ptr2.next;

    /* Move both pointers at the same pace,
    they will meet at loop starting node */
    while (ptr2 != ptr1)
    {
        ptr1 = ptr1.next;
        ptr2 = ptr2.next;
    }
    return ptr1;
}

/* This function detects and find
loop starting node in the list*/
static Node detectAndgetLoopstarting(Node head)
{
    Node slow_p = head, fast_p = head,loop_start = null;

    //Start traversing list and detect loop
    while (slow_p != null && fast_p != null &&
            fast_p.next != null)
    {
        slow_p = slow_p.next;
        fast_p = fast_p.next.next;

        /* If slow_p and fast_p meet then find
        the loop starting node*/
        if (slow_p == fast_p)
        {
            loop_start = getLoopstart(slow_p, head);
            break;
        }
    }

    // Return starting node of loop
    return loop_start;
}

// Utility function to check if
// a linked list with loop is
// palindrome with given starting point.
static bool isPalindromeUtil(Node head,
                            Node loop_start)
{
    Node ptr = head;
    Stack<int> s = new Stack<int> ();

    // Traverse linked list until last node
    // is equal to loop_start and store the
    // elements till start in a stack
    int count = 0;
    while (ptr != loop_start || count != 1)
    {
        s.Push(ptr.data);
        if (ptr == loop_start)
            count = 1;
        ptr = ptr.next;
    }
    ptr = head;
    count = 0;

    // Traverse linked list until last node is
    // equal to loop_start second time
    while (ptr != loop_start || count != 1)
    {
        // Compare data of node with the top of stack
        // If equal then continue
        if (ptr.data == s.Peek())
            s.Pop();

        // Else return false
        else
            return false;

        if (ptr == loop_start)
            count = 1;
        ptr = ptr.next;
    }

    // Return true if linked list is palindrome
    return true;
}

// Function to find if linked list
// is palindrome or not
static bool isPalindrome(Node head)
{
    // Find the loop starting node
    Node loop_start = detectAndgetLoopstarting(head);

    // Check if linked list is palindrome
    return isPalindromeUtil(head, loop_start);
}

static Node newNode(int key)
{
    Node temp = new Node();
    temp.data = key;
    temp.next = null;
    return temp;
}

/* Driver code*/
public static void Main(String[] args)
{
    Node head = newNode(50);
    head.next = newNode(20);
    head.next.next = newNode(15);
    head.next.next.next = newNode(20);
    head.next.next.next.next = newNode(50);

    /* Create a loop for testing */
    head.next.next.next.next.next = head.next.next;

    if(isPalindrome(head) == true)
        Console.WriteLine("Palindrome");
    else
        Console.WriteLine("Not Palindrome");
}
}

/* This code is contributed by 29AjayKumar */

Javascript

<script>
// javascript program to check if a linked list
// with loop is palindrome or not.class GfG {

    /* Link list node */
    class Node {
        constructor() {
            this.data = 0;
            this.next = null;
        }
    }
    /*
     * Function to find loop starting node. loop_node --> Pointer to one of the loop
     * nodes head --> Pointer to the start node of the linked list
     */
    function getLoopstart(loop_node,  head) {
        var ptr1 = loop_node;
        var ptr2 = loop_node;

        // Count the number of nodes in loop
        var k = 1, i;
        while (ptr1.next != ptr2) {
            ptr1 = ptr1.next;
            k++;
        }

        // Fix one pointer to head
        ptr1 = head;

        // And the other pointer to k
        // nodes after head
        ptr2 = head;
        for (i = 0; i < k; i++)
            ptr2 = ptr2.next;

        /*
         * Move both pointers at the same pace, they will meet at loop starting node
         */
        while (ptr2 != ptr1) {
            ptr1 = ptr1.next;
            ptr2 = ptr2.next;
        }
        return ptr1;
    }

    /*
     * This function detects and find loop starting node in the list
     */
    function detectAndgetLoopstarting(head) {
        var slow_p = head, fast_p = head, loop_start = null;

        // Start traversing list and detect loop
        while (slow_p != null && fast_p != null && fast_p.next != null) {
            slow_p = slow_p.next;
            fast_p = fast_p.next.next;

            /*
             * If slow_p and fast_p meet then find the loop starting node
             */
            if (slow_p == fast_p) {
                loop_start = getLoopstart(slow_p, head);
                break;
            }
        }

        // Return starting node of loop
        return loop_start;
    }

    // Utility function to check if
    // a linked list with loop is
    // palindrome with given starting point.
    function isPalindromeUtil(head,  loop_start) {
        var ptr = head;
        var s =  [];

        // Traverse linked list until last node
        // is equal to loop_start and store the
        // elements till start in a stack
        var count = 0;
        while (ptr != loop_start || count != 1) {
            s.push(ptr.data);
            if (ptr == loop_start)
                count = 1;
            ptr = ptr.next;
        }
        ptr = head;
        count = 0;

        // Traverse linked list until last node is
        // equal to loop_start second time
        while (ptr != loop_start || count != 1) {
            // Compare data of node with the top of stack
            // If equal then continue
            var stk = s.pop();
            if (ptr.data == stk);


            // Else return false
            else{
            s.push(stk);
                return false;
                }

            if (ptr == loop_start)
                count = 1;
            ptr = ptr.next;
        }

        // Return true if linked list is palindrome
        return true;
    }

    // Function to find if linked list
    // is palindrome or not
    function isPalindrome(head) {
        // Find the loop starting node
        var loop_start = detectAndgetLoopstarting(head);

        // Check if linked list is palindrome
        return isPalindromeUtil(head, loop_start);
    }

    function newNode(key) {
        var temp = new Node();
        temp.data = key;
        temp.next = null;
        return temp;
    }

    /* Driver code */

        var head = newNode(50);
        head.next = newNode(20);
        head.next.next = newNode(15);
        head.next.next.next = newNode(20);
        head.next.next.next.next = newNode(50);

        /* Create a loop for testing */
        head.next.next.next.next.next = head.next.next;

        if (isPalindrome(head) == true)
            document.write("Palindrome");
        else
            document.write("Not Palindrome");


// This code contributed by aashish1995
</script>

Output

Palindrome

Time Complexity: O(n) 
Auxiliary Space: O(n) 

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