# Check linked list with a loop is palindrome or not

Last Updated : 06 Jul, 2022

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` `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 s = ``new` `Stack (); `   `    ``// 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

 ``

Output

`Palindrome`

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

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