# Find length of loop/cycle in given Linked List

Given the head of a linked list. The task is to find if a loop exists in the linked list if **yes** then return the **length of the loop** in the linked list else return **0**.

**Examples:**

Input:linked list =Output:4

Explanation: The loop is present in the below-linked list and the length of the loop is 4.

Input:linked list = 4 -> 3 -> 7 -> 9 -> 2Output:0

**Approach:** Below is the idea to solve the problem:

Floyd’s Cycle detection algorithm terminates when

fastandslowpointers meet at a common point. It is also known that this common point is one of the loop nodes. Store the address of this common point in a pointer variableptr. Then initialize a counter with1and start from thecommon pointand keeps on visiting the next node and increasing the counter till the common pointer is reached again. At that point, the value of the counter will be equal to the length of the loop.

Follow the below steps to implement the idea:

- Find the common point in the loop by using the Floyd’s Cycle detection algorithm
- Store the pointer in a temporary variable and keep a
**count = 0** - Traverse the linked list until the same node is reached again and increase the
**count**while moving to next node. - Print the count as length of loop

Below is the implementation of the above approach:

## C++

`// C++ program to count number of nodes` `// in loop in a linked list if loop is` `// present` `#include <bits/stdc++.h>` `using` `namespace` `std;` `/* Link list node */` `struct` `Node {` ` ` `int` `data;` ` ` `struct` `Node* next;` `};` `// Returns count of nodes present in loop.` `int` `countNodes(` `struct` `Node* n)` `{` ` ` `int` `res = 1;` ` ` `struct` `Node* temp = n;` ` ` `while` `(temp->next != n) {` ` ` `res++;` ` ` `temp = temp->next;` ` ` `}` ` ` `return` `res;` `}` `/* This function detects and counts loop` `nodes in the list. If loop is not there` `in then returns 0 */` `int` `countNodesinLoop(` `struct` `Node* list)` `{` ` ` `struct` `Node *slow_p = list, *fast_p = list;` ` ` `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 at` ` ` `some point then there is a loop */` ` ` `if` `(slow_p == fast_p)` ` ` `return` `countNodes(slow_p);` ` ` `}` ` ` `/* Return 0 to indicate that` ` ` `there is no loop*/` ` ` `return` `0;` `}` `struct` `Node* newNode(` `int` `key)` `{` ` ` `struct` `Node* temp` ` ` `= (` `struct` `Node*)` `malloc` `(` `sizeof` `(` `struct` `Node));` ` ` `temp->data = key;` ` ` `temp->next = NULL;` ` ` `return` `temp;` `}` `// Driver Code` `int` `main()` `{` ` ` `struct` `Node* head = newNode(1);` ` ` `head->next = newNode(2);` ` ` `head->next->next = newNode(3);` ` ` `head->next->next->next = newNode(4);` ` ` `head->next->next->next->next = newNode(5);` ` ` `/* Create a loop for testing */` ` ` `head->next->next->next->next->next = head->next;` ` ` `cout << countNodesinLoop(head) << endl;` ` ` `return` `0;` `}` `// This code is contributed by SHUBHAMSINGH10` |

## C

`// C program to count number of nodes` `// in loop in a linked list if loop is` `// present` `#include <stdio.h>` `#include <stdlib.h>` `/* Link list node */` `struct` `Node {` ` ` `int` `data;` ` ` `struct` `Node* next;` `};` `// Returns count of nodes present in loop.` `int` `countNodes(` `struct` `Node* n)` `{` ` ` `int` `res = 1;` ` ` `struct` `Node* temp = n;` ` ` `while` `(temp->next != n) {` ` ` `res++;` ` ` `temp = temp->next;` ` ` `}` ` ` `return` `res;` `}` `/* This function detects and counts loop` ` ` `nodes in the list. If loop is not there` ` ` `in then returns 0 */` `int` `countNodesinLoop(` `struct` `Node* list)` `{` ` ` `struct` `Node *slow_p = list, *fast_p = list;` ` ` `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 at some point` ` ` `then there is a loop */` ` ` `if` `(slow_p == fast_p)` ` ` `return` `countNodes(slow_p);` ` ` `}` ` ` `/* Return 0 to indicate that there is no loop*/` ` ` `return` `0;` `}` `struct` `Node* newNode(` `int` `key)` `{` ` ` `struct` `Node* temp` ` ` `= (` `struct` `Node*)` `malloc` `(` `sizeof` `(` `struct` `Node));` ` ` `temp->data = key;` ` ` `temp->next = NULL;` ` ` `return` `temp;` `}` `/* Driver program to test above function*/` `int` `main()` `{` ` ` `struct` `Node* head = newNode(1);` ` ` `head->next = newNode(2);` ` ` `head->next->next = newNode(3);` ` ` `head->next->next->next = newNode(4);` ` ` `head->next->next->next->next = newNode(5);` ` ` `/* Create a loop for testing */` ` ` `head->next->next->next->next->next = head->next;` ` ` `printf` `(` `"%d \n"` `, countNodesinLoop(head));` ` ` `return` `0;` `}` |

## Java

`// Java program to count number of nodes` `// in loop in a linked list if loop is` `// present` `import` `java.io.*;` `class` `GFG {` ` ` `/* Link list node */` ` ` `static` `class` `Node {` ` ` `int` `data;` ` ` `Node next;` ` ` `Node(` `int` `data)` ` ` `{` ` ` `this` `.data = data;` ` ` `next = ` `null` `;` ` ` `}` ` ` `}` ` ` `// Returns count of nodes present in loop.` ` ` `static` `int` `countNodes(Node n)` ` ` `{` ` ` `int` `res = ` `1` `;` ` ` `Node temp = n;` ` ` `while` `(temp.next != n) {` ` ` `res++;` ` ` `temp = temp.next;` ` ` `}` ` ` `return` `res;` ` ` `}` ` ` `/* This function detects and counts loop` ` ` `nodes in the list. If loop is not there` ` ` `in then returns 0 */` ` ` `static` `int` `countNodesinLoop(Node list)` ` ` `{` ` ` `Node slow_p = list, fast_p = list;` ` ` `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 at some point` ` ` `then there is a loop */` ` ` `if` `(slow_p == fast_p)` ` ` `return` `countNodes(slow_p);` ` ` `}` ` ` `/* Return 0 to indicate that there is no loop*/` ` ` `return` `0` `;` ` ` `}` ` ` `static` `Node newNode(` `int` `key)` ` ` `{` ` ` `Node temp = ` `new` `Node(key);` ` ` `return` `temp;` ` ` `}` ` ` `/* Driver program to test above function*/` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `Node head = newNode(` `1` `);` ` ` `head.next = newNode(` `2` `);` ` ` `head.next.next = newNode(` `3` `);` ` ` `head.next.next.next = newNode(` `4` `);` ` ` `head.next.next.next.next = newNode(` `5` `);` ` ` `/* Create a loop for testing */` ` ` `head.next.next.next.next.next = head.next;` ` ` `System.out.println(countNodesinLoop(head));` ` ` `}` `}` `// This code is contributed by inder_verma.` |

## Python3

`# Python 3 program to find the number` `# of nodes in loop in a linked list` `# if loop is present` `# Python Code to detect a loop and` `# find the length of the loop` `# Node defining class` `class` `Node:` ` ` `# Function to make a node` ` ` `def` `__init__(` `self` `, val):` ` ` `self` `.val ` `=` `val` ` ` `self` `.` `next` `=` `None` `# Linked List defining and loop` `# length finding class` `class` `LinkedList:` ` ` `# Function to initialize the` ` ` `# head of the linked list` ` ` `def` `__init__(` `self` `):` ` ` `self` `.head ` `=` `None` ` ` `# Function to insert a new` ` ` `# node at the end` ` ` `def` `AddNode(` `self` `, val):` ` ` `if` `self` `.head ` `is` `None` `:` ` ` `self` `.head ` `=` `Node(val)` ` ` `else` `:` ` ` `curr ` `=` `self` `.head` ` ` `while` `(curr.` `next` `):` ` ` `curr ` `=` `curr.` `next` ` ` `curr.` `next` `=` `Node(val)` ` ` `# Function to create a loop in the` ` ` `# Linked List. This function creates` ` ` `# a loop by connecting the last node` ` ` `# to n^th node of the linked list,` ` ` `# (counting first node as 1)` ` ` `def` `CreateLoop(` `self` `, n):` ` ` `# LoopNode is the connecting node to` ` ` `# the last node of linked list` ` ` `LoopNode ` `=` `self` `.head` ` ` `for` `_ ` `in` `range` `(` `1` `, n):` ` ` `LoopNode ` `=` `LoopNode.` `next` ` ` `# end is the last node of the Linked List` ` ` `end ` `=` `self` `.head` ` ` `while` `(end.` `next` `):` ` ` `end ` `=` `end.` `next` ` ` `# Creating the loop` ` ` `end.` `next` `=` `LoopNode` ` ` `# Function to detect the loop and return` ` ` `# the length of the loop if the returned` ` ` `# value is zero, that means that either` ` ` `# the linked list is empty or the linked` ` ` `# list doesn't have any loop` ` ` `def` `detectLoop(` `self` `):` ` ` `# if linked list is empty then there` ` ` `# is no loop, so return 0` ` ` `if` `self` `.head ` `is` `None` `:` ` ` `return` `0` ` ` `# Using Floyd’s Cycle-Finding` ` ` `# Algorithm/ Slow-Fast Pointer Method` ` ` `slow ` `=` `self` `.head` ` ` `fast ` `=` `self` `.head` ` ` `flag ` `=` `0` `# to show that both slow and fast` ` ` `# are at start of the Linked List` ` ` `while` `(slow ` `and` `slow.` `next` `and` `fast ` `and` ` ` `fast.` `next` `and` `fast.` `next` `.` `next` `):` ` ` `if` `slow ` `=` `=` `fast ` `and` `flag !` `=` `0` `:` ` ` `# Means loop is confirmed in the` ` ` `# Linked List. Now slow and fast` ` ` `# are both at the same node which` ` ` `# is part of the loop` ` ` `count ` `=` `1` ` ` `slow ` `=` `slow.` `next` ` ` `while` `(slow !` `=` `fast):` ` ` `slow ` `=` `slow.` `next` ` ` `count ` `+` `=` `1` ` ` `return` `count` ` ` `slow ` `=` `slow.` `next` ` ` `fast ` `=` `fast.` `next` `.` `next` ` ` `flag ` `=` `1` ` ` `return` `0` `# No loop` `# Setting up the code` `# Making a Linked List and adding the nodes` `myLL ` `=` `LinkedList()` `myLL.AddNode(` `1` `)` `myLL.AddNode(` `2` `)` `myLL.AddNode(` `3` `)` `myLL.AddNode(` `4` `)` `myLL.AddNode(` `5` `)` `# Creating a loop in the linked List` `# Loop is created by connecting the` `# last node of linked list to n^th node` `# 1<= n <= len(LinkedList)` `myLL.CreateLoop(` `2` `)` `# Checking for Loop in the Linked List` `# and printing the length of the loop` `loopLength ` `=` `myLL.detectLoop()` `if` `myLL.head ` `is` `None` `:` ` ` `print` `(` `"Linked list is empty"` `)` `else` `:` ` ` `print` `(` `str` `(loopLength))` `# This code is contributed by _Ashutosh` |

## C#

`// C# program to count number of nodes` `// in loop in a linked list if loop is` `// present` `using` `System;` `class` `GFG {` ` ` `/* Link list node */` ` ` `class` `Node {` ` ` `public` `int` `data;` ` ` `public` `Node next;` ` ` `public` `Node(` `int` `data)` ` ` `{` ` ` `this` `.data = data;` ` ` `next = ` `null` `;` ` ` `}` ` ` `}` ` ` `// Returns count of nodes present in loop.` ` ` `static` `int` `countNodes(Node n)` ` ` `{` ` ` `int` `res = 1;` ` ` `Node temp = n;` ` ` `while` `(temp.next != n) {` ` ` `res++;` ` ` `temp = temp.next;` ` ` `}` ` ` `return` `res;` ` ` `}` ` ` `/* This function detects and counts loop` ` ` `nodes in the list. If loop is not there` ` ` `in then returns 0 */` ` ` `static` `int` `countNodesinLoop(Node list)` ` ` `{` ` ` `Node slow_p = list, fast_p = list;` ` ` `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 at some point` ` ` `then there is a loop */` ` ` `if` `(slow_p == fast_p)` ` ` `return` `countNodes(slow_p);` ` ` `}` ` ` `/* Return 0 to indicate that there is no loop*/` ` ` `return` `0;` ` ` `}` ` ` `static` `Node newNode(` `int` `key)` ` ` `{` ` ` `Node temp = ` `new` `Node(key);` ` ` `return` `temp;` ` ` `}` ` ` `/* Driver code*/` ` ` `public` `static` `void` `Main(String[] args)` ` ` `{` ` ` `Node head = newNode(1);` ` ` `head.next = newNode(2);` ` ` `head.next.next = newNode(3);` ` ` `head.next.next.next = newNode(4);` ` ` `head.next.next.next.next = newNode(5);` ` ` `/* Create a loop for testing */` ` ` `head.next.next.next.next.next = head.next;` ` ` `Console.WriteLine(countNodesinLoop(head));` ` ` `}` `}` `// This code is contributed by Rajput-Ji` |

## Javascript

`<script>` `// javascript program to count number of nodes` `// in loop in a linked list if loop is` `// present` ` ` `/* Link list node */` `class Node {` ` ` `constructor(data) {` ` ` `this` `.data = data;` ` ` `this` `.next = ` `null` `;` ` ` `}` `}` ` ` `// Returns count of nodes present in loop.` ` ` `function` `countNodes( n) {` ` ` `var` `res = 1;` ` ` `temp = n;` ` ` `while` `(temp.next != n) {` ` ` `res++;` ` ` `temp = temp.next;` ` ` `}` ` ` `return` `res;` ` ` `}` ` ` `/*` ` ` `* This function detects and counts loop nodes in the list. If loop is not there` ` ` `* in then returns 0` ` ` `*/` ` ` `function` `countNodesinLoop( list) {` ` ` `var` `slow_p = list, fast_p = list;` ` ` `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 at some point then there is a loop` ` ` `*/` ` ` `if` `(slow_p == fast_p)` ` ` `return` `countNodes(slow_p);` ` ` `}` ` ` `/* Return 0 to indicate that there is no loop */` ` ` `return` `0;` ` ` `}` ` ` `function` `newNode(key) {` ` ` `temp = ` `new` `Node(key);` ` ` `return` `temp;` ` ` `}` ` ` `/* Driver program to test above function */` ` ` ` ` `head = newNode(1);` ` ` `head.next = newNode(2);` ` ` `head.next.next = newNode(3);` ` ` `head.next.next.next = newNode(4);` ` ` `head.next.next.next.next = newNode(5);` ` ` `/* Create a loop for testing */` ` ` `head.next.next.next.next.next = head.next;` ` ` `document.write(countNodesinLoop(head));` `// This code contributed by gauravrajput1` `</script>` |

**Output**

4

**Time complexity: **O(N), Only one traversal of the linked list is needed.**Auxiliary Space: **O(1), As no extra space is required.

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