Detect loop or cycle in a linked list

Last Updated : 24 Apr, 2024

Given a linked list, check if the linked list has a loop (cycle) or not. The below diagram shows a linked list with a loop.Â

Detect loop in a linked list using Hashing:

The idea is to insert the nodes in the hashmap and whenever a node is encountered that is already present in the hashmap then return true.

Follow the steps below to solve the problem:

• Traverse the list individually and keep putting the node addresses in a Hash Table.Â
• At any point, if NULL is reached then return falseÂ
• If the next of the current nodes points to any of the previously stored nodes in Â Hash then return true.

Below is the implementation of the above approach:

C++ ```// C++ program to detect loop in a linked list #include <bits/stdc++.h> using namespace std; /* Link list node */ struct Node { int data; struct Node* next; Node(int x) { data = x; next = NULL; } }; void push(struct Node** head_ref, int new_data) { /* allocate node and put in the data*/ struct Node* new_node = new Node(new_data); /* link the old list of the new node */ new_node->next = (*head_ref); /* move the head to point to the new node */ (*head_ref) = new_node; } // Returns true if there is a loop in linked list // else returns false. bool detectLoop(struct Node* h) { unordered_set<Node*> s; while (h != NULL) { // If this node is already present // in hashmap it means there is a cycle // (Because you will be encountering the // node for the second time). if (s.find(h) != s.end()) return true; // If we are seeing the node for // the first time, insert it in hash s.insert(h); h = h->next; } return false; } /* Driver program to test above function*/ int main() { /* Start with the empty list */ struct Node* head = NULL; push(&head, 20); push(&head, 4); push(&head, 15); push(&head, 10); /* Create a loop for testing */ head->next->next->next->next = head; if (detectLoop(head)) cout << "Loop Found"; else cout << "No Loop"; return 0; } ``` Java ```// Java program to detect loop in a linked list import java.util.*; public class LinkedList { static Node head; // head of list /* Linked list Node*/ static class Node { int data; Node next; Node(int x) { data = x; next = null; } } /* Inserts a new Node at front of the list. */ static public void push(int new_data) { /* 1 & 2: Allocate the Node & Put in the data*/ Node new_node = new Node(new_data); /* 3. Make next of new Node as head */ new_node.next = head; /* 4. Move the head to point to new Node */ head = new_node; } // Returns true if there is a loop in linked // list else returns false. static boolean detectLoop(Node h) { HashSet<Node> s = new HashSet<Node>(); while (h != null) { // If we have already has this node // in hashmap it means there is a cycle // (Because you we encountering the // node second time). if (s.contains(h)) return true; // If we are seeing the node for // the first time, insert it in hash s.add(h); h = h.next; } return false; } /* Driver program to test above function */ public static void main(String[] args) { LinkedList llist = new LinkedList(); llist.push(20); llist.push(4); llist.push(15); llist.push(10); /*Create loop for testing */ llist.head.next.next.next.next = llist.head; if (detectLoop(head)) System.out.println("Loop Found"); else System.out.println("No Loop"); } } // This code is contributed by Arnav Kr. Mandal. ``` Python3 ```# Python3 program to detect loop # in the linked list # Node class class Node: # Constructor to initialize # the node object def __init__(self, x): self.data = x self.next = None class LinkedList: # Function to initialize head def __init__(self): self.head = None # Function to insert a new # node at the beginning def push(self, new_data): new_node = Node(new_data) new_node.next = self.head self.head = new_node # Utility function to print it # the linked LinkedList def printList(self): temp = self.head while(temp): print(temp.data, end=" ") temp = temp.next def detectLoop(self): s = set() temp = self.head while (temp): # If we already have # this node in hashmap it # means there is a cycle # (Because we are encountering # the node second time). if (temp in s): return True # If we are seeing the node for # the first time, insert it in hash s.add(temp) temp = temp.next return False # Driver program for testing llist = LinkedList() llist.push(20) llist.push(4) llist.push(15) llist.push(10) # Create a loop for testing llist.head.next.next.next.next = llist.head if(llist.detectLoop()): print("Loop Found") else: print("No Loop ") # This code is contributed by Gitanjali. ``` C# ```// C# program to detect loop in a linked list using System; using System.Collections.Generic; class LinkedList { // head of list public Node head; /* Linked list Node*/ public class Node { public int data; public Node next; public Node(int x) { data = x; next = null; } } /* Inserts a new Node at front of the list. */ public void push(int new_data) { /* 1 & 2: Allocate the Node & Put in the data*/ Node new_node = new Node(new_data); /* 3. Make next of new Node as head */ new_node.next = head; /* 4. Move the head to point to new Node */ head = new_node; } // Returns true if there is a loop in linked // list else returns false. public static bool detectLoop(Node h) { HashSet<Node> s = new HashSet<Node>(); while (h != null) { // If we have already has this node // in hashmap it means there is a cycle // (Because you we encountering the // node second time). if (s.Contains(h)) return true; // If we are seeing the node for // the first time, insert it in hash s.Add(h); h = h.next; } return false; } /* Driver code*/ public static void Main(String[] args) { LinkedList llist = new LinkedList(); llist.push(20); llist.push(4); llist.push(15); llist.push(10); /*Create loop for testing */ llist.head.next.next.next.next = llist.head; if (detectLoop(llist.head)) Console.WriteLine("Loop Found"); else Console.WriteLine("No Loop"); } } // This code has been contributed by 29AjayKumar ``` Javascript ```<script> // JavaScript program to detect loop in a linked list var head; // head of list /* Linked list Node */ class Node { constructor(x) { this.data = x; this.next = null; } } /* Inserts a new Node at front of the list. */ function push(new_data) { /* * 1 & 2: Allocate the Node & Put in the data */ var new_node = new Node(new_data); /* 3. Make next of new Node as head */ new_node.next = head; /* 4. Move the head to point to new Node */ head = new_node; } // Returns true if there is a loop in linked // list else returns false. function detectLoop(h) { var s = new Set(); while (h != null) { // If we have already has this node // in hashmap it means there is a cycle // (Because you we encountering the // node second time). if (s.has(h)) return true; // If we are seeing the node for // the first time, insert it in hash s.add(h); h = h.next; } return false; } /* Driver program to test above function */ push(20); push(4); push(15); push(10); /* Create loop for testing */ head.next.next.next.next = head; if (detectLoop(head)) document.write("Loop Found"); else document.write("No Loop"); // This code is contributed by todaysgaurav </script> ```

Output
```Loop Found
```

Time complexity: O(N), Only one traversal of the loop is needed.
Auxiliary Space: O(N),Â N is the space required to store the value in the hashmap.

Detect loop in a linked list by Modification In Node Structure:

The idea is to modify the node structure by adding flag in it and mark the flag whenever visit the node.

Follow the steps below to solve the problem:

• Have a visited flag with each node.
• Traverse the linked list and keep marking visited nodes.
• If you see a visited node again then there is a loop.

Below is the implementation of the above approach.

C++ ```// C++ program to detect loop in a linked list #include <bits/stdc++.h> using namespace std; /* Link list node */ struct Node { int data; struct Node* next; int flag; Node(int x) { data = x; next = NULL; flag = 0; } }; void push(struct Node** head_ref, int new_data) { /* allocate node */ struct Node* new_node = new Node(new_data); /* link the old list of the new node */ new_node->next = (*head_ref); /* move the head to point to the new node */ (*head_ref) = new_node; } // Returns true if there is a loop in linked list // else returns false. bool detectLoop(struct Node* h) { while (h != NULL) { // If this node is already traverse // it means there is a cycle // (Because you we encountering the // node for the second time). if (h->flag == 1) return true; // If we are seeing the node for // the first time, mark its flag as 1 h->flag = 1; h = h->next; } return false; } /* Driver program to test above function*/ int main() { /* Start with the empty list */ struct Node* head = NULL; push(&head, 20); push(&head, 4); push(&head, 15); push(&head, 10); /* Create a loop for testing */ head->next->next->next->next = head; if (detectLoop(head)) cout << "Loop Found"; else cout << "No Loop"; return 0; } // This code is contributed by Geetanjali ``` C ```// C program to detect loop in a linked list #include <stdbool.h> #include <stdio.h> #include <stdlib.h> /* Link list node */ typedef struct Node { int data; struct Node* next; int flag; } Node; void push(struct Node** head_ref, int new_data) { /* allocate node */ struct Node* new_node = (Node*)malloc(sizeof(Node)); /* put in the data */ new_node->data = new_data; new_node->flag = 0; /* link the old list of the new node */ new_node->next = (*head_ref); /* move the head to point to the new node */ (*head_ref) = new_node; } // Returns true if there is a loop in linked list // else returns false. bool detectLoop(struct Node* h) { while (h != NULL) { // If this node is already traverse // it means there is a cycle // (Because you we encountering the // node for the second time). if (h->flag == 1) return true; // If we are seeing the node for // the first time, mark its flag as 1 h->flag = 1; h = h->next; } return false; } /* Driver program to test above function*/ int main() { /* Start with the empty list */ struct Node* head = NULL; push(&head, 20); push(&head, 4); push(&head, 15); push(&head, 10); /* Create a loop for testing */ head->next->next->next->next = head; if (detectLoop(head)) printf("Loop Found"); else printf("No Loop"); return 0; } // This code is contributed by Aditya Kumar (adityakumar129) ``` Java ```// Java program to detect loop in a linked list import java.util.*; class GFG { // Link list node static class Node { int data; Node next; int flag; Node(int x) { data = x; next = null; flag = 0; } }; static Node push(Node head_ref, int new_data) { // Allocate node Node new_node = new Node(new_data); // Link the old list of the new node new_node.next = head_ref; // Move the head to point to the new node head_ref = new_node; return head_ref; } // Returns true if there is a loop in linked // list else returns false. static boolean detectLoop(Node h) { while (h != null) { // If this node is already traverse // it means there is a cycle // (Because you we encountering the // node for the second time). if (h.flag == 1) return true; // If we are seeing the node for // the first time, mark its flag as 1 h.flag = 1; h = h.next; } return false; } // Driver code public static void main(String[] args) { // Start with the empty list Node head = null; head = push(head, 20); head = push(head, 4); head = push(head, 15); head = push(head, 10); // Create a loop for testing head.next.next.next.next = head; if (detectLoop(head)) System.out.print("Loop Found"); else System.out.print("No Loop"); } } // This code is contributed by Rajput-Ji ``` Python3 ```# Python3 program to detect loop in a linked list ''' Link list node ''' class Node: def __init__(self, x): self.data = x self.next = None self.flag = 0 def push(head_ref, new_data): ''' allocate node and put in the data''' new_node = Node(new_data) new_node.flag = 0 ''' link the old list of the new node ''' new_node.next = (head_ref) ''' move the head to point to the new node ''' (head_ref) = new_node return head_ref # Returns true if there is a loop in linked list # else returns false. def detectLoop(h): while (h != None): # If this node is already traverse # it means there is a cycle # (Because you we encountering the # node for the second time). if (h.flag == 1): return True # If we are seeing the node for # the first time, mark its flag as 1 h.flag = 1 h = h.next return False ''' Driver program to test above function''' if __name__ == '__main__': ''' Start with the empty list ''' head = None head = push(head, 20) head = push(head, 4) head = push(head, 15) head = push(head, 10) ''' Create a loop for testing ''' head.next.next.next.next = head if (detectLoop(head)): print("Loop Found") else: print("No Loop") ``` C# ```// C# program to detect loop in a linked list using System; class GFG { // Link list node class Node { public int data; public Node next; public int flag; public Node(int x) { data = x; next = null; flag = 0; } }; static Node push(Node head_ref, int new_data) { // Allocate node Node new_node = new Node(new_data); // Link the old list of the new node new_node.next = head_ref; // Move the head to point to the new node head_ref = new_node; return head_ref; } // Returns true if there is a loop in linked // list else returns false. static bool detectLoop(Node h) { while (h != null) { // If this node is already traverse // it means there is a cycle // (Because you we encountering the // node for the second time). if (h.flag == 1) return true; // If we are seeing the node for // the first time, mark its flag as 1 h.flag = 1; h = h.next; } return false; } // Driver code public static void Main(string[] args) { // Start with the empty list Node head = null; head = push(head, 20); head = push(head, 4); head = push(head, 15); head = push(head, 10); // Create a loop for testing head.next.next.next.next = head; if (detectLoop(head)) Console.Write("Loop Found"); else Console.Write("No Loop"); } } // This code is contributed by pratham76 ``` Javascript ```<script> // JavaScript program to detect loop in a linked list // Link list node class Node { constructor(x) { this.data = x; this.next = null; this.flag = 0; } } function push( head_ref, new_data) { // Allocate node let new_node = new Node(); // Put in the data new_node.data = new_data; new_node.flag = 0; // Link the old list of the new node new_node.next = head_ref; // Move the head to point to the new node head_ref = new_node; return head_ref; } // Returns true if there is a loop in linked // list else returns false. function detectLoop(h) { while (h != null) { // If this node is already traverse // it means there is a cycle // (Because you we encountering the // node for the second time). if (h.flag == 1) return true; // If we are seeing the node for // the first time, mark its flag as 1 h.flag = 1; h = h.next; } return false; } // Driver code // Start with the empty list let head = null; head = push(head, 20); head = push(head, 4); head = push(head, 15); head = push(head, 10); // Create a loop for testing head.next.next.next.next = head; if (detectLoop(head)) document.write("Loop Found"); else document.write("No Loop"); // This code is contributed by rag2127 </script> ```

Output
```Loop Found
```

Time complexity: O(N), Only one traversal of the loop is needed.
Auxiliary Space: O(1)

Detect loop in a linked list using Floyd’s Cycle-Finding Algorithm:

This algorithm is used to find a loop in a linked list. It uses two pointers one moving twice as fast as the other one. The faster one is called the faster pointer and the other one is called the slow pointer.

Follow the steps below to solve the problem:

• Traverse linked list using two pointers.
• Move one pointer(slow_p) by one and another pointer(fast_p) by two.
• If these pointers meet at the same node then there is a loop. If pointers do not meet then the linked list doesn’t have a loop.

Illustration:

Implementation of Floyd’s Cycle-Finding Algorithm:Â Â

C++ ```// C++ program to detect loop in a linked list #include <bits/stdc++.h> using namespace std; /* Link list node */ class Node { public: int data; Node* next; Node(int x) { data = x; next = NULL; } }; void push(Node** head_ref, int new_data) { /* allocate node and put in the data*/ Node* new_node = new Node(new_data); /* link the old list of the new node */ new_node->next = (*head_ref); /* move the head to point to the new node */ (*head_ref) = new_node; } int detectLoop(Node* list) { 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 == fast_p) { return 1; } } return 0; } /* Driver code*/ int main() { /* Start with the empty list */ Node* head = NULL; push(&head, 20); push(&head, 4); push(&head, 15); push(&head, 10); /* Create a loop for testing */ head->next->next->next->next = head; if (detectLoop(head)) cout << "Loop Found"; else cout << "No Loop"; return 0; } // This is code is contributed by Nidhi goel. ``` C ```// C program to detect loop in a linked list #include <stdio.h> #include <stdlib.h> /* Link list node */ struct Node { int data; struct Node* next; }; void push(struct Node** head_ref, int new_data) { /* allocate node */ struct Node* new_node = (struct Node*)malloc(sizeof(struct Node)); /* put in the data */ new_node->data = new_data; /* link the old list of the new node */ new_node->next = (*head_ref); /* move the head to point to the new node */ (*head_ref) = new_node; } int detectLoop(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 == fast_p) { return 1; } } return 0; } /* Driver program to test above function*/ int main() { /* Start with the empty list */ struct Node* head = NULL; push(&head, 20); push(&head, 4); push(&head, 15); push(&head, 10); /* Create a loop for testing */ head->next->next->next->next = head; if (detectLoop(head)) printf("Loop Found"); else printf("No Loop"); return 0; } ``` Java ```// Java program to detect loop in a linked list import java.io.*; class LinkedList { Node head; // head of list /* Linked list Node*/ class Node { int data; Node next; Node(int x) { data = x; next = null; } } /* Inserts a new Node at front of the list. */ public void push(int new_data) { /* 1 & 2: Allocate the Node & Put in the data*/ Node new_node = new Node(new_data); /* 3. Make next of new Node as head */ new_node.next = head; /* 4. Move the head to point to new Node */ head = new_node; } void detectLoop() { Node slow_p = head, fast_p = head; int flag = 0; 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 == fast_p) { flag = 1; break; } } if (flag == 1) System.out.println("Loop Found"); else System.out.println("No Loop"); } /* Driver program to test above functions */ public static void main(String args[]) { LinkedList llist = new LinkedList(); llist.push(20); llist.push(4); llist.push(15); llist.push(10); /*Create loop for testing */ llist.head.next.next.next.next = llist.head; llist.detectLoop(); } } /* This code is contributed by Rajat Mishra. */ ``` Python ```# Python program to detect loop in the linked list # Node class class Node: # Constructor to initialize the node object def __init__(self, x): self.data = x self.next = None class LinkedList: # Function to initialize head def __init__(self): self.head = None # Function to insert a new node at the beginning def push(self, new_data): new_node = Node(new_data) new_node.next = self.head self.head = new_node # Utility function to print it the linked LinkedList def printList(self): temp = self.head while(temp): print(temp.data) temp = temp.next def detectLoop(self): slow_p = self.head fast_p = self.head while(slow_p and fast_p and fast_p.next): slow_p = slow_p.next fast_p = fast_p.next.next if slow_p == fast_p: return 1 return 0 # Driver program for testing llist = LinkedList() llist.push(20) llist.push(4) llist.push(15) llist.push(10) # Create a loop for testing llist.head.next.next.next.next = llist.head if(llist.detectLoop()): print("Loop Found") else: print("No Loop") # This code is contributed by Nikhil Kumar Singh(nickzuck_007) ``` C# ```// C# program to detect loop in a linked list using System; public class LinkedList { Node head; // head of list /* Linked list Node*/ public class Node { public int data; public Node next; public Node(int x) { data = x; next = null; } } /* Inserts a new Node at front of the list. */ public void push(int new_data) { /* 1 & 2: Allocate the Node & Put in the data*/ Node new_node = new Node(new_data); /* 3. Make next of new Node as head */ new_node.next = head; /* 4. Move the head to point to new Node */ head = new_node; } Boolean detectLoop() { Node slow_p = head, fast_p = head; 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 == fast_p) { return true; } } return false; } /* Driver code */ public static void Main(String[] args) { LinkedList llist = new LinkedList(); llist.push(20); llist.push(4); llist.push(15); llist.push(10); /*Create loop for testing */ llist.head.next.next.next.next = llist.head; Boolean found = llist.detectLoop(); if (found) { Console.WriteLine("Loop Found"); } else { Console.WriteLine("No Loop"); } } } // This code is contributed by Princi Singh ``` Javascript ```<script> // Javascript program to detect loop in a linked list let head; // head of list /* Linked list Node*/ class Node { constructor(x) { this.data = x; this.next = null; } } /* Inserts a new Node at front of the list. */ function push(new_data) { /* 1 & 2: Allocate the Node & Put in the data*/ let new_node = new Node(new_data); /* 3. Make next of new Node as head */ new_node.next = head; /* 4. Move the head to point to new Node */ head = new_node; } function detectLoop() { let slow_p = head, fast_p = head; let flag = 0; 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 == fast_p) { flag = 1; break; } } if (flag == 1) document.write("Loop Found<br>"); else document.write("No Loop<br>"); } // Driver code push(20); push(4); push(15); push(10); // Create loop for testing head.next.next.next.next = head; detectLoop(); // This code is contributed by avanitrachhadiya2155 </script> ```

Output
```Loop Found
```

Time complexity: O(N), Only one traversal of the loop is needed.
Auxiliary Space: O(1).Â

Detect loop in a linked list by Marking visited nodes without modifying Node structure:

The idea is to point the current node of the linked list to a node which is created. Whenever a node’s next is pointing to that node it means loop is there.

Follow the steps below to solve the problem:

• A temporary node is created.Â
• The next pointer of each node that is traversed is made to point to this temporary node.Â
• This way we are using the next pointer of a node as a flag to indicate whether the node has been traversed or not.Â
• Every node is checked to see if the next is pointing to a temporary node or not.
• In the case of the first node of the loop, the second time we traverse it this condition will be true, hence we find that loop exists.Â
• If we come across a node that points to null then the loop doesnâ€™t exist.

Below is the implementation of the above approach:

C++ ```// C++ program to return first node of loop #include <bits/stdc++.h> using namespace std; struct Node { int data; struct Node* next; Node(int x) { data = x; next = NULL; } }; // A utility function to print a linked list void printList(Node* head) { while (head != NULL) { cout << head->data << " "; head = head->next; } cout << endl; } // Function to detect first node of loop // in a linked list that may contain loop bool detectLoop(Node* head) { // Create a temporary node Node* temp = new Node(0); while (head != NULL) { // This condition is for the case when there is no // loop if (head->next == NULL) return false; // Check if next is already pointing to temp if (head->next == temp) return true; // Store the pointer to the next node // in order to get to it in the next step Node* next = head->next; // Make next point to temp head->next = temp; // Get to the next node in the list head = next; } return false; } /* Driver program to test above function*/ int main() { Node* head = new Node(1); head->next = new Node(2); head->next->next = new Node(3); head->next->next->next = new Node(4); head->next->next->next->next = new Node(5); /* Create a loop for testing(5 is pointing to 3) */ head->next->next->next->next->next = head->next->next; bool found = detectLoop(head); if (found) cout << "Loop Found"; else cout << "No Loop"; return 0; } ``` C ```// C++ program to return first node of loop #include <stdbool.h> #include <stdio.h> #include <stdlib.h> typedef struct Node { int data; struct Node* next; } Node; Node* newNode(int x) { Node* temp = (Node*)malloc(sizeof(Node)); temp->data = x; temp->next = NULL; return temp; } // A utility function to print a linked list void printList(Node* head) { while (head != NULL) { printf("%d ", head->data); head = head->next; } printf("\n"); } // Function to detect first node of loop // in a linked list that may contain loop bool detectLoop(Node* head) { // Create a temporary node Node* temp = (Node*)malloc(sizeof(Node)); while (head != NULL) { // This condition is for the case when there is no // loop if (head->next == NULL) return false; // Check if next is already pointing to temp if (head->next == temp) return true; // Store the pointer to the next node // in order to get to it in the next step Node* next = head->next; // Make next point to temp head->next = temp; // Get to the next node in the list head = next; } return false; } /* Driver program to test above function*/ int main() { 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(5 is pointing to 3) */ head->next->next->next->next->next = head->next->next; bool found = detectLoop(head); if (found) printf("Loop Found"); else printf("No Loop"); return 0; } // This code is contributed by Aditya Kumar (adityakumar129) ``` Java ```// Java program to return first node of loop public class GFG { static class Node { int data; Node next; Node(int x) { data = x; next = null; } }; // A utility function to print a linked list static void printList(Node head) { while (head != null) { System.out.print(head.data + " "); head = head.next; } System.out.println(); } // Function to detect first node of loop // in a linked list that may contain loop static boolean detectLoop(Node head) { // Create a temporary node Node temp = new Node(0); while (head != null) { // This condition is for the case // when there is no loop if (head.next == null) { return false; } // Check if next is already // pointing to temp if (head.next == temp) { return true; } // Store the pointer to the next node // in order to get to it in the next step Node next = head.next; // Make next point to temp head.next = temp; // Get to the next node in the list head = next; } return false; } // Driver code public static void main(String args[]) { Node head = new Node(1); head.next = new Node(2); head.next.next = new Node(3); head.next.next.next = new Node(4); head.next.next.next.next = new Node(5); // Create a loop for testing(5 is pointing to 3) / head.next.next.next.next.next = head.next.next; boolean found = detectLoop(head); if (found) System.out.println("Loop Found"); else System.out.println("No Loop"); } }; // This code is contributed by Arnab Kundu ``` Python3 ```# Python3 program to return first node of loop # A binary tree node has data, pointer to # left child and a pointer to right child # Helper function that allocates a new node # with the given data and None left and # right pointers class newNode: def __init__(self, x): self.data = x self.left = None # A utility function to print a linked list def printList(head): while (head != None): print(head.data, end=" ") head = head.next print() # Function to detect first node of loop # in a linked list that may contain loop def detectLoop(head): # Create a temporary node temp = "" while (head != None): # This condition is for the case # when there is no loop if (head.next == None): return False # Check if next is already # pointing to temp if (head.next == temp): return True # Store the pointer to the next node # in order to get to it in the next step next = head.next # Make next point to temp head.next = temp # Get to the next node in the list head = next return False # Driver Code 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(5 is pointing to 3) head.next.next.next.next.next = head.next.next found = detectLoop(head) if (found): print("Loop Found") else: print("No Loop") # This code is contributed by SHUBHAMSINGH10 ``` C# ```// C# program to return first node of loop using System; public class GFG { public class Node { public int data; public Node next; public Node(int x) { data = x; next = null; } }; // A utility function to print a linked list static void printList(Node head) { while (head != null) { Console.Write(head.data + " "); head = head.next; } Console.WriteLine(); } // Function to detect first node of loop // in a linked list that may contain loop static Boolean detectLoop(Node head) { // Create a temporary node Node temp = new Node(0); while (head != null) { // This condition is for the case // when there is no loop if (head.next == null) { return false; } // Check if next is already // pointing to temp if (head.next == temp) { return true; } // Store the pointer to the next node // in order to get to it in the next step Node next = head.next; // Make next point to temp head.next = temp; // Get to the next node in the list head = next; } return false; } // Driver code public static void Main(String[] args) { Node head = new Node(1); head.next = new Node(2); head.next.next = new Node(3); head.next.next.next = new Node(4); head.next.next.next.next = new Node(5); // Create a loop for testing(5 is pointing to 3) head.next.next.next.next.next = head.next.next; Boolean found = detectLoop(head); if (found) { Console.WriteLine("Loop Found"); } else { Console.WriteLine("No Loop"); } } } ``` Javascript ```<script> // Javascript program to return first node of loop class Node { constructor(x) { this.data = x; this.next = null; } } // A utility function to print a linked list function printList(head) { while (head != null) { document.write(head.key + " "); head = head.next; } document.write("<br>"); } // Function to detect first node of loop // in a linked list that may contain loop function detectLoop(head) { // Create a temporary node let temp = new Node(); while (head != null) { // This condition is for the case // when there is no loop if (head.next == null) { return false; } // Check if next is already // pointing to temp if (head.next == temp) { return true; } // Store the pointer to the next node // in order to get to it in the next step let next = head.next; // Make next point to temp head.next = temp; // Get to the next node in the list head = nex; } return false; } // Driver code let head = new Node(1); head.next = new Node(2); head.next.next = new Node(3); head.next.next.next = new Node(4); head.next.next.next.next = new Node(5); // Create a loop for testing(5 is pointing to 3) / head.next.next.next.next.next = head.next.next; let found = detectLoop(head); if (found) document.write("Loop Found"); else document.write("No Loop"); // This code is contributed by ab2127 </script> ```

Output
```Loop Found
```

Time complexity: O(N).Â Only one traversal of the loop is needed.
Auxiliary Space: O(1)Â

Detect loop in a linked list by Storing length:

The idea is to store the length of the list from first node and last node, increment last node till reaches NULL or number of nodes in last is greater the current between first and last nodes.

Follow the steps below to solve the problem:

• In this method, two pointers are created, first (always points to head) and last.Â
• Each time the last pointer moves calculate no of nodes between the first and last.Â
• check whether the current no of nodes > previous no of nodesÂ
• If yes we proceed by moving the last pointerÂ
• Else it means we’ve reached the end of the loop, so return output accordingly.

Below is the implementation of the above approach:

C++ ```#include <bits/stdc++.h> using namespace std; struct Node { int data; struct Node* next; Node(int x) { data = x; next = NULL; } }; // A utility function to print a linked list void printList(Node* head) { while (head != NULL) { cout << head->data << " "; head = head->next; } cout << endl; } /*returns distance between first and last node every time * last node moves forwards*/ int distance(Node* first, Node* last) { /*counts no of nodes between first and last*/ int counter = 0; Node* curr; curr = first; while (curr != last) { counter += 1; curr = curr->next; } return counter + 1; } // Function to detect first node of loop // in a linked list that may contain loop bool detectLoop(Node* head) { // Create a temporary node Node* temp = new Node(0); Node *first, *last; /*first always points to head*/ first = head; /*last pointer initially points to head*/ last = head; /*current_length stores no of nodes between current * position of first and last*/ int current_length = 0; /*prev_length stores no of nodes between previous * position of first and last*/ int prev_length = -1; while (current_length > prev_length && last != NULL) { // set prev_length to current length then update the // current length prev_length = current_length; // distance is calculated current_length = distance(first, last); // last node points the next node last = last->next; } if (last == NULL) { return false; } else { return true; } } /* Driver program to test above function*/ int main() { Node* head = new Node(1); head->next = new Node(2); head->next->next = new Node(3); head->next->next->next = new Node(4); head->next->next->next->next = new Node(5); /* Create a loop for testing(5 is pointing to 3) */ head->next->next->next->next->next = head->next->next; bool found = detectLoop(head); if (found) cout << "Loop Found"; else cout << "No Loop Found"; return 0; } ``` C ```// C program to return first node of loop #include <stdbool.h> #include <stdio.h> #include <stdlib.h> typedef struct Node { int data; struct Node* next; } Node; Node* newNode(int data) { Node* temp = (Node*)malloc(sizeof(Node)); temp->data = data; temp->next = NULL; return temp; } // A utility function to print a linked list void printList(Node* head) { while (head != NULL) { printf("%d ", head->data); head = head->next; } printf("\n"); } /*returns distance between first and last node every time * last node moves forwards*/ int distance(Node* first, Node* last) { /*counts no of nodes between first and last*/ int counter = 0; Node* curr; curr = first; while (curr != last) { counter += 1; curr = curr->next; } return counter + 1; } // Function to detect first node of loop // in a linked list that may contain loop bool detectLoop(Node* head) { // Create a temporary node Node* temp = (Node *)malloc(sizeof(Node)); Node *first, *last; /*first always points to head*/ first = head; /*last pointer initially points to head*/ last = head; /*current_length stores no of nodes between current * position of first and last*/ int current_length = 0; /*prev_length stores no of nodes between previous * position of first and last*/ int prev_length = -1; while (current_length > prev_length && last != NULL) { // set prev_length to current length then update the // current length prev_length = current_length; // distance is calculated current_length = distance(first, last); // last node points the next node last = last->next; } if (last == NULL) return false; else return true; } /* Driver program to test above function*/ int main() { 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(5 is pointing to 3) */ head->next->next->next->next->next = head->next->next; bool found = detectLoop(head); if (found) printf("Loop Found"); else printf("No Loop Found"); return 0; } // This code is contributed by Aditya Kumar (adityakumar129) ``` Java ```// Java program to return first node of loop import java.util.*; class GFG { static class Node { int data; Node next; Node(int x) { data = x; next = null; } }; // A utility function to print a linked list static void printList(Node head) { while (head != null) { System.out.print(head.data + " "); head = head.next; } System.out.println(); } /*returns distance between first and last node every time * last node moves forwards*/ static int distance(Node first, Node last) { /*counts no of nodes between first and last*/ int counter = 0; Node curr; curr = first; while (curr != last) { counter += 1; curr = curr.next; } return counter + 1; } // Function to detect first node of loop // in a linked list that may contain loop static boolean detectLoop(Node head) { // Create a temporary node Node temp = new Node(0); Node first, last; /*first always points to head*/ first = head; /*last pointer initially points to head*/ last = head; /*current_length stores no of nodes between current * position of first and last*/ int current_length = 0; /*current_length stores no of nodes between previous * position of first and last*/ int prev_length = -1; while (current_length > prev_length && last != null) { // set prev_length to current length then update the // current length prev_length = current_length; // distance is calculated current_length = distance(first, last); // last node points the next node last = last.next; } if (last == null) { return false; } else { return true; } } /* Driver program to test above function*/ public static void main(String[] args) { Node head = new Node(1); head.next = new Node(2); head.next.next = new Node(3); head.next.next.next = new Node(4); head.next.next.next.next = new Node(5); /* Create a loop for testing(5 is pointing to 3) */ head.next.next.next.next.next = head.next.next; boolean found = detectLoop(head); if (found) System.out.print("Loop Found"); else System.out.print("No Loop Found"); } } // This code is contributed by gauravrajput1 ``` Python3 ```# Python program to return first node of loop class newNode: def __init__(self, x): self.data = x self.left = None # A utility function to print a linked list def printList(head): while (head != None) : print(head.data, end=" ") head = head.next; print() # returns distance between first and last node every time # last node moves forwards def distance(first, last): # counts no of nodes between first and last counter = 0 curr = first while (curr != last): counter = counter + 1 curr = curr.next return counter + 1 # Function to detect first node of loop # in a linked list that may contain loop def detectLoop(head): # Create a temporary node temp = "" # first always points to head first = head; # last pointer initially points to head last = head; # current_length stores no of nodes between current # position of first and last current_length = 0 #current_length stores no of nodes between previous # position of first and last*/ prev_length = -1 while (current_length > prev_length and last != None) : # set prev_length to current length then update the # current length prev_length = current_length # distance is calculated current_length = distance(first, last) # last node points the next node last = last.next; if (last == None) : return False else : return True # 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(5 is pointing to 3) head.next.next.next.next.next = head.next.next; found = detectLoop(head) if (found) : print("Loop Found") else : print("No Loop Found") # This code is contributed by ihritik ``` C# ```// C# program to return first node of loop using System; public class GFG { public class Node { public int data; public Node next; public Node(int x) { data = x; next = null; } }; // A utility function to print a linked list static void printList(Node head) { while (head != null) { Console.Write(head.data + " "); head = head.next; } Console.WriteLine(); } /*returns distance between first and last node every time * last node moves forwards*/ static int distance(Node first, Node last) { /*counts no of nodes between first and last*/ int counter = 0; Node curr; curr = first; while (curr != last) { counter += 1; curr = curr.next; } return counter + 1; } // Function to detect first node of loop // in a linked list that may contain loop static bool detectLoop(Node head) { Node first, last; /*first always points to head*/ first = head; /*last pointer initially points to head*/ last = head; /*current_length stores no of nodes between current * position of first and last*/ int current_length = 0; /*current_length stores no of nodes between previous * position of first and last*/ int prev_length = -1; while (current_length > prev_length && last != null) { // set prev_length to current length then update the // current length prev_length = current_length; // distance is calculated current_length = distance(first, last); // last node points the next node last = last.next; } if (last == null) { return false; } else { return true; } } /* Driver program to test above function*/ public static void Main(String[] args) { Node head = new Node(1); head.next = new Node(2); head.next.next = new Node(3); head.next.next.next = new Node(4); head.next.next.next.next = new Node(5); /* Create a loop for testing(5 is pointing to 3) */ head.next.next.next.next.next = head.next.next; bool found = detectLoop(head); if (found) Console.Write("Loop Found"); else Console.Write("No Loop Found"); } } ``` Javascript ```<script> // Javascript program to return first node of loop class Node { constructor(x) { this.data = x; this.next = null; } } // A utility function to print a linked list function printList(head) { while (head != null) { document.write(head.data + " "); head = head.next; } document.write("</br>"); } /*returns distance between first and last node every time last node moves forwards*/ function distance(first, last) { /*counts no of nodes between first and last*/ let counter = 0; let curr; curr = first; while (curr != last) { counter += 1; curr = curr.next; } return counter + 1; } // Function to detect first node of loop // in a linked list that may contain loop function detectLoop(head) { // Create a temporary node let temp = new Node(); let first, last; /*first always points to head*/ first = head; /*last pointer initially points to head*/ last = head; /*current_length stores no of nodes between current position of first and last*/ let current_length = 0; /*current_length stores no of nodes between previous position of first and last*/ let prev_length = -1; while (current_length > prev_length && last != null) { // Set prev_length to current length // then update the current length prev_length = current_length; // Distance is calculated current_length = distance(first, last); // Last node points the next node last = last.next; } if (last == null) { return false; } else { return true; } } // Driver code let head = new Node(1); head.next = new Node(2); head.next.next = new Node(3); head.next.next.next = new Node(4); head.next.next.next.next = new Node(5); /* Create a loop for testing(5 is pointing to 3) */ head.next.next.next.next.next = head.next.next; let found = detectLoop(head); if (found) document.write("Loop Found"); else document.write("No Loop Found"); // This code is contributed by divyeshrabadiya07 </script> ```

Output
```Loop Found
```

Time complexity: O(N2), For every node calculate the length of that node from the head by traversing.
Auxiliary Space: O(1)