# Detect Cycle in a Linked List using Map

Given a Linked List, check if the linked list has a loop or not.

There are various methods shown here: Detect Cycle in Linked List

Example

Input: 20->4->54->6->NULL
Output: No loop is detected.
Explanation:
While traversing the linked list we reached the end of linked list. Therefore no loop is present in linked list.

Input: 20->4->5->10->20
Output: Loop detected.
Explanation:
While traversing the linked list we reached the node with value 10 is linked with the head node which depicts a loop in the linked list. Therefore loop is present in linked list.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. Create a map which will store the visited node in linked list.
2. Traverse the linked list and do the following:
• Check whether the current node is present in the map or not.
• If the current node is not present in the map then, insert the current node in the map.
• If the Node is present in the map, the loop in a linked list is detected.
3. If we reached to Null Node while traversing the linked list then, the given linked list has no loop present in it.

Below is the implementation of above approach:

 `// C++ program to detect loop in ` `// given linked list using map ` `#include ` `using` `namespace` `std; ` ` `  `// Structure for a node in Linked List ` `struct` `Node { ` `    ``int` `data; ` `    ``Node* next; ` `}; ` ` `  `// Function to create Linked List ` `// Node ` `Node* newNode(``int` `d) ` `{ ` `    ``Node* temp = ``new` `Node; ` `    ``temp->data = d; ` `    ``temp->next = NULL; ` `    ``return` `temp; ` `} ` ` `  `// Declaration of Map to keep ` `// mark of visited Node ` `map vis; ` `bool` `flag = 0; ` ` `  `// Function to check cycle in Linked ` `// List ` `void` `check(Node* head) ` `{ ` `    ``// If head is NULL return ; ` `    ``if` `(head == NULL) { ` `        ``flag = 0; ` `        ``return``; ` `    ``} ` ` `  `    ``// Mark the incoming Node as ` `    ``// visited if it is not visited yet ` `    ``if` `(!vis[head]) { ` `        ``vis[head] = ``true``; ` `        ``check(head->next); ` `    ``} ` ` `  `    ``// If a visited Node is found ` `    ``// Update the flag value to 1 ` `    ``// and return ; ` `    ``else` `{ ` `        ``flag = 1; ` `        ``return``; ` `    ``} ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``// Create a head Node ` `    ``Node* head = newNode(20); ` ` `  `    ``// Inserting Node in Linked List ` `    ``head->next = newNode(4); ` `    ``head->next->next = newNode(5); ` `    ``head->next->next->next = newNode(10); ` ` `  `    ``// Just to make a cycle ` `    ``head->next->next->next->next = head; ` ` `  `    ``// Function that detect cycle in ` `    ``// Linked List ` `    ``check(head); ` ` `  `    ``// If flag is true, loop is found ` `    ``if` `(flag) ` `        ``cout << ``"Loop detected."``; ` ` `  `    ``// If flag is false, No Loop ` `    ``// detected ` `    ``else` `        ``cout << ``"No Loop Found."``; ` `    ``cout << endl; ` ` `  `    ``return` `0; ` `} `

Output:

```Loop detected.
```

Time Complexity: O(N*log N)
Auxiliary Space: O(N)

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