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dsa-solutions/lc-solutions/0100-0199/0141-linked-list-cycles.md

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+---
+id: linked-list-cycle
+title: Linked List Cycle(LeetCode)
+sidebar_label: 0141-Linked List Cycle
+tags:
+  - Linked list
+  - Hash Table
+  - Two pointer
+description: Given head, the head of a linked list, determine if the linked list has a cycle in it.
+---
+
+## Problem Statement
+
+Given `head`, the head of a linked list, determine if the linked list has a cycle in it.
+
+There is a cycle in a linked list if there is some node in the list that can be reached again by continuously following the `next` pointer. Internally, `pos` is used to denote the index of the node that tail's `next` pointer is connected to. Note that `pos` is not passed as a parameter.
+
+Return `true` if there is a cycle in the linked list. Otherwise, return `false`.
+
+### Examples
+
+**Example 1:**
+
+![image](https://github.com/PradnyaGaitonde/codeharborhub.github.io/assets/116059908/7da67d86-c090-49ad-9ed1-7e342a0e650a)
+
+```plaintext
+Input: head = [3,2,0,-4], pos = 1
+Output: true
+Explanation: There is a cycle in the linked list, where the tail connects to the 1st node (0-indexed).
+```
+
+**Example 2:**
+
+![image](https://github.com/PradnyaGaitonde/codeharborhub.github.io/assets/116059908/9d7aa2ed-77b7-4f92-b6da-2360bb1c6cd1)
+
+```plaintext
+Input: head = [1,2], pos = 0
+Output: true
+Explanation: There is a cycle in the linked list, where the tail connects to the 0th node.
+```
+
+**Example 3:**
+
+![image](https://github.com/PradnyaGaitonde/codeharborhub.github.io/assets/116059908/b0f0c2aa-747e-4c74-975b-a68cc61cafb7)
+
+```plaintext
+Input: head = [1], pos = -1
+Output: false
+Explanation: There is no cycle in the linked list.
+```
+
+### Constraints
+
+- The number of the nodes in the list is in the range `[0, 104]`.
+- `-105 <= Node.val <= 105`
+- `pos` is `-1` or a valid index in the linked-list.
+
+## Solution
+
+This algorithm, also known as Floyd's Cycle-Finding Algorithm or the "tortoise and the hare algorithm," is used to detect cycles in a linked list. It uses two pointers, one moving at twice the speed of the other, to detect if the linked list contains a cycle.
+
+### Approach 
+
+#### Algorithm
+
+1. Initialize two pointers, `slow` and `fast`, pointing to the head of the linked list.
+2. Move `slow` one step at a time and `fast` two steps at a time.
+3. If `fast` reaches the end of the list (i.e., `fast` or `fast->next` is `NULL`), then there is no cycle, so return false.
+4. If `fast` meets `slow` at any point during traversal, then there is a cycle in the linked list, so return true.
+
+#### Implementation
+
+```C++
+class Solution {
+public:
+    bool hasCycle(ListNode *head) {
+        ListNode *fast = head;
+        ListNode *slow = head;
+
+        // Traverse the linked list
+        while (fast != NULL && fast->next != NULL) {
+            fast = fast->next->next; // Move fast pointer two steps
+            slow = slow->next;       // Move slow pointer one step
+
+            // Check if fast and slow pointers meet
+            if (fast == slow) {
+                return true; // Cycle detected
+            }
+        }
+
+        return false; // No cycle found
+    }
+};
+```
+
+### Complexity Analysis
+
+- **Time complexity**: The slow pointer traverses the list once, and the fast pointer traverses it twice. Therefore, the time complexity is O(N), where N is the number of nodes in the linked list.
+- **Space complexity**: The algorithm uses only two pointers (`slow` and `fast`) and has a constant space complexity of O(1).
+
+### Conclusion
+
+The Floyd's Cycle-Finding Algorithm is an efficient way to detect cycles in a linked list using only two pointers and constant space. It is a popular algorithm due to its simplicity and effectiveness in solving this problem.