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Given a linked list, how can we check if the linked list has loop or not. The diagram below shows a linked list with a loop. 2 4 Describe your algorithm and keep the posting to the topic.

Given a linked list, how can we check if the linked list has loop or not. The diagram below shows a linked list with a loop. 2 4 Describe your algorithm and keep the posting to the topic.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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**Detecting a Loop in a Linked List** Given a linked list, how can we check if the linked list has a loop or not? The diagram below shows a linked list with a loop. ### Diagram Explanation The linked list in question has the following structure: - Node 1 points to Node 2. - Node 2 points to Node 3. - Node 3 points to Node 4. - Node 4 points to Node 5. - Node 5 points back to Node 2, creating a loop. ``` 1 -> 2 -> 3 -> 4 -> 5 ^ | |______________| ``` ### Algorithm to Detect a Loop One of the most commonly used algorithms to detect a loop in a linked list is Floyd’s Cycle-Finding Algorithm, also known as the Tortoise and the Hare algorithm. Here’s how it works: 1. **Initialize Pointers**: Start with two pointers, both set to the head of the linked list. One pointer moves one step at a time (the "tortoise"), and the other moves two steps at a time (the "hare"). 2. **Traverse the List**: - Move the tortoise and hare forward as described (one step and two steps, respectively). - If the hare encounters a `null` (i.e., the end of the list), then there is no loop. 3. **Loop Detection**: - If there is a loop, sooner or later the hare will meet the tortoise within the loop. Thus, at some point, both pointers will be equal. ### Example Step-by-Step Let's illustrate with the given linked list: - **Step 1**: Initialize `tortoise` and `hare` to the head of the list (Node 1). - **Step 2**: Move `tortoise` to Node 2 and `hare` to Node 3. - **Step 3**: Move `tortoise` to Node 3 and `hare` to Node 5. - **Step 4**: Move `tortoise` to Node 4 and `hare` back to Node 3. - **Step 5**: Move `tortoise` to Node 5 and `hare` to Node 5. At Step 5, `tortoise` and `hare` meet at Node 5, indicating
Transcribed Image Text:**Detecting a Loop in a Linked List** Given a linked list, how can we check if the linked list has a loop or not? The diagram below shows a linked list with a loop. ### Diagram Explanation The linked list in question has the following structure: - Node 1 points to Node 2. - Node 2 points to Node 3. - Node 3 points to Node 4. - Node 4 points to Node 5. - Node 5 points back to Node 2, creating a loop. ``` 1 -> 2 -> 3 -> 4 -> 5 ^ | |______________| ``` ### Algorithm to Detect a Loop One of the most commonly used algorithms to detect a loop in a linked list is Floyd’s Cycle-Finding Algorithm, also known as the Tortoise and the Hare algorithm. Here’s how it works: 1. **Initialize Pointers**: Start with two pointers, both set to the head of the linked list. One pointer moves one step at a time (the "tortoise"), and the other moves two steps at a time (the "hare"). 2. **Traverse the List**: - Move the tortoise and hare forward as described (one step and two steps, respectively). - If the hare encounters a `null` (i.e., the end of the list), then there is no loop. 3. **Loop Detection**: - If there is a loop, sooner or later the hare will meet the tortoise within the loop. Thus, at some point, both pointers will be equal. ### Example Step-by-Step Let's illustrate with the given linked list: - **Step 1**: Initialize `tortoise` and `hare` to the head of the list (Node 1). - **Step 2**: Move `tortoise` to Node 2 and `hare` to Node 3. - **Step 3**: Move `tortoise` to Node 3 and `hare` to Node 5. - **Step 4**: Move `tortoise` to Node 4 and `hare` back to Node 3. - **Step 5**: Move `tortoise` to Node 5 and `hare` to Node 5. At Step 5, `tortoise` and `hare` meet at Node 5, indicating
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