Problem Link :- leetcode-142
Problem statement
Given the head of a linked list, return the node where the cycle begins. If there is no cycle, return null.
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 (0-indexed). It is -1 if there is no cycle. Note that pos is not passed as a parameter.
Do not modify the linked list.
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 (0-indexed). It is -1 if there is no cycle. Note that pos is not passed as a parameter.
Do not modify the linked list.
Significance of problem
The significance of the problem statement lies in its application to detecting cycles in linked lists, a common issue in data structures. Identifying and understanding cycles is crucial for preventing infinite loops and optimizing algorithms. The provided code efficiently solves this problem using Floyd's Tortoise and Hare algorithm, offering a practical illustration of an algorithm widely employed in various computing scenarios.
Beyond the technical aspect, the problem teaches a fundamental concept of pointer manipulation in linked lists. It demonstrates how two pointers moving at different speeds can be strategically utilized to detect a cycle and determine its starting point. This approach not only optimizes the time complexity of the solution but also provides a valuable insight into algorithmic design.
Moreover, the problem underscores the importance of non-destructive operations on linked lists. The instruction not to modify the linked list emphasizes the need for solutions that work within existing structures, a consideration critical in real-world applications where data integrity is paramount.
In essence, mastering the cycle detection problem enhances problem-solving skills, offering a deeper understanding of linked list manipulation and introducing a widely applicable algorithmic technique. This problem serves as a stepping stone for developers, imparting skills that are foundational to efficient and robust coding practices in diverse programming scenarios.
Beyond the technical aspect, the problem teaches a fundamental concept of pointer manipulation in linked lists. It demonstrates how two pointers moving at different speeds can be strategically utilized to detect a cycle and determine its starting point. This approach not only optimizes the time complexity of the solution but also provides a valuable insight into algorithmic design.
Moreover, the problem underscores the importance of non-destructive operations on linked lists. The instruction not to modify the linked list emphasizes the need for solutions that work within existing structures, a consideration critical in real-world applications where data integrity is paramount.
In essence, mastering the cycle detection problem enhances problem-solving skills, offering a deeper understanding of linked list manipulation and introducing a widely applicable algorithmic technique. This problem serves as a stepping stone for developers, imparting skills that are foundational to efficient and robust coding practices in diverse programming scenarios.
Easiest Explanation
Let's say you have a race track where runners run around in a loop. You want to know where the starting point of the track is, but you can't see the whole track at once.
To figure it out, you can use the turtle and rabbit method again. You can have one person walk around the track at a slow pace, and another person run around the track at a faster pace. If the track is a simple oval shape with no extra loops or twists, then the fast runner will eventually catch up to the slow walker at the starting point.
However, if there are extra loops or twists in the track, then the fast runner might catch up to the slow walker at a different spot on the track, but not at the starting point. In that case, you can have both the walker and the runner start again at the same time, but this time the walker starts a little bit ahead of the starting line. When the fast runner catches up to the walker this time, you'll be at the starting point.
This method can be used in other situations where you need to find the starting point of a loop or cycle, such as a clock with a rotating hand or a conveyor belt with a repeating pattern.
I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.
To figure it out, you can use the turtle and rabbit method again. You can have one person walk around the track at a slow pace, and another person run around the track at a faster pace. If the track is a simple oval shape with no extra loops or twists, then the fast runner will eventually catch up to the slow walker at the starting point.
However, if there are extra loops or twists in the track, then the fast runner might catch up to the slow walker at a different spot on the track, but not at the starting point. In that case, you can have both the walker and the runner start again at the same time, but this time the walker starts a little bit ahead of the starting line. When the fast runner catches up to the walker this time, you'll be at the starting point.
This method can be used in other situations where you need to find the starting point of a loop or cycle, such as a clock with a rotating hand or a conveyor belt with a repeating pattern.
I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.
class Solution:
def detectCycle(self, head: ListNode) -> ListNode:
slow = head
fast = head
while fast and fast.next:
slow = slow.next
fast = fast.next.next
if slow == fast:
slow = head
while slow != fast:
slow = slow.next
fast = fast.next
return slow
return None
class Solution { public: ListNode *detectCycle(ListNode *head) { ListNode *slow = head; ListNode *fast = head; while(fast != NULL && fast->next != NULL){ slow = slow->next; fast = fast->next->next; if(slow == fast){ slow = head; while(slow != fast){ slow = slow->next; fast = fast->next; } return slow; } } return NULL; } };
Here's how the function works:
we will be sloving this problem using Floyd's Tortoise and Hare Algorithm or Two Pointer Approach
1. We start by creating two pointers, slow and fast, and we set them both to point to the head of the linked list.
2. We then enter a while loop that runs as long as fast is not null and fast->next (the next node after fast) is not null. This is the turtle and hare algorithm mentioned earlier, where the slow pointer moves one step at a time, and the fast pointer moves two steps at a time.
3. If there is no cycle in the linked list, then the fast pointer will eventually reach the end of the list, and the while loop will exit. At this point, the function returns NULL, indicating that there is no cycle.
4. If there is a cycle in the linked list, then the fast pointer will eventually catch up to the slow pointer as they traverse the cycle. At this point, we know there is a cycle, and we move on to the next step.
5. We reset the slow pointer to the head of the linked list, and then we move both the slow and fast pointers one step at a time until they meet again. When they meet, the node where they meet is the starting point of the cycle, and we return this node.
6. If there is no cycle, the function will exit the loop in step 2 and return NULL.
Overall, this function uses the turtle and hare algorithm to detect a cycle in the linked list, and then uses the same algorithm to find the starting node of the cycle. The time complexity of this function is O(n), where n is the length of the linked list.
1. We start by creating two pointers, slow and fast, and we set them both to point to the head of the linked list.
2. We then enter a while loop that runs as long as fast is not null and fast->next (the next node after fast) is not null. This is the turtle and hare algorithm mentioned earlier, where the slow pointer moves one step at a time, and the fast pointer moves two steps at a time.
3. If there is no cycle in the linked list, then the fast pointer will eventually reach the end of the list, and the while loop will exit. At this point, the function returns NULL, indicating that there is no cycle.
4. If there is a cycle in the linked list, then the fast pointer will eventually catch up to the slow pointer as they traverse the cycle. At this point, we know there is a cycle, and we move on to the next step.
5. We reset the slow pointer to the head of the linked list, and then we move both the slow and fast pointers one step at a time until they meet again. When they meet, the node where they meet is the starting point of the cycle, and we return this node.
6. If there is no cycle, the function will exit the loop in step 2 and return NULL.
Overall, this function uses the turtle and hare algorithm to detect a cycle in the linked list, and then uses the same algorithm to find the starting node of the cycle. The time complexity of this function is O(n), where n is the length of the linked list.
Learning Outcomes
Solving the linked list cycle detection problem yields valuable learning outcomes in both algorithmic thinking and linked list manipulation. Firstly, the implementation of Floyd's Tortoise and Hare algorithm enhances one's understanding of efficient cycle detection techniques. This algorithm, leveraging two pointers at different speeds, provides an elegant solution applicable not only to linked lists but also to various scenarios requiring cycle detection.
Secondly, the problem reinforces the significance of pointer manipulation in data structures. By strategically advancing pointers while traversing the linked list, the solution showcases a practical application of pointer arithmetic, a fundamental skill for navigating and manipulating complex data structures efficiently.
Furthermore, the instruction not to modify the linked list emphasizes the importance of non-destructive algorithms, encouraging developers to design solutions that respect existing data structures. This consideration is particularly relevant in scenarios where data integrity is crucial, reinforcing the principle of writing robust and reliable code.
Secondly, the problem reinforces the significance of pointer manipulation in data structures. By strategically advancing pointers while traversing the linked list, the solution showcases a practical application of pointer arithmetic, a fundamental skill for navigating and manipulating complex data structures efficiently.
Furthermore, the instruction not to modify the linked list emphasizes the importance of non-destructive algorithms, encouraging developers to design solutions that respect existing data structures. This consideration is particularly relevant in scenarios where data integrity is crucial, reinforcing the principle of writing robust and reliable code.
Conclusion
In conclusion, the linked list cycle detection problem illuminates key principles in algorithmic problem-solving and data structure manipulation. The implementation of Floyd's Tortoise and Hare algorithm not only provides an efficient solution to the specific challenge of cycle detection but also imparts a fundamental understanding of how clever pointer manipulation can address complex scenarios. This problem serves as a practical tutorial in leveraging pointers within a linked list, offering insights applicable to broader programming challenges.
Furthermore, the instruction to avoid modifying the linked list emphasizes the importance of non-destructive algorithms, promoting a coding ethos centered on data integrity. This consideration resonates in real-world applications where maintaining the integrity of existing data structures is paramount.
By mastering this problem, developers cultivate skills vital to constructing robust, efficient, and non-destructive algorithms. The learned techniques extend beyond linked lists, influencing problem-solving strategies across various domains in computer science. In essence, the linked list cycle detection problem serves as a pedagogical gateway, fostering a deeper comprehension of algorithms, pointers, and coding best practices that contribute to the development of well-rounded and effective programmers.
Furthermore, the instruction to avoid modifying the linked list emphasizes the importance of non-destructive algorithms, promoting a coding ethos centered on data integrity. This consideration resonates in real-world applications where maintaining the integrity of existing data structures is paramount.
By mastering this problem, developers cultivate skills vital to constructing robust, efficient, and non-destructive algorithms. The learned techniques extend beyond linked lists, influencing problem-solving strategies across various domains in computer science. In essence, the linked list cycle detection problem serves as a pedagogical gateway, fostering a deeper comprehension of algorithms, pointers, and coding best practices that contribute to the development of well-rounded and effective programmers.
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