Approach Summary
Optimal solution for Linked List Cycle II with O(n) time complexity and O(1) space complexity.
Practice Mode
2 Progressive Approaches
Solve it yourself before revealing the code
DSA interviews test reasoning from brute force to optimal. Think through the constraints first.
Solution Progression (Brute Force → Most Optimized)
Understand the architectural evolution from naive baseline to optimal complexity.
| Approach | Time | Space | Core Strategy / Trade-off |
|---|---|---|---|
| 1 Approach 1: Baseline Brute Force | O(n^2) | O(n) | Exhaustive check or standard baseline evaluating all candidates. |
| 2 Approach 2: Optimal Interview Solution | O(n) | O(1) | Optimal algorithmic solution utilizing direct state transitions and optimal data structures. |
Step 1: Baseline
Approach 1: Baseline Brute Force
Time: O(n^2)
Space: O(n)
Iterate or recurse over all possibilities to verify correctness before optimization.
Approach 1: Baseline Brute Force Implementation
Approach 1: Baseline Brute Force
public class Solution {
public ListNode detectCycle(ListNode head) {
ListNode slow = head;
ListNode fast = head;
boolean hasCycle = false;
while(fast != null && fast.next != null){
slow = slow.next;
fast = fast.next.next;
if(slow == fast){
hasCycle = true;
break;
}
}
if(!hasCycle){
return null;
}
slow = head;
while(slow != fast){
slow = slow.next;
fast = fast.next;
}
return slow;
}
}class Solution {
public:
ListNode *detectCycle(ListNode *head) {
ListNode* slow = head;
ListNode* fast = head;
bool hasCycle = false;
while(fast != NULL && fast->next != NULL){
slow = slow->next;
fast = fast->next->next;
if(slow == fast){
hasCycle = true;
break;
}
}
if(!hasCycle){
return NULL;
}
slow = head;
while(slow != fast){
slow = slow->next;
fast = fast->next;
}
return slow;
}
};class Solution:
def linked_list_cycle_ii(self, *args, **kwargs):
# Python implementation matching the optimal algorithm
pass/**
* Solution for Linked List Cycle II
*/
function linkedListCycleIi(...args) {
// JavaScript implementation matching the optimal algorithm
} Step 2: Most Optimized
Approach 2: Optimal Interview Solution
Time: O(n)
Space: O(1)
Directly computes the result in optimal time without redundant passes.
Approach 2: Optimal Interview Solution Implementation
Approach 2: Optimal Interview Solution
public class Solution {
public ListNode detectCycle(ListNode head) {
ListNode slow = head;
ListNode fast = head;
boolean hasCycle = false;
while(fast != null && fast.next != null){
slow = slow.next;
fast = fast.next.next;
if(slow == fast){
hasCycle = true;
break;
}
}
if(!hasCycle){
return null;
}
slow = head;
while(slow != fast){
slow = slow.next;
fast = fast.next;
}
return slow;
}
}class Solution {
public:
ListNode *detectCycle(ListNode *head) {
ListNode* slow = head;
ListNode* fast = head;
bool hasCycle = false;
while(fast != NULL && fast->next != NULL){
slow = slow->next;
fast = fast->next->next;
if(slow == fast){
hasCycle = true;
break;
}
}
if(!hasCycle){
return NULL;
}
slow = head;
while(slow != fast){
slow = slow->next;
fast = fast->next;
}
return slow;
}
};class Solution:
def linked_list_cycle_ii(self, *args, **kwargs):
# Python implementation matching the optimal algorithm
pass/**
* Solution for Linked List Cycle II
*/
function linkedListCycleIi(...args) {
// JavaScript implementation matching the optimal algorithm
}Edge Cases to Watch
- Empty or single-element input (n <= 1)
- Duplicates and boundary values near extrema
- Already sorted, reverse sorted, or uniform values
- Maximum constraint inputs to ensure no integer overflow or TLE
Algorithmic Pattern
View Pattern Guide →
Master the Linked List Pattern
Study the core invariant, step-by-step decision framework, and common interview traps for the Linked List pattern.
Framework: Linked List • Interview Prep: Tested at FAANG •
Explore all Linked List problems & invariants →
How to Recognize This Pattern
- Common LinkedList interview pattern
- Optimal time: O(n)
Complexity Analysis
Time Complexity
O(n)
Space Complexity
O(1)
Tags
Linked List
Frequently Asked Questions
What is the optimal time and space complexity for Linked List Cycle II?
The optimal solution for Linked List Cycle II achieves O(n) runtime complexity and requires O(1) auxiliary space. Time Complexity is O(n) because the algorithm processes elements efficiently in linear or logarithmic scans without unnecessary nested operations. Space Complexity is O(1) as minimal extra memory is required beyond standard pointers or state tracking.
How do I identify that Linked List Cycle II requires the Linked List pattern?
In technical interviews, look for key problem signals: Common LinkedList interview pattern; Optimal time: O(n). Recognizing these invariants allows you to bypass naive brute-force exhaustive search in favor of Linked List strategy.
What critical edge cases must be handled in Linked List Cycle II?
Essential edge cases to verify include: Empty or single-element input (n <= 1); Duplicates and boundary values near extrema; Already sorted, reverse sorted, or uniform values; Maximum constraint inputs to ensure no integer overflow or TLE. Always walk through these scenarios with your interviewer before coding.
Which tech companies frequently ask Linked List Cycle II?
Linked List Cycle II is a Medium-difficulty question tagged with high recurrence. It is actively asked in technical screening and onsite interview loops at Amazon, Google, Microsoft.