Linked List Cycle
Recognize the pattern
Brute force idea
The naive version of Linked List Cycle sounds like this: Store visited nodes in a set. That direct path helps you understand the question, but it tends to treat every possibility as brand new instead of learning from earlier steps.
Better approach
A calmer way to see Linked List Cycle is this: Floyd's tortoise and hare: slow moves 1 step, fast moves 2. The goal is not to be clever for its own sake, but to remember the one relationship that keeps the solution grounded as you move forward.
Key invariant
The truth you want to protect throughout Linked List Cycle is this: If there's a cycle, the fast pointer will eventually catch the slow pointer from behind. If that remains true after every update, the rest of the reasoning has a stable place to stand.
Watch out for
One easy way to drift off course in Linked List Cycle is this: Not checking for null — fast or fast.next could be null in a non-cyclic list. The fix is usually to return to the meaning of each move, not just the steps themselves.