Algorithms / Fast Slow Pointers

Least You Need to Know: Fast/Slow Pointers, Middle Nodes, and Cycle Entry

Fast and slow pointers turn repeated traversal into relative-motion reasoning. The same idea explains finding middle nodes, detecting linked-list cycles, and locating the entry point after a cycle is found.

The least you need to know

If a fast pointer moves twice as quickly as a slow pointer, their relative speed is one step per round.
In an acyclic list, the fast pointer eventually reaches `null`.
In a cyclic list, fast and slow pointers must eventually meet inside the cycle.
After a meeting, resetting one pointer to the head and moving both one step at a time finds the cycle entry.
The same fast/slow setup also finds middle nodes without counting the list first.

Key notation

slow pointer moving one step per round

fast pointer moving two steps per round

cycle entry first node on the loop reached from the head

Tiny worked example

Move `slow` by one node and `fast` by two nodes.
If `fast` hits `null`, the list ends and there is no cycle.
If they meet, a cycle exists.
Reset one pointer to the head; moving both one step per round makes them meet again at the cycle entry.

Common mistakes

Students often think a meeting point is automatically the cycle entry.
Students often forget to guard `fast` and `fast.next` before advancing by two.
Students often miss that middle-node problems are the same relative-speed pattern without cycles.

How to recognize this kind of problem

The structure is a linked list or repeated-next-pointer chain.
The prompt asks for a middle node, cycle existence, or cycle start.
Relative speed is easier than explicit length counting.