Why increase pointer by two while finding loop in linked list, why not 3,4,5?

Question

I had a look at question already which talk about algorithm to find loop in a linked list. I have read Floyd\'s cycle-finding algorithm solution, mentioned at lot of places

Answer 1

If the fast pointer moves 3 steps and slow pointer at 1 step, it is not guaranteed for both pointers to meet in cycles containing even number of nodes. If the slow pointer moved at 2 steps, however, the meeting would be guaranteed.

In general, if the hare moves at H steps, and tortoise moves at T steps, you are guaranteed to meet in a cycle iff H = T + 1.

Consider the hare moving relative to the tortoise.

• Hare's speed relative to the tortoise is H - T nodes per iteration.

• Given a cycle of length N =(H - T) * k, where k is any positive integer, the hare would skip every H - T - 1 nodes (again, relative to the tortoise), and it would be impossible to for them to meet if the tortoise was in any of those nodes.

• The only possibility where a meeting is guaranteed is when H - T - 1 = 0.

Hence, increasing the fast pointer by x is allowed, as long as the slow pointer is increased by x - 1.