Linked list loop detection algorithm

Question

I read some interview question online about how would you find if there's a loop in a linked list, and solution ( Floyd's cycle-finding algorithm ) is to have two pointers, one is 2x faster than the other, and check if they meet again.

My question is: Why can't I just keep one pointer fixed, just move the other pointer forward by 1 step each time?

Answer 1

Because maybe not the complete linkedList is within the loop.

For a linked list lasso detection algorithm, you need two pointers:

As long as the first pointer is where the cowboy is, no loop is detected. But if you move it stepwise forward, it will eventually enter the loop.

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BTW, lasso is the terminus technicus from graph theory, cowboy isn't.

Answer 2

Because the first (non-moving) pointer might not lie within the loop, so the pointers would never meet. (Remember that a loop may consist of only part of the list.)

Answer 3

Because the loop may not contain the element pointed to by the first pointer.

For example, if the first pointer points to element 1 and the linked list has a loop later on (1->2->3->4->2), your algorithm won't detect it.