How can you detect a loop in a linked list?

To detect a loop in a linked list, we can use the Floyd's Cycle-Finding Algorithm, also known as the Tortoise and Hare Algorithm. This algorithm uses two pointers, one moving at a slower pace (tortoise) and the other moving at a faster pace (hare), to traverse the linked list.

Here is the step-by-step process to detect a loop in a linked list:

1. Initialize both pointers (tortoise and hare) to the head of the linked list.
2. Move the tortoise pointer one step at a time, and the hare pointer two steps at a time.
3. Repeat step 2 until either the hare pointer reaches the end of the linked list (indicating no loop) or the tortoise and hare pointers meet (indicating a loop).
4. If the hare pointer reaches the end of the linked list without meeting the tortoise pointer, then there is no loop in the linked list.
5. If the tortoise and hare pointers meet at some point, it confirms the presence of a loop in the linked list.

The reason this algorithm works is that if there is a loop in the linked list, the faster hare pointer will eventually catch up to the slower tortoise pointer within the loop. If there is no loop, the hare pointer will reach the end of the linked list before catching up to the tortoise pointer.

Once a loop is detected, we can also find the starting point of the loop by resetting one of the pointers (let's say hare) to the head of the linked list and then moving both pointers (tortoise and hare) one step at a time until they meet again. The meeting point will be the starting point of the loop.

Overall, the Floyd's Cycle-Finding Algorithm provides an efficient way to detect and find the starting point of a loop in a linked list with a time complexity of O(n), where n is the number of nodes in the linked list.