Regarding Floyd's cycle-finding algorithm

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In summary, Floyd's cycle-finding algorithm, developed by Robert Floyd, is a method for detecting cycles in data using two pointers. The time complexity is O(n) and it can be used for any type of data as long as elements can be compared. However, it can only detect cycles and not their location, and is limited to data structures that can be traversed in one direction.
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cyberfrenzy
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Well I understand what is happening - the tortoise moving 1 step, and the hare moving 2 steps and finally coinciding at a point. But I want a mathematical proof of this - ie; when you have 2 counters moving in a cycle, one going 1 step, the other 2 steps, then they finally meet at a point.
 
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Suppose that they start M places apart (suitably oriented) on a cycle of size N. How many places apart are they after k steps?
 

FAQ: Regarding Floyd's cycle-finding algorithm

What is Floyd's cycle-finding algorithm?

Floyd's cycle-finding algorithm, also known as the tortoise and hare algorithm, is a method for detecting cycles in a linked list or sequence of data. It was developed by Robert Floyd in 1967 and is named after him.

How does Floyd's cycle-finding algorithm work?

The algorithm works by using two pointers, one that moves at a faster rate than the other. If there is a cycle in the data, the faster pointer will eventually "catch up" to the slower pointer, indicating the presence of a cycle.

What is the time complexity of Floyd's cycle-finding algorithm?

The time complexity of the algorithm is O(n), where n is the number of elements in the data. This makes it a very efficient algorithm for detecting cycles.

Can Floyd's cycle-finding algorithm be used for any type of data?

Yes, the algorithm can be used for any type of data as long as there is a way to compare two elements and determine if they are equal.

Are there any limitations to Floyd's cycle-finding algorithm?

One limitation of the algorithm is that it can only detect cycles, not the location of the cycle. It also requires the data to be traversable in one direction, making it unsuitable for certain types of data structures.

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