Solution: Circular Array Loop

Explore how to identify cycles in a circular array of non-zero integers by using the fast and slow pointers method. Understand the conditions for cycle detection, how to efficiently traverse the array, and the tradeoffs in time complexity. This lesson helps you implement cycle detection algorithms to solve problems involving circular lists.

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Statement
Solution
- Naive approach
- Optimized approach using fast and slow pointers

Statement

There is a circular list of non-zero integers called nums. Each number in the list tells you how many steps to move forward or backward from your current position:

If nums[i] is positive, move nums[i] steps forward.
If nums[i] is negative, move nums[i] steps backward.

As the list is circular:

Moving forward from the last element takes you back to the first element.
Moving backward from the first element takes you to the last element.

A cycle in this list means:

You keep moving according to the numbers, and you end up repeating a sequence of indexes.
All numbers in the cycle have the same sign (either all positive or all negative).
The cycle length is greater than 1 (it involves at least two indexes).

Return true if such a cycle exists in the list or false otherwise.