Solution: Circular Array Loop

Explore the fast and slow pointers approach to detect cycles in a circular integer array. Learn to identify cycles where all elements have the same sign and how to efficiently verify them with O(1) space complexity.

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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.