You are given a circular array A of positive and negative integers. If a number k at an index is positive, then move forward k steps. Conversely, if it's negative (-k), move backward k steps. Write a program to determine if there is a loop (or a cycle) in A.
- Since the array is circular, you may assume that the last element's next element is the first element, and the first element's previous element is the last element.
- A cycle must start and end at the same index
- Cycle's length > 1.
- Movements in a cycle must all follow a single direction. In other words, a cycle must not consist of both forward and backward movements.
Input: A = [2,-1,1,2,2] Output: true Explanation: There is a cycle, from index 0 -> 2 -> 3 -> 0. The cycle's length is 3.
Input: A = [1, 1, 1, 1, 1, 1] Output: true Explanation: Whole array forms a cycle.
Input: A = [-2,1,-1,-2,-2] Output: false Explanation: The movement from index 1 -> 2 -> 1 -> ... is not a cycle, because movement from index 1 -> 2 is a forward movement, but movement from index 2 -> 1 is a backward movement. All movements in a cycle must follow a single direction.