457 - Circular Array Loop\.

Medium

You are playing a game involving a circular array of non-zero integers nums. Each nums[i] denotes the number of indices forward/backward you must move if you are located at index i:

• If nums[i] is positive, move nums[i] steps forward , and

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

Since the array is circular , you may assume that moving forward from the last element puts you on the first element, and moving backwards from the first element puts you on the last element.

A cycle in the array consists of a sequence of indices seq of length k where:

• Following the movement rules above results in the repeating index sequence seq[0] -> seq[1] -> ... -> seq[k - 1] -> seq[0] -> ...

• Every nums[seq[j]] is either all positive or all negative.

• k > 1

Return true if there is a cycle in nums, or false otherwise.

Example 1:

Input: nums = 2,-1,1,2,2

Output: true

Explanation: There is a cycle from index 0 -> 2 -> 3 -> 0 -> ... The cycle's length is 3.

Example 2:

Input: nums = -1,2

Output: false

Explanation: The sequence from index 1 -> 1 -> 1 -> ... is not a cycle because the sequence's length is 1. By definition the sequence's length must be strictly greater than 1 to be a cycle.

Example 3:

Input: nums = -2,1,-1,-2,-2

Output: false

Explanation: The sequence from index 1 -> 2 -> 1 -> ... is not a cycle because nums1 is positive, but nums2 is negative. Every nums[seqj] must be either all positive or all negative.

Constraints:

• 1 <= nums.length <= 5000

• -1000 <= nums[i] <= 1000

• nums[i] != 0

Follow up: Could you solve it in O(n) time complexity and O(1) extra space complexity?