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:
nums[i] is positive, move nums[i] steps forward, andnums[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.
\n\nA cycle in the array consists of a sequence of indices seq of length k where:
seq[0] -> seq[1] -> ... -> seq[k - 1] -> seq[0] -> ...nums[seq[j]] is either all positive or all negative.k > 1Return true if there is a cycle in nums, or false otherwise.
\n
Example 1:
\n\n\nInput: nums = [2,-1,1,2,2]\nOutput: true\nExplanation:\nThere is a cycle from index 0 -> 2 -> 3 -> 0 -> ...\nThe cycle's length is 3.\n\n\n
Example 2:
\n\n\nInput: nums = [-1,2]\nOutput: false\nExplanation:\nThe sequence from index 1 -> 1 -> 1 -> ... is not a cycle because the sequence's length is 1.\nBy definition the sequence's length must be strictly greater than 1 to be a cycle.\n\n\n
Example 3:
\n\n\nInput: nums = [-2,1,-1,-2,-2]\nOutput: false\nExplanation:\nThe sequence from index 1 -> 2 -> 1 -> ... is not a cycle because nums[1] is positive, but nums[2] is negative.\nEvery nums[seq[j]] must be either all positive or all negative.\n\n\n
\n
Constraints:
\n\n1 <= nums.length <= 5000-1000 <= nums[i] <= 1000nums[i] != 0\n
Follow up: Could you solve it in O(n) time complexity and O(1) extra space complexity?
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