# 457. Circular Array Loop

## 1. Question

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 indexi:

• 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 seqof length k where:

• Following the movement rules above results in the repeating index sequence seq -> seq -> ... -> seq[k - 1] -> seq -> ...
• Every nums[seq[j]] is either all positive or all negative.

k > 1 Return true if there is a cycle in nums, orfalse otherwise.

## 2. Examples

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 nums is positive, but nums is negative.
Every nums[seq[j]] must be either all positive or all negative.


## 3. 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?

## 5. Solutions

class Solution {
public boolean circularArrayLoop(int[] nums) {
for (int i = 0; i < nums.length; i++) {
int[] visited = new int[nums.length];
if (nums[i] == 0) {
continue;
}
visited[i]++;
int p = nums[i];
while (flag(p, nums[next])) {
if (visited[next] > 1) {
return true;
}
visited[next]++;

int curr = next;
if (curr == next) {
break;
}
}
}
return false;
}

private boolean flag(int a, int b) {
if ((a >= 0 && b >= 0) || (a <= 0 && b <= 0)) {
return true;
}
return false;
}

private int advice(int curr, int[] nums) {
curr += nums[curr];
curr %= nums.length;
curr += nums.length;
curr %= nums.length;
return curr;
}
}