457. Circular Array Loop

You are given a circular array `nums` 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. 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.

Determine if there is a loop (or a cycle) in `nums`. A cycle must start and end at the same index and the cycle's length > 1. Furthermore, movements in a cycle must all follow a single direction. In other words, a cycle must not consist of both forward and backward movements.

Example 1:

```Input: [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: [-1,2]
Output: false
Explanation: The movement from index 1 -> 1 -> 1 ... is not a cycle, because the cycle's length is 1. By definition the cycle's length must be greater than 1.
```

Example 3:

```Input: [-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.```

Note:

1. -1000 ≤ nums[i] ≤ 1000
2. nums[i] ≠ 0
3. 1 ≤ nums.length ≤ 5000

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

457. Circular Array Loop
``````struct Solution;

impl Solution {
fn circular_array_loop(mut nums: Vec<i32>) -> bool {
let n = nums.len();
for i in 0..n {
if Self::next(&nums, i) == i {
nums[i] = 0;
}
}
for i in 0..n {
if nums[i] == 0 {
continue;
}
let mut slow = i;
let mut fast = i;
while nums[slow] * nums[Self::next(&nums, fast)] > 0
&& nums[slow] * nums[Self::next(&nums, Self::next(&nums, fast))] > 0
{
slow = Self::next(&nums, slow);
fast = Self::next(&nums, Self::next(&nums, fast));
if slow == fast {
return true;
}
}
let mut j = i;
let val = nums[i];
while nums[j] * val > 0 {
let next = Self::next(&nums, j);
nums[j] = 0;
j = next;
}
}
false
}

fn next(nums: &[i32], index: usize) -> usize {
let n = nums.len();
let index = index as i32 + nums[index];
let index = if index < 0 {
n as i32 + (index % n as i32)
} else {
index % n as i32
};
(index as usize) % n
}
}

#[test]
fn test() {
let nums = vec![2, -1, 1, 2, 2];
let res = true;
assert_eq!(Solution::circular_array_loop(nums), res);
let nums = vec![-1, 2];
let res = false;
assert_eq!(Solution::circular_array_loop(nums), res);
let nums = vec![-2, 1, -1, -2, -2];
let res = false;
assert_eq!(Solution::circular_array_loop(nums), res);
let nums = vec![-1];
let res = false;
assert_eq!(Solution::circular_array_loop(nums), res);
}
``````