# 0565. Array Nesting

<https://leetcode.com/problems/array-nesting>

## Description

You are given an integer array `nums` of length `n` where `nums` is a permutation of the numbers in the range `[0, n - 1]`.

You should build a set `s[k] = {nums[k], nums[nums[k]], nums[nums[nums[k]]], ... }` subjected to the following rule:

* The first element in `s[k]` starts with the selection of the element `nums[k]` of `index = k`.
* The next element in `s[k]` should be `nums[nums[k]]`, and then `nums[nums[nums[k]]]`, and so on.
* We stop adding right before a duplicate element occurs in `s[k]`.

Return *the longest length of a set* `s[k]`.

**Example 1:**

```
**Input:** nums = [5,4,0,3,1,6,2]
**Output:** 4
**Explanation:** 
nums[0] = 5, nums[1] = 4, nums[2] = 0, nums[3] = 3, nums[4] = 1, nums[5] = 6, nums[6] = 2.
One of the longest sets s[k]:
s[0] = {nums[0], nums[5], nums[6], nums[2]} = {5, 6, 2, 0}
```

**Example 2:**

```
**Input:** nums = [0,1,2]
**Output:** 1
```

**Constraints:**

* `1 <= nums.length <= 105`
* `0 <= nums[i] < nums.length`
* All the values of `nums` are **unique**.

## ac

```java
class Solution {
    public int arrayNesting(int[] nums) {
        Set<Integer> set = new HashSet<>();
        int max = 0;
        for (int i = 0; i < nums.length; i++) {
            int cnt = 0;
            int j = i;
            while (set.add(nums[j])) {
                cnt++;
                j = nums[j];
            }
            max = Math.max(max, cnt);
        }

        return max;
    }
}

/*
1) start from each i, add visited elements to set; 2) after visiting, update max length;
*/
```


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