# Array Nesting Problem

## Description

LeetCode Problem 565.

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:

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

Example 2:

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

Constraints:

• 1 <= nums.length <= 10^5
• 0 <= nums[i] < nums.length
• All the values of nums are unique.

## Sample C++ Code

The idea is to, start from every number, find circles in those index-pointer-chains. Every time we find a set (a circle) mark every number as visited (-1) so that next time we won’t step on it again.

``````1
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class Solution {
public:
int arrayNesting(vector<int>& a) {
size_t maxsize = 0;
for (int i = 0; i < a.size(); i++) {
size_t size = 0;
for (int k = i; a[k] >= 0; size++) {
int ak = a[k];
a[k] = -1; // mark a[k] as visited;
k = ak;
}
maxsize = max(maxsize, size);
}

return maxsize;
}
};
``````