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In this approach, we use an auxiliary 'visited' array to keep track of the elements that have already been included in any set s[k]. For each unvisited element at index i, we keep iterating through the sequence by accessing nums[nums[i]] until we encounter an element already visited. Each time we reach an unvisited element, we mark it as visited, and increment the length of the current sequence. We keep track of the longest length among all sequences generated from each starting index.
Time Complexity: O(N), where N is the number of elements in the array, as each element is visited at most once.
Space Complexity: O(N) due to the additional 'visited' array.
1import java.util.Arrays;
2
3public class Solution {
4 public int arrayNesting(int[] nums) {
5 boolean[] visited = new boolean[nums.length];
6 int max_length = 0;
7 for (int i = 0; i < nums.length; i++) {
8 if (!visited[i]) {
9 int start = i, length = 0;
10 do {
11 visited[start] = true;
12 start = nums[start];
13 length++;
14 } while (!visited[start]);
15 max_length = Math.max(max_length, length);
16 }
17 }
18 return max_length;
19 }
20
21 public static void main(String[] args) {
22 Solution solution = new Solution();
23 int[] nums = {5, 4, 0, 3, 1, 6, 2};
24 System.out.println(solution.arrayNesting(nums));
25 }
26}The Java solution maintains a boolean array to mark visited indices, facilitating sequence formation from each unvisited index within an outer loop. The inner loop continues following indices until an index reoccurs. The use of Math.max() updates the longest length, and the final value is returned.
This approach minimizes space usage by modifying the input array itself as a marker of visited nodes. By setting each visited position to a sentinel value (e.g., -1 or a number outside the expected range), we can achieve the same iterative closure tracking. We simply iterate over each number and trace the sequence until we circle back to a marked node. This is an improvement on memory constraints when needing to handle particularly large datasets.
Time Complexity: O(N), executing a linear pass through the nodes.
Space Complexity: O(1), modifying input without auxiliary space.
JavaScript carries out position work by utilizing the derived in-situ signifiers within the main sequence of values, safely distinguishing completed cycles post-processing maximizations. With only required steps followed, this method embodies a concise, purposeful strategy on avoiding uniform steps repeated ambiguously.