565. Array Nesting

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A zero-indexed array A consisting of N different integers is given. The array contains all integers in the range [0, N - 1].

Sets S[K] for 0 <= K < N are defined as follows:

S[K] = { A[K], A[A[K]], A[A[A[K]]], … }.

Sets S[K] are finite for each K and should NOT contain duplicates.

Write a function that given an array A consisting of N integers, return the size of the largest set S[K] for this array.

Example 1:

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Input: A = [5,4,0,3,1,6,2]
Output: 4
Explanation:
A[0] = 5, A[1] = 4, A[2] = 0, A[3] = 3, A[4] = 1, A[5] = 6, A[6] = 2.
One of the longest S[K]:
S[0] = {A[0], A[5], A[6], A[2]} = {5, 6, 2, 0}

Note:

N is an integer within the range [1, 20,000].
The elements of A are all distinct.
Each element of array A is an integer within the range [0, N-1].

解法1： O(N) Time + O(N) Space

用DFS的思想，同时记录所访问过的元素。对于每一个未被访问过的元素跑一遍DFS，直到碰到已经访问过的元素位置，同时更新一下最大的值。
C++

1

Java

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public class Solution {
    public int arrayNesting(int[] nums) {
        // union find
        if (nums == null || nums.length == 0) {
            return 0;
        }
        boolean[] visited = new boolean[nums.length];
        int res = Integer.MIN_VALUE;
        for (int i = 0; i < nums.length; i++) {
            int cnt = 0;
            int current = i;
            while (!visited[current]) {
                cnt++;
                visited[current] = true;
                current = nums[current];
            }
            res = Math.max(res, cnt);
        }
        return res;
    }
}