Struct and Compute tree height based on an input pattern

let's say I have this input

5

4 -1 4 1 1

Explanation: The first line contains the number of nodes . The second line contains integer numbers from −1 to − 1 — parents of nodes. If the -th one of them (0 ≤ ≤ − 1) is −1, node is the root, otherwise, it’s 0-based index of the parent of -th node.

0 1 2 3 4

4 -1 4 1 1

Now we can see that the node number 1 is the root because −1 corresponds to it in the second line. Also, we know that the nodes number 3 and number 4 are children of the root node 1. Also, we know that the nodes number 0 and number 2 are children of the node 4.

I must take this data and struct a tree. base on that input. However, I'm provided with one suggestion that I still can't fathom.

"Suggestion: Take advantage of the fact that the labels for each tree node are integers in the range 0..−1: you can store each node in an array whose index is the label of the node. By storing the nodes in an array, you have (1) access to any node given its label.

allocate []

for ← 0 to − 1:

[] =new

Then, read each parent index:

for ℎ_ ← 0 to − 1:

read _

if _ == −1:

← ℎ_

else:

[_].ℎ([ℎ_])"

I tried to do the following:

set up a hashmap. the key is parents. and its children in an array list. since ill always be appending. the goal here is to compute the height of this tree. In my hashmap, I have all the parents as the Key and all the children in the tree are the value which is represented as an ArrayList. the tree might not be binary therefore I might have a node with more than 2 children. if this implementation is a tree! why. why it's a tree and how could you name a tree since u don't have a Node class and the root is like any other parent. and if it is a tree. how do I even compute its height?

void setUpTree() {
        tree = new HashMap<>(n);
        int num;
        for (int i = 0; i < n; i++) {
            num = parent[i];
            if (num == -1)
                tree.put(i, new ArrayList<>());
            else {
                tree.computeIfAbsent(num, k -> new ArrayList<>());
                tree.get(num).add(i);
            }
        }
    }

the task itself is inscrutable to me since the tree is implemented using an Array. I implemented the setUpTree method based on what I understood I have no idea if I'm on the right track. and if so. how to even compute the height. I'd appreciate any explanation or a hint. thank you.

The complete starter code for Context:

public class tree_height {

static class FastScanner {
    StringTokenizer tok = new StringTokenizer("");
    BufferedReader in;

    FastScanner() {
        in = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() throws IOException {
        while (!tok.hasMoreElements())
            tok = new StringTokenizer(in.readLine());
        return tok.nextToken();
    }

    int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
}

public static class TreeHeight {
    int n;
    int[] parent;
    HashMap<Integer, ArrayList<Integer>> tree;

    void read() throws IOException {
        FastScanner in = new FastScanner();
        n = in.nextInt();
        parent = new int[n];
        for (int i = 0; i < n; i++) {
            parent[i] = in.nextInt();
        }
    }

   //the implementation of the algorithm provided in the suggestion
    void setUpTree() {
        tree = new HashMap<>(n);
        int num;
        for (int i = 0; i < n; i++) {
            num = parent[i];
            if (num == -1)
                tree.put(i, new ArrayList<>());
            else {
                tree.computeIfAbsent(num, k -> new ArrayList<>());
                tree.get(num).add(i);
            }
        }
    }

    int computeHeight() {
        //set up the tree to compute its height
        setUpTree();

        //Compute tree height here
}

static public void main(String[] args) throws IOException {
    new Thread(null, new Runnable() {
        public void run() {
            try {
                new tree_height().run();
            } catch (IOException ignored) {
            }
        }
    }, "1", 1 << 26).start();
}

public void run() throws IOException {
    TreeHeight tree = new TreeHeight();
    tree.read();
    System.out.println(tree.computeHeight());
}