How can I solve " exceeded execution timeout period" error in my code?

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C#

Hello. I am learning about different Data Structures from a course in Coursera and I am just a beginner.
I had one exercise which was for finding the maximum height or maximum depth of a tree(but not just for binary trees). But unfortunately, my code does not pass all the tests in the specified time but it works correctly.
Here is the exercise description:

Task. You are given a description of a rooted tree. Your task is to compute and output its height. Recall that the height of a (rooted) tree is the maximum depth of a node or the maximum distance from a leaf to the root. You are given an arbitrary tree, not necessarily a binary tree.
Input Format. The first line contains the number of nodes 𝑛. The second line contains 𝑛 integer numbers from −1 to 𝑛 − 1 — parents of nodes. If the 𝑖-th one of them (0 ≤ 𝑖 ≤ 𝑛 − 1) is −1, node 𝑖 is the root, otherwise it’s 0-based index of the parent of 𝑖-th node. It is guaranteed that there is exactly one root.
It is guaranteed that the input represents a tree.
Constraints. 1 ≤ 𝑛 ≤ 105.
Output Format. Output the height of the tree.



Sample 1.
Input:

5
4 -1 4 1 1

Output:

3

The input means that there are 5 nodes with numbers from 0 to 4, node 0 is a child of node 4, node 1 is the root, node 2 is a child of node 4, node 3 is a child of node 1, and node 4 is a child of node 1. To see this, let us write numbers of nodes from 0 to 4 in one line, and the numbers are given in the input in the second line underneath:

0 1 2 3 4
4 -1 4 1 1

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

The height of this tree is 3 because the number of vertices on the path from root 1 to leaf 2 is 3.



Sample 2.
Input:

5
-1 0 4 0 3

Output:

4

Explanation:
The input means that there are 5 nodes with numbers from 0 to 4, node 0 is the root, node 1 is a child of node 0, node 2 is a child of node 4, node 3 is a child of node 0, and node 4 is a child of node 3. The height of this tree is 4 because the number of nodes on the path from root 0 to leaf 2 is 4.

What I have tried:

Here is my code:

public long Solve(long nodeCount, long[] tree)
{
    // 
    long max_height = 0;
    for (long i = 0; i < nodeCount; i++)
    {
        long h = 0;
        long current = i;
        while (current != -1)
        {
            h++;
            current = tree[current];
        }
        max_height = Math.Max(h, max_height);
    }
    return max_height;
}

There is a total of 24 test cases for this exercise and my code shows "Time Limit error" after the 20th testcase.

I will be really grateful for any help.

Thanks.