Find the height of the tree represented as array

Reference :-
http://www.geeksforgeeks.org/amazon-interview-experience-set-134-campus-sde
"Attempt 2 F2F – Round 3: Q3"

Problem statement :-

An array is given whose every ith index is the child node of a[i] as shown in the example below. The root node is represented by -1. 

Find the height of the tree.I did it in linear time.

Input: parent[] = {1 2 -1 2}

index                     0 1 2  3

for index 2 value is -1. So it is root   2
for index and index 3 value is 2. So they are child of 2  
          2
        /  \
       1    3
     
for index 0 value is 1. So it is child of 1

         2
        /  \
       1    3
      /    
     0

Height of this tree is 3

My approach :- 

Height of the tree  = maximum number in the array + 1 =  2+1 =3

Another example

Input: parent[] = 1 3 -1  2  1
Index                  0 1  2  3  4

Tree is 
     2
    /
   3
  /
 1
/ \
0  4
    \
     5

Height of this tree is 5


My approach :- 
Height of the tree  = maximum number in the array + 1 =  4+1 =5