Height of n-ary tree if parent array is given

Given a parent array P, where P[i] indicates the parent of the ith node in the tree(assume parent of root node id indicated with -1). Find the height of the tree.

Examples:

Input : array[] = [-1 0 1 6 6 0 0 2 7]
Output : height = 5
Tree formed is: 
 0
 / | \
 5 1 6
 / | \
 2 4 3
 /
 7
 /
 8 

1. Start at each node and keep going to its parent until we reach -1. 
2. Also, keep track of the maximum height between all nodes.  

Implementation:

Height of the given tree is: 5

Time Complexity : O( N^2 )
Auxiliary Space: O( 1 ) 

Optimized approach: We use dynamic programming. We store the height from root to each node in an array. So, if we know the height of the root to a node, then we can get the height from the root to the node child by simply adding 1. 

Implementation:

Height of the given tree is: 5

Time complexity :- O(n) 
Auxiliary Space:- O(n)