Finding maximum and minimum in union find algorithm

This post is a problem based on union find algorithm. For the algorithm, please see "Weighted Quick Union With Path Compression - Coursera Algorithms"

Problem: Given an element, find the max/min of it's connected components tree.

Following is my, probably brute force, solution to find max/min. For this, we use extra arrays to store the max and min values. We updated the max and min only for root nodes. For all other nodes, just find the root and it's max/min.

Weighted Quick Union With Path Compression - Coursera Algorithms

Weighted Quick Union can be improved further by path compression. The idea here is to avoid flatten the tree. After computing the root of a node,  we set the id of each examined node to point to that root.

Running Time:
For M union-find operations on N elements, running time  ≤ c ( N + M lg* N ) array accesses. 

lg*N = number of times we have to take log of N to get 1.

It's almost linear and union find doesn't have any linear algorithm.

Following is the program: