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: