Quick Union algorithm : It is used to check whether two nodes are connected or not. If both nodes have the same root then they are connected else not connected. Connecting two nodes means make one's root point to other's root.

quick_union.py

"""
Implementation of Quick Union algorithm in python.

Link: https://class.coursera.org/algs4partI-002/lecture/7

"""

def get_root(lis,item):
    """
    return the root of an item
    """
    root=item
    while lis[root] != root:
        root = lis[root]
    return root    

def connected(lis,item1,item2):
    """
    Checks if two items are connected
    or not.
    Connected means both items have the
    same root
    """
    root1=get_root(lis,item1)
    root2= get_root(lis,item2)
    return True if root1==root2 else False

def quick_union(lis,item1,item2):
    """
    Join two nodes(join their roots)
    """
    root1=get_root(lis,item1)
    root2= get_root(lis,item2)
    if root1 != root2:
        lis[root1]=root2
    else:
        print "Already connected"