You’ve Already Seen Amortization
Hashtable doubling
Some insert() operations take time O(n) due to table
doubling
Amortized expected time per op is still O(1)
Union/Find with weighted union and path
compression
Worst-case time for union() is O(1)
Worst-case time for find() is O(log n)
Worst-case time for a sequence of n operations (starting
from singletons) is O(n a(n))
Amortized time per operation is O(a(n))
CS409 - Spring 2000
3