Define amortized complexity. How does it differ from average-case complexity? Give an example of a data...
Define amortized complexity. How does it differ from average-case complexity? Give an example of a data structure for which the amortized time complexity is lower than the worst-case time complexity. Give an example of a data structure for which the average-case time complexity is lower than the worst-case time complexity
Homework Answers
Amortized complexity
If T1, T2, …, Tk be the complexities of a sequence of operations on
a data structure. The amortized complexity of a single operation in
this sequence is equal to sum of all complexities divided by number
of operations(T1 + T2 + …+ Tk) / k.
Average case analysis relies on probabilistic assumptions about the
data structures and operations in order to compute an expected
running time of an algorithm.
For Dynamic array the amortized time complexity is lower than the worst-case time complexity.Amortized complexity =O(1)while worst-case complexity = O(n)
For Binary Search Tree(BST)data structure the average-case time
complexity is lower than the worst-case time complexity.
Average time = O(log(n))
Worst case = O(n)
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