Introduction
Growth of Functions
Discrete Mathematics
Andrei Bulatov
Discrete Mathematics – Growth of Functions
192
Complexity of Algorithms
How to measure what the efficiency of an algorithm is?
Sorting algorithms: given a sequence of numbers, arrange it in the
increasing order.
Longer sequences require more time.
The (time) complexity of a sorting algorithm is a function
f such
that processing a sequence of length
n
requires
f(n) seconds.
Not good:
 computers are different, so,
f(n)
is illdefined
 different sequences of the same length may require different time
The (worst case) (time) complexity of a sorting algorithm is a
function
f
such that processing a sequence of length
n
requires at
most
f(n) steps.
Discrete Mathematics – Growth of Functions
193
Comparing Algorithms
There are more than 20 different sorting algorithms. Which one is
the best?
Consider two of them: bubble sort and merge sort. We use the
same computer, so we can measure in seconds, rather than in
steps.
n
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 Spring '10
 AndreiBulatov
 1 m, 5m, 1 m

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