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19a-Growth-of-Functions

# 19a-Growth-of-Functions - Growth of Introduction Functions...

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Growth of Functions Discrete Mathematics

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Discrete Mathematics – Growth of Functions 19-2 Previous Lecture Countable sets Integers and rationals Uncountable sets Cantor diagonalization
Discrete Mathematics – Growth of Functions 19-3 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 ill-defined - 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.

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Discrete Mathematics – Growth of Functions 19-4 Comparing Algorithms There are more than 20 different sorting algorithms. Which one is the best?
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19a-Growth-of-Functions - Growth of Introduction Functions...

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