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# 19 - Growth of Introduction Functions Discrete Mathematics...

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Introduction Growth of Functions Discrete Mathematics Andrei Bulatov

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Discrete Mathematics – Growth of Functions 19-2 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.
Discrete Mathematics – Growth of Functions 19-3 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.

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19 - Growth of Introduction Functions Discrete Mathematics...

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