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@@ -47,7 +47,7 @@ Which company has the “best” algorithm?
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In this course we will focus on the intuition of order notation. This topic will be covered again, in more depth, in
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later computer science courses.
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- Definition: Algorithm A is order f(n) — denoted O(f(n)) — if constants k and n<sup>0</sup> exist such that A requires no more than k * f(n) time units (operations) to solve a problem of size n ≥ n<sup>0</sup>.
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- Definition: Algorithm A is order f(n) — denoted O(f(n)) — if constants k and n<sub>0</sub> exist such that A requires no more than k * f(n) time units (operations) to solve a problem of size n ≥ n<sub>0</sub>.
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- For example, algorithms requiring 3n + 2, 5n − 3, and 14 + 17n operations are all O(n).
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This is because we can select values for k and n0 such that the definition above holds. (What values?)
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Likewise, algorithms requiring n<sup>2</sup>/10 + 15n − 3 and 10000 + 35n<sup>2</sup> are all O(n<sup>2</sup>).
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