November 15

November 15 - CSCI 2670 Introduction to Theory of Computing...

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CSCI 2670 Introduction to Theory of Computing November 15, 2005
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November 15, 2005 Agenda •Today – Comparing complexity of different computing models • This week – Finish 7.1 and do 7.2
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November 15, 2005 Announcement • Office hours changed tomorrow – 11:30 to 1:00 instead of 11:00 – 12:30
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November 15, 2005 Analyzing algorithms • We can examine an algorithm to determine how long it will take to halt on an input of length n • The amount of time to complete is called the algorithms complexity class Definition: Let t:N N be a function. The time complexity class, TIME(t(n)), is defined as follows. TIME(t(n))={L|L is a language decided by an O(t(n)) time TM}
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November 15, 2005 Another example • Finding minimum element in a set • Amount of time depends on the structure of the input • If set is a sorted array? – O(1) • If set is an unsorted array? – O(n) • If set is a balanced sorted tree? –O(
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November 15, 2005 Importance of model • The complexity of our algorithms depends on assumptions about our • The complexity of an algorithm can vary depending on the machine we use • Recall we assume reasonable encoding of all numbers – Any integer of value v should take O(log v) space
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November 15 - CSCI 2670 Introduction to Theory of Computing...

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