COP3502_15_Summations - Fun With Summations Computer...

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Computer Science Department University of Central Florida Fun With Summations COP 3502 – Computer Science I
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Fun With Summations page 2 Summations Is this a Math class? Why do we study summations? In order to effectively approximate algorithms We NEED mathematical tools It is not always as simply as doing a 4 second examination of a for loop and deciphering the Big-O time So for iterative algorithms We use summations as the tool (discussed today) For recursive algorithms, this doesn’t work We need yet another tool Recurrence relations (coming after the exam)
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Fun With Summations page 3 Summations Definition: In very basic terms, a summation is the addition of a set of numbers. Example: Let’s say we want to sum the integers from 1 to 5 Here, the “i” is just a variable. Let’s look at this notation in more detail… = 5 1 i i 5 4 3 2 1 + + + + = 15 =
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Fun With Summations page 4 Summations A summation: or is like a for loop:         for ( int j = m; j <= n; j++ )              sum += f(j); = n m j j f ) ( ) ( j f n index of upper limit lower limit Here, f(j) is simply a function in terms of j Just like f(x) = 2x+1 is a function in terms of x. f(j) is simply some function in terms of j. So what is f(j)?
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Fun With Summations page 5 Summations Example con’d: Since “i” is just a variable, we can use any variable name… We also recognize that a summation is merely summing (adding) the values of some given function This far, we’ve only looked at this most simply function: f(i) = i And then we summed up those i terms.
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COP3502_15_Summations - Fun With Summations Computer...

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