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How to Think About Algorithms by Jeff Edmonds

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26 Adding-Made-Easy Approximations

image

Sums arise often in the study of computer algorithms. For example, if the ith iteration of a loop takes time f(i) and it loops n times, then the total time is f(1) + f(2) + f(3) + · · · + f(n). This we denote as image. It can be approximated by the integral image, because the first is the area under the stairs of height f(i) and the second under the curve f(x). (In fact, both ∑ (from the Greek letter sigma) and (from the ...

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