Data Structures and Algorithms Using Python and C++ by David M. Reed

By David M. Reed

THIS publication is meant to be used in a conventional college-level information constructions direction (commonly often called CS2). This ebook assumes that scholars have realized the fundamental syntax of Python and been uncovered to using latest sessions. most standard CS1 classes that use Python may have lined the entire precious subject matters, and a few could have coated the various themes coated during this publication. we've came upon that the majority scholars effectively finishing a CS1 path understand how to exploit sessions, yet lots of them want extra adventure to profit how you can layout and write their very own sessions.

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For example, we know that a linear search will take twice as long to discover that a number is not in a list when the size of the list doubles. It would be more informative to say that the asymptotic growth rate of linear search is not just bounded by n, but it is n. 8 is used to describe situations where we have a tight upper (and lower) bound. To formally prove an algorithm is 8(f(n)) we must find constants Cl , C2 , and no such that the number of steps for the algorithm is greater than clf(n) and the number of steps is less than c2 f (n) for all n > no.

By the way, printing something or placing information in a file are also examples of side effects. When we said above that functions should generally not print any­ thing unless that is part of their stated functionality, we were really just identifying one special case of (potentially) undocumented side effects. [1]J Algorith Ana lysis m When we start dealing with programs that contain collections of data, we often need to know more about a function than just its pre- and postconditions. Dealing with a list of 10 or even 100 exam scores is no problem, but a list of customers for an online business might contain tens or hundreds of thousands of items.

That sum is just double the original, so dividing by 2 gives use this formula: n( n + 1 ) /2. Expanding this produces a quadratic polynomial, so we can conclude this code fragment has running time 0(n2 ) . Finally, here's a little example using a while loop. n = input ( ' enter n : ' ) while n > 1 : n = n II 2 # I I is integer divis ion This code is a little different from all the other code fragments. We have a loop, but it does not execute n times. Each time through the loop, n is divided by 2 so we need to determine how many times it will take to reach 1 .

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