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Binsearch not updating
(If it does become false, then the code is wrong.) Choosing the correct invariant — one that properly expresses the intent of an algorithm — is a key part of the design of code (as opposed to the design of APIs); and ensuring that the invariant remains true is a key part of the actual coding.
Roughly speaking, if your invariant properly expresses the intent of the algorithm, and if your code properly maintains the invariant, then that is enough for you to be confident that the code, if it terminates, yields the correct answer.
By approaching the same problem from two different directions, I give myself the best chance of avoiding mistakes; whereas if I add in the same direction both times, I am liable to repeat a “favourite mistake” like adding 8 7 and making the result 13 rather than 15.
So this article on invariants is both part 1 of the new writing-correct-code series and part 4a of the binary-search series. A few people have complained about the sushi pictures on this blog, so before I plough into the article proper, here is something completely different.
In previous articles, I’ve complained about using testing as a crutch (note: about their code. In this mini-series, I want to draw attention to a few concepts that will be patronisingly familiar to most of you who have CS degrees, but which will hopefully be helpful to any avocational programmers hoping to tighten up their code.
(To help us concentrate on the algorithm, we’ll assume that the values are all integers — we could do this with templates and generics and whatnot, but for our current purposes that would only obscure the algorithmic issues that we want to concentrate on.).
But if we are allowed to assume that the array is sorted (in ascending order) then we can do much better.
I’m struggling with my article numbering now :-) Regular readers will have noticed that I am running a whole bunch of series in parallel on this blog: one reviewing programming books, one on the issue of simplicity in programming, one reviewing Series 5 of [amazon.com, uk] has led through a sequence of digressions and become a series of its own on binary search.
Binsearch not updating
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This is part 4 of that series: when I’ve finished part 4, I will — at last! But since part 4 is about the distinctly non-trivial subject of writing correct code, it will itself have to be composed of multiple sub-parts.Through the use of a simple but powerful technique, I was able to write compact, clear code in a short time; and be pretty confident, even before I tested it, that it was correct.That last point is important not as some kind of macho posturing, but because it means that the tests, when I run them, are giving a second distinct line of sight on the problem.The point is not necessarily to go through the code in small pedantic steps like this, but to spend some time up front understand what the invariant is, keep that invariant in mind while coding, and understand the resulting code to whatever depth seems appropriate.It takes much longer to read about this (and longer to write about it! Writing the C function above took two or three minutes; just being explicitly aware of the invariant was nine tenths of the battle.There are several candidate representations, none of them greatly better or worse than the others: we could keep track of the highest and lowest array indexes that might hold , or the lowest index and the size of the range; or use asymmetric indexes, where we maintain the index to the base of the current range and the index that points past the end.For this version of the routine, I’m going to arbitrarily choose to represent the range by two variables, if it’s present.For very small arrays that difference is negligible; but when searching in an array of a million elements, binary search needs 20 probes rather than 500,000 on average for a linear search.In informal terms, the invariant for this algorithm is: “if the sought value is present in the array at all, then it is present in the current range”.But note that in this article I will go rather overboard for the purposes of explanation, and use a level of detail that I would never normally use for a program as trivial as a binary search.So: I am not suggesting that we should invest this level of analysis in every loop we ever write.