## React for the algebra enthusiast – Part 2

In Part 1, I explained how algebra can shed some light on a quite restricted class of react-apps. Today, I will lift one of the restrictions. This step needs a new kind of algebraic structure:

## Categories

Category theory is a large branch of pure mathematics, with many facets and applications. Most of the latter are internal to pure mathematics. Since I have a very special application in mind, I will give you a definition which is less general than the most common ones.

Categories can be thought of as generalized monoids. At the same time, a Category is a labelled, directed multigraph with some extra structure. Here is a picture of a labelled directed multigraph – its nodes are labelled with upper case letters and its edges are labelled with lower case letters:

If such a graph happens to be a category, the nodes are called objects and the edges morphisms. The idea is, that the objects are changed or morphed into other objects by the morphisms. We will write $h:A\to B$ for a morphism from object $A$ to object $B$.

But I said something about extra structure and that categories generalize monoids. This extra structure is essentially a monoid structure on the morphisms of a category, except that there is a unit for each object called identity and the operation “$\_\circ\_$” can only be applied to morphisms, if they form “a line”. For example, if we have morphisms like k and i in the picture below, in a category, there will be a new morphism “$k\circ i$“:

Note that “$i$” is on the right in “$k\circ i$” but it is the first morphism if you follow the direction indicated by the arrows. This comes from function composition in mathematics, which suffers from the same weirdness by some historical accident. For now that just means that chains of morphisms have to be read from right to left to make sense of them.

For the indentities and the operation “$\_\circ\_$“, we can ask for the same laws to hold as in a monoid, which will complete the definition of a category:

## Definition (not as general as it could be…)

A category consists of the following data:

• A set of objects A,B,…
• A set of morphisms $f : A_1\to B_1, g:A_2\to B_2,\dots$
• An operation “$\_\circ\_$” which for all (consecutive) pairs of morphisms $f:A\to B$ and $g:B\to C$ returns a morphism $g \circ f : A \to C$
• For any object a morphism $\mathrm{id}_A : A\to A$

Such that the following laws hold:

• $\_\circ\_$ ” is associative: For all morphisms $f : A \to B$, $g : B\to C$ and $h : C\to D$, we have: $h \circ (g \circ f) = (h \circ g) \circ f$
• The identities are left and right neutral: For all morphisms $f: A\to B$ we have: $f \circ \mathrm{id}_A=\mathrm{id}_B \circ f$

## Examples

Before we go to our example of interest, let us look at some examples:

• Any monoid is a category with one object O and for each element m of the monoid a morphism $m:O\to O$. “$m\circ n$” is defined to be $m\cdot n$.
• The graph below can be extended to a category by adding the morhpisms $ef: B\to B, fe: A\to A, efe: A\to B, fef: B\to A, \dots$ and an identity for $A$ and $B$. The operation “$\_\circ\_$” is defined as juxtaposition, where we treat the identities as empty sequences. So for example, $ef\circ efe$ is $efefe: A\to B$.
• More generally: Let $G$ be a labelled directed graph with edges $e_1,\dots,e_r$ and nodes $n_1,\dots,n_l$. Then there is a category $C_G$ with objects $n_1,\dots,n_l$ and morphisms all sequences of consectutive edges – including the empty sequence for any node.

## Action Categories

So let’s generalize Part 1 with our new tool. Our new scope are react-apps, which have actions without parameters, but now, action can not neccessarily be applied in any order. If an action can be fired, may now depend on the state of the app.

The smallest example I can think of, where we can see whats new, is an app with two states, let’s call them ON and OFF and two actions, let’s say SWITCH_ON and SWITCH_OFF:

Let us also say, that the action SWITCH_ON can only be fired in state OFF and SWITCH_OFF only in state ON. The category for that graph has as its morphims the possible sequences of actions. Now, if we follow the path of part 1, the obvious next step is to say that SWITCH_ON after SWITCH_OFF (and the other way around) is the same as the empty action-sequence — which leads us to…

## Quotients

We made a pretty hefty generalization from monoids to categories, but the theory for quotients remains essentially the same. As we defined equivalence relations on the elements of a monoid, we can define equivalence relations on the morphisms of a category. As last time, this is problematic in general, but turns out to just work if we replace sequences of morphisms in the action category with matching source and target.

So in the example above, it is ok to say that SWITCH_ON SWITCH_OFF is the empty sequence on ON and SWITCH_OFF SWITCH_ON is the empty sequence on OFF (keep in mind that the first action to be executed is on the right). Then any action sequence can be reduced to simply SWITCH_ON, SWITCH_OFF or an empty sequence (not the empty sequence, because we have two of them with different source and target). And in this case, the quotient category will be what we drew above, but as a category.

Of course, this is not an example where any high-powered math is needed to get any insights. So far, these posts where just about understanding how the math works. For the next part of this series, my plan is to show how existing tools can be used to calculate larger examples.

## React for the algebra enthusiast – Part 1

When I learned to use the react framework, I always had the feeling that it is written in a very mathy way. Since simple googling did not give me any hints if this was a consideration in the design, I thought it might be worth sharing my thoughts on that. I should mention that I am sure others have made the same observations, but it might help algebraist to understand react faster and mathy computer scientiests to remember some algebra.

## Free monoids

In abstract algebra, a monoid is a set M together with a binary operation “$\cdot$” satisfying these two laws:

• There is a neutral element “e”, such that: $\forall x \in M: x \cdot e = e \cdot x = e$
• The operation is associative, i.e. $\forall x,y,z \in M: x \cdot (y\cdot z) = (x\cdot y) \cdot z$

Here are some examples:

• Any set with exactly one element together with the unique choice of operation on it.
• The natural numbers $\mathbb{N}=\{0,1,2,\dots \}$ with addition.
• The one-based natural numbers $\mathbb{N}_1=\{1,2,3,\dots\}$ with multiplication.
• The Integers $\mathbb Z$ with addition.
• For any set M, the set of maps from M to M is a monoid with composition of maps.
• For any set A, we can construct the set List(A), consisting of all finite lists of elements of A. List(A) is a monoid with concatenation of lists. We will denote lists like this: $[1,2,3,\dots]$

Monoids of the form List(A) are called free. With “of the form” I mean that the elements of the sets can be renamed so that sets and operations are the same. For example, the monoid $\mathbb{N}$ with addition and List({1}) are of the same form, witnessed by the following renaming scheme:

$0 \mapsto []$

$1 \mapsto [1]$

$2 \mapsto [1,1]$

$3 \mapsto [1,1,1]$

$\dots$

— so addition and appending lists are the same operation under this identification.

With the exception of $\mathbb{N}_1$, the integers and the monoid of maps on a set, all of the examples above are free monoids. There is also a nice abstract definition of “free”, but for the purpose at hand to describe a special kind of monoid, it is good enough to say, that a monoid M is free, if there is a set A such that M is of the form List(A).

## Action monoids

A react-app (and by that I really mean a react+redux app) has a set of actions. An action always has a type, which is usally a string and a possibly empty list of arguments.

Let us stick to a simple app for now, where each action just has a type and nothing else. And let us further assume, that actions can appear in arbirtrary sequences. That means any action can be fired in any state. The latter simplification will keep us clear from more advanced algebra for now.

For a react-app, sequences of actions form a free monoid. Let us look at a simple example: Suppose our app is a counter which starts with “0” and has an increment (I) and decrement (D) action. Then the sequences of action can be represented by strings like

ID, IIDID, DDD, IDI, …

which form a free monoid with juxtaposition of strings. I have to admit, so far this is not very helpful for a practitioner – but I am pretty sure the next step has at least some potential to help in a complicated situation:

## Quotients

Quotients of sets by an equivalence relation are a very basic tool of modern math. For a monoid, it is not clear if a quotient of its underlying set will still be a monoid with the “same” operations.

Let us look at an example, where everything goes well. In the example from above, the counter should show the same integer if we decrement and then increment (or the other way around). So we could say that the two action sequences

• ID and
• DI

do really nothing and should be considered equivalent to the empty action sequence. So let’s say that any sequence of actions is equivalent to the same sequence with any occurence of “DI” or “ID” deleted. So for example we get:

IIDIIDD $\sim$ I

With this rule, we can reduce any sequence to an equivalent one that is a sequence of Is, a sequence of Ds or empty. So the quotient monoid can be identified with the integers (in two different ways, but that’s ok) and addition corresponds to juxtaposition of action sequences.

The point of this example and the moral of this post is, that we can take a syntactic description (the monoid of action sequences), which is easy to derive from the source code and look at a quotient of the action monoid by a reasonable relation to arrive at some algebraic structure which has a lot to do with the semantic of the app.

So the question remains, if this works just well for an example or if we have a general recipe.

Here is a problem in the general situation: Let $x,y,z\in M$ be elements of a monoid $M$ with operation “$\cdot$” and $\sim$ be an equivalence relation such that $x$ is identified with $y$. Then, denoting equivalence classes with $[\_]$ it is not clear if $[x] \cdot [y]$ should be defined to be $[x\cdot z]$ or $[y\cdot z]$.

Fortunately problems like that disappear for free monoids like our action monoid and equivalence relations constructed in a specific way. As you can see on wikipedia, it is always ok to take the equivalence relation generated by the same kind of identifications we made above: Pick some pairs of sequences which are known “to do the same” from a semantic point of view (like “ID” and “DI” did the same as the empty sequence) and declare sequences to be equivalent, if they arise by replacing sequences known to be the same.

So the approach is that general: It works for apps, where actions do not have parameters and can be fired in any order and for equivalence relations generated by defining finitely many action sequences to do the same. The “any order” is a real restriction, but this post also has a “Part 1” in the title…

## The inevitable emergence of domain events

If you’ve ever encountered code that cannot be modified anymore because business relies on a specific side effect of it, you’ve encountered an implicit domain event.

Even if you’ve read the original Domain Driven Design book by Eric Evans, you’ve probably still not heard about domain events (or DDD Domain Events), as he didn’t include them in the book. He talked about it a lot since then, for example in this talk in 2009 in the first 30 minutes.

## Domain Events

In short, domain events are occurrences of “something that domain experts care about”. You should always be on the lookout for these events, because they are integral parts of the interface between the technical world and the domain world. In your source code, both worlds condense as the same things, so it isn’t easy (or downright impossible) to tell them apart. But if you are familiar with the concept of “pure fabrication”, you probably know that a single line of code can clearly belong to the technical fabric and still be relevant for the domain. Domain events are one possibility to separate the belongings again. But you have to listen to your domain experts, and they probably still don’t tell you the full story about what they care about.

## Revealed by Refactoring

To underline my point, I want to tell you a story about a software project in a big organization. The software is already in production when my consulting job brings me into contact with the source code. We talked about a specific part of the code that screamed “pure fabrication” with just a few lines of domain code in between. Our goal was to refactor the code into two parts, one for the domain code and the other, bigger one for the technical part. In the technical part, some texts get logged into the logfile, like “item successfully written to the database” and “database connection closed”. It were clearly technical aspects of the code that got logged.

One of the texts had a spelling error in it and I reached out to correct it. A developer stopped me: “Don’t do that! They filter for that exact phrase.”. That surprised me. Nothing in the code indicated the relevance of that log statement, least of all the necessity of that typo. And I didn’t know who “they” were and that the logfiles got searched. So I asked a lot of questions and finally understood the situation:

## Implicit Domain Events

The developers implemented the requirements of the domain experts as given in the specification documents. Nothing in there specified the exact text or even presence of logfile entries. But after the software was done and in production, the business side (including the domain experts) needed to know how many items were added to the system in a given period. And because they needed the information right away and couldn’t wait for the next development cycle, they contacted the operation department (that is separated from the development department) and got copies of the logfiles. They scanned the logfiles with some crude regular expression magic for the entries (like “item written to the database”) and got their result. The question was answered, the problem solved and the solution even worked a second time – and a third time, and so on. The one-time makeshift script was used permanently and repeatedly, in fact, it ran every hour and scanned for new items, because it became apparent that the business not only needed the statistics, but wanted to start a business process for each new item (like an editorial review of sorts) in a timely manner.

## Pinned Code

Over the course of a few weeks, the purely technical logfile entry line in the source code got pinned and converted to a crucial domain requirement without any formal specification or even notification. Nothing in the source code hinted at the importance of this line or its typo. No test, no comment, no code structure. The line looked exactly the same as before, but suddenly played in another league. Every modification at this place or its surrounding code could hamper the business. Performing a well-intended refactoring could be seen as direct sabotage. The code was sacred, but in the unspoken kind. The code became a minefield.

## Extracting the Domain Event

The whole hostage situation could be resolved by revealing the domain event and making it explicit. Let’s say that we model an “item added” domain event and post it in addition to the logfile entry. How we post it is up to the requirement or capabilities of the business department. An HTTP request to another service for every new item is a simple and viable solution. A line of text in a dedicated event log file would be another option. Even an e-mail sent to an human recipient could be discussed. Anything that separates the technical logfile from the business view on the system is better than forbidden code. After the separation, we can refactor the technical parts to our liking and still have tests in place that ensure that the domain event gets posted.

## Domain Events are important

These domain events are important parts of your system, because they represent things (or actions) that the business cares about. Even if the business only remembers them after the fact, try to incorporate them in an explicit manner into your code. Not only will you be able to tell domain code and technical code apart easily, but you’ll also get this precious interface between business and tech. Make a list of all your domain events and you’ll know how your system is seen in the domain expert world. Everything else is more or less just details.

What story about implicit domain events comes to your mind? Tell us in a comment or write a blog entry about it. We want to hear from you!

## A Game Optimization War Story

As our customers surely know, I’m not working here on fridays. This is because that’s the time I allocate to my side project, an arcade real-time strategy game called abstractanks. It is a passion project above all else, but of course, I am also learning a lot, much of which I can apply to my “day job” here as well. Today I want to share the story of how I optimized a critical bit of code in that game.

# The Big Slowdown

While working on scripted missions, one main element I am using is to make a group of units attack when you enter an area (a.k.a. a zone-trigger). This seems easy enough, but was causing massive slowdowns as soon as the enemy group started moving. My average logic frame-time jumped from 0.3 ms to more than 1500 ms, which essentially makes the game unplayable. When seeing a performance problem, your first instinct should always be to profile it. So I booted up WPR/WPA and did just that. Once I had the profile, I followed the most-sampled path in the stack and found my way to the supposed culprit: the parking algorithm.

# Context

When optimizing, you need as much context as you possible to find the best possible course of action. So let me explain how that algorithm fits into the broader picture.

## Parking

My main game-mechanic is moving around your units. You do this by selecting a group and then clicking somewhere on the map to issue the move-order. In addition to path-finding process, this also runs an algorithm I call park-planning (as in parking a car). It makes sure that the units know to position themselves around the target point in a roughly circular shape once they arrive. It is essential to the interaction of this mechanic with the capturing of objectives, which are circular as well. Before this was implemented, the units would just decelerate after passing the target point. This caused them to “overshot” and miss the objectives, which was frustrating to the players: they clicked in the right place, but the units would not stop there, but slightly behind it. To make things worse, units arriving later, would bump into those that were already there, further pushing them away and clumping up.

## AI Moving

In my particular case, the AI enemy was repeatedly issuing move-orders to close in on the intruder – the player. Since the player group usually also moved, the AI was trying to adapt by changing the move order every frame (effectively working at around 2000 APMs).

## Diving into the code

My park-planning implementation is divided into two steps: finding enough parking spots, and then assigning units to it. The profiler was showing that the first part was the problem while the assignment was negligible in terms of run-time. Historically, the first step was reusing and extending some code I first wrote for spawning units, which worked like this:

optional<v2> GameWorld::FindFreePosition(v2 Center, std::vector<v2> const& Occupied)
{
auto CheckPosition = [&](v2 Candiate)
{
if (!IsPassable(Candidate))
return false;

if (OverlapsWith(Occupied))
return false;

return !FriendlyUnitOccupies(Candidate);
};

if (CheckPosition(Center))
return Center;

{
// Roll a random starting angle
auto AngleOffset = RandomAngle();
auto Angle = 0.f;
while (Angle < 2*Pi)
{
auto Candidate = Center + AngleVector(Angle + AngleOffset)*Radius;
if (CheckPosition(Candidate))
return Candidate;

// Move along this circle
Angle += 2*Pi*Radius / UNIT_SIZE / OVERSAMPLING_FACTOR;
}

}
return none;
}


Note that all the functions in the CheckPosition lambda are “size aware” and respect the UNIT_SIZE – so they are slightly more complex than what the pseudo-code here would have you believe.
The occupied parameter was added for the parking-position finding. It successively fills up the std::vector with positions and uses them once it found enough.

Back to the profiling results: They were showing that most of the time was spent in the FriendlyUnitOccupies, followed by IsPassable and and then OverlapsWith. FriendlyUnitOccupies dominated the time by about 8x times the rest. That function uses a quad-tree to accelerate spatial queries for other units.

# Next steps

Obviously, this code uses pretty simplistic approach to the problem – basically just brute-forcing it. But that’s good now there are many different paths to take, many optimization opportunities. My approach was a relatively simple change that got the frame time back down below 1 ms, but before I did that, I considered many and tested a few other different approaches. I will talk about that in detail in my next post. How would you approach this?

## Analysing a React web app using SonarQube

Many developers especially from the Java world may know the code analysis platform SonarQube (formerly SONAR). While its focus was mostly integration all the great analysis tools for Java the modular architecture allows plugging tools for other languages to provide linter results and code coverage under the same web interface.

We are a polyglot bunch and are using more and more React in addition to our Java, C++, .Net and “what not” projects. Of course we would like the same quality overview for these JavaScript projects as we are used to in other ecosystems. So I tried SonarQube for react.

# The start

Using SonarQube to analyse a JavaScript project is as easy as for the other languages: Just provide a sonar-project.properties file specifying the sources and some paths for analysis results and there you go. It may look similar to the following for a create-react-app:

sonar.projectKey=myproject:webclient
sonar.projectName=Webclient for my cool project
sonar.projectVersion=0.3.0

#sonar.language=js
sonar.sources=src
sonar.exclusions=src/tests/**
sonar.tests=src/tests
sonar.sourceEncoding=UTF-8

#sonar.test.inclusions=src/tests/**/*.test.js
sonar.coverage.exclusions=src/tests/**

sonar.junit.reportPaths=test-results/test-report.junit.xml
sonar.javascript.lcov.reportPaths=coverage/lcov.info


For the coverage you need to add some settings to your package.json, too:

{ ...
"devDependencies": {
"enzyme": "^3.3.0",
"eslint": "^4.19.1",
"eslint-plugin-react": "^7.7.0",
"jest-junit": "^3.6.0"
},
"jest": {
"collectCoverageFrom": [
"src/**/*.{js,jsx}",
"!**/node_modules/**",
"!build/**"
],
"coverageReporters": [
"lcov",
"text"
]
},
"jest-junit": {
"output": "test-results/test-report.junit.xml"
},
...
}


This is all nice but the set of built-in rules for JavaScript is a bit thin and does not fit React apps nicely.

# ESLint to the recue

But you can make SonarQube use ESLint and thus become more useful.

First you have to install the ESLint Plugin for SonarQube from github.

Second you have to setup ESLint to your liking using eslint --init in your project. That results in a eslintrc.js similar to this:

module.exports = {
'env': {
'browser': true,
'commonjs': true,
'es6': true
},
'extends': 'eslint:recommended',
'parserOptions': {
'ecmaFeatures': {
'jsx': true
},
'sourceType': 'module'
},
'plugins': [
'react'
],
'rules': {
'indent': [
'error',
2
],
'linebreak-style': [
'error',
'unix'
],
'quotes': [
'error',
'single'
],
'semi': [
'error',
'always'
]
}
};



Lastly enable the ESLint ruleset for your project in sonarqube and look at the results. You may need to tune one thing or another but you will get some useful static analysis helping you to improve your code quality further.

SonarQube makes static code analysis easy for a plethora of languages and environments. In many of our newer projects we use gradle as our buildsystem and jenkins as our continuous integration server. Integrating sonarqube in such a setup can be done in a couple of ways, the most straightforward being

• Letting jenkins invoke the gradle build and execute the SonarQube scanner

I chose the latter one because I did not want to add further dependencies to the build process.

# Configuration of the SonarQube scanner

The SonarQube scanner must be configured by property file called sonar-project.properties by default:

# must be unique in a given SonarQube instance
sonar.projectKey=domain:project
# this is the name and version displayed in the SonarQube UI. Was mandatory prior to SonarQube 6.1.
sonar.projectName=My cool project
sonar.projectVersion=23

sonar.sources=src/main/java
sonar.tests=src/test/java
sonar.java.binaries=build/classes/java/main
sonar.java.libraries=../lib/**/*.jar
sonar.java.test.libraries=../lib/**/*.jar
sonar.junit.reportPaths=build/test-results/test/
sonar.jacoco.reportPaths=build/jacoco/test.exec

sonar.modules=application,my_library,my_tools

# Encoding of the source code. Default is default system encoding
sonar.sourceEncoding=UTF-8
sonar.java.source=1.8

sonar.links.ci=http://${my_jenkins}/view/job/MyCoolProject sonar.links.issue=http://${my_jira}/browse/MYPROJ


After we have done that we can submit our project to the SonarQube scanner using the jenkins SonarQube plugin and its “Execute SonarQube Scanner” build step.

# Optional: Adding code coverage to our build

Even our gradle-based projects aim to be self-contained. That means we usually do not use repositories like mavenCentral for our dependencies but store them all in a lib directory along the project. If we want to add code coverage to such a project we need to add jacoco in the version corresponding to the jacoco-gradle-plugin to our libs in build.gradle:

allprojects {
apply plugin: 'java'
apply plugin: 'jacoco'
sourceCompatibility = 1.8

jacocoTestReport {
reports {
xml.enabled true
}
jacocoClasspath = files('../lib/org.jacoco.core-0.7.9.jar',
'../lib/org.jacoco.report-0.7.9.jar',
'../lib/org.jacoco.ant-0.7.9.jar',
'../lib/asm-all-5.2.jar'
)
}
}


# Gotchas

Our jenkins build job consists of 2 steps:

2. Submit project to SonarQube’s scanner

By default gradle stops execution on failure. That means later tasks like jacocoTestReport are not executed if a test fails. We need to invoke gradle with the --continue switch to always run all of our tasks.

## Analyzing iOS crash dumps with Xcode

The best way to analyze a crash in an iOS app is if you can reproduce it directly in the iOS simulator in debug mode or on a local device connected to Xcode. Sometimes you have to analyze a crash that happened on a device that you do not have direct access to. Maybe the crash was discovered by a tester who is located in a remote place. In this case the tester must transfer the crash information to the developer and the developer has to import it in Xcode. The iOS and Xcode functionalities for this workflow are a bit hidden, so that the following step-by-step guide can help.

### Finding the crash dumps

iOS stores crash dumps for every crash that occured. You can find them in the Settings app in the deeply nested menu hierarchy under Privacy -> Analytics -> Analytics Data.

There you can select the crash dump. If you tap on a crash dump you can see its contents in a JSON format. You can select this text and send it to the developer. Unfortunately there is no “Select all” option, you have to select it manually. It can be quite long because it contains the stack traces of all the threads of the app.

### Importing the crash dump in Xcode

To import the crash dump in Xcode you must save it first in a file with the file name extension “.crash”. Then you open the Devices dialog in Xcode via the Window menu:

To import the crash dump you must have at least one device connected to your Mac, otherwise you will find that you can’t proceed to the next step. It can be any iOS device. Select the device to open the device information panel:

Here you find the “View Device Logs” button to open the following Device Logs dialog:

To import the crash dump into this dialog select the “All Logs” tab and drag & drop the “.crash” file into the panel on the left in the dialog.

Initially the stack traces in the crash dump only contain memory addresses as hexadecimal numbers. To resolve these addresses to human readable symbols of the code you have to “re-symbolicate” the log. This functionality is hidden in the context menu of the crash dump:

Now you’re good to go and you should finally be able to find the cause of the crash.

## Developer power tools: Big O = big impact

Scalability and performance are often used interchangeable but they are very different. The big O notation helps in talking about scalability.

Scalability and performance are often used interchangeable but they are very different. The resource consumption of a program is its performance. So performance looks at a specific part of a program, say the user activating an action and tries to fix the input and circumstances.
Scalability defines how the resource consumption of a program changes when additional resources are added or the input size increases. So a program can have good performance (it runs fast) but when the load increases it can behavely badly (a bad scalability). Take bubble sort for example. Since the algorithm has low overhead it runs fast with small arrays but when the arrays get bigger the runtime gets worse. It doesn’t scale.
There are many ways to improve scalability here we look at one particular: reducing algorithmic complexity. The time complexity of an algorithm is measured with the big T notation. The T notation describes the time behavior of the algorithm when the input size changes. Say you have an algorithm that takes n objects and needs 4 times as long with an overhead of 2. This would be:

T(n) = 4n + 2


Often the correct numbers are not necessary, you just want to have a magnitude. This is where the big O notation comes into play. It describes the asymptotical upper bound or just the behaviour of the fastest growing part. In the above case this would be:

T(n) = 4n + 2 = O(n)


We call such an algorithm linear because the resource consumption grows linear with the increase in input size. Why does this matter? Let’s look at an example.

Say we have a list of numbers and want to know the highest. How long would this take? A straight forward implementation would look like this:

int max = Integer.MIN_VALUE;
for (int number : list) {
if (number > max) {
max = number;
}
}


So we need if the size of the number list is n we need n compare operations. So our algorithm is linear. What if we have two lists of length n? We just our algorithm twice and compare both maximums so it would be

T(n) = 2n + 1 = O(n)


also linear.
Why does this all matter? If our algorithm runs quadratic, so O(n^2) and our input size is n = 1000, we need a multitude of 1 million operations. If it is linear it just needs a multitude of 1000 operations, much less. Reducing the complexity of an algorithm can be business critical or the difference between getting an instant result or losing a customer because he waited too long.
Time complexity isn’t the only complexity you can measure other resources like space can also be measured with big O. I hope this clears some questions and if you have further ones please feel free and leave a comment.

## A mindset for inherited source code

This article outlines a mindset for developers to deal with existing, probably inherited code bases. You’ll have to be an archeologist, a forensicist and a minefield clearer all at once.

One field of expertise our company provides is the continuation of existing software projects. While this sounds very easy to accomplish, in reality, there are a few prerequisites that a software project has to provide to be continuable. The most important one is the source code of the system, obviously. If the source code is accessible (this is a problem more often than you might think!), the biggest hurdle is now the mindset and initial approach of the developers that inherit it.

### The mindset

Most developers have a healthy “greenfield” project mindset. There is a list of requirements, so start coding and fulfill them. If the code obstructs the way to your goal, you reshape it in a meaningful manner. The more experience you have with developing software, the better the resulting design and architecture of the code will be. Whether you apply automatic tests to your software (and when) is entirely your decision. In short: You are the master of the code and forge it after your vision. This is a great mindset for projects in the early phases of development. But it will actively hinder you in later phases of your project or in case you inherit foreign code.

For your own late-phase projects and source code written by another team, another mindset provides more value. The “brownfield” metaphor doesn’t describe the mindset exactly. I have three metaphors that describe parts of it for me: You’ll need to be an archeologist, a forensicist (as in “securer of criminal evidence”) and a minefield clearer. If you hear the word archeologist, don’t think of Indiana Jones, but of somebody sitting in the scorching desert, clearing a whole football field from sand with only a shaving brush and his breath. If you think about being a forensicist, don’t think of your typical hero criminalist who rearranges the photos of the crime scene to reveal a hidden hint, but the guy in a white overall who has to take all the photos without disturbing the surrounding (and being disturbed by it). If you think about the minefield clearer: Yes, you are spot on. He has to rely on his work and shouldn’t move too fast in any direction.

### The initial approach

This sets the scene for your initial journey inside foreign source code: Don’t touch anything or at least be extra careful, only dust it off in the slightest possible manner. Watch where you step in and don’t get lost. Take a snapshot, mental or written, of anything suspicious you’ll encounter. There will be plenty of temptation to lose focus and instantly improve the code. Don’t fall for it. Remember the forensicist: what would the detective in charge of this case say if you “improved the scenery a bit” to get better photos? This process reminds me so much of a common approach to the game “Minesweeper” that I included the minefield clearer in the analogy. You start somewhere on the field and mark every mine you indirectly identify without ever really revealing them.

Most likely, you don’t find any tests or an issue tracker where you can learn about the development history. With some luck, you’ll have a commit history with meaningful comments. Use the blame view as often as you can. This is your archeological skills at work: Separating layers and layers of code all mingled in one place. A good SCM system can clear up a total mess for you and reveal the author’s intent for it. Without tests, issues and versioning, you cannot distinguish between a problem and a solution, accidental and deliberate complexity or a bug and a feature. Everything could mean something and even be crucial for the whole system or just be useless excess code (so-called “live weight” because the code will be executed, but with no effect in terms of features). To name an example, if you encounter a strange sleep() call (or multiple calls in a row), don’t eliminate or change them! The original author probably “fixed” a nasty bug with it that will come back sooner than you know it.

### Walking on broken glass

And this is what you should do: Leave everything in its place, broken, awkward and clumsy, and try to separate your code from “their” code as much as possible. The rationale is to be able to differentiate between “their” mess and “your” mess and make progress on your part without breaking the already existing features. If you cannot wait any longer to clean up some of the existing code, make sure to release into production often and in a timely manner, so you still know what changed if something goes wrong. If possible, try to release two different kinds of new versions:

• One kind of new version only incorporates refactorings to the existing code. If anything goes wrong or seems suspicious, you can easily bail out and revert to the previous version without losing functionality.
• The other kind only contains new features, added with as little change to existing code as possible. Hopefully, this release will not break existing behaviour. If it does, you should double-check your assumptions about the code. If reasonably achievable, do not assume anything or at least write an automatic test to validate your assumption.

Personally, I call this approach the “tick-tock” release cycle, modelled after the release cycle of Intel for its CPUs.

### Changing gears

A very important aspect of software development is to know when to “change gears” and switch from greenfield to brownfield or from development to maintainance mode. The text above describes the approach with inherited code, where the gear change is externally triggered by transferring the source code to a new team. But in reality, you need to apply most of the practices on your own source code, too. As soon as your system is in “production”, used in the wild and being filled with precious user data, it changes into maintainance mode. You cannot change existing aspects as easily as before.
In his book “Implementation Patterns” (2008), Kent Beck describes the development of frameworks among other topics. One statement is:

While in conventional development reducing complexity to a minimum is a valuable strategy for making the code easy to understand, in framework development it is often more cost-effective to add complexity in order to enhance the framework developer’s ability to improve the framework without breaking client code.
(Chapter 10, page 118)

I not only agree with this statement but think that it partly applies to “conventional development” in maintainance mode, too. Sometimes, the code needs additional complexity to cope with existing structures and data. This is the moment when you’ve inherited your own code.

## Clang, The Friendly Compiler

Clang C/C++ compiler can be called The Friendly Compiler, since it makes it much easier to find and understand compile errors and potential bugs in your code. Go use it!

A while back I suggested to make friends with your compiler as a basis for developing high quality code. My focus then was GCC since it was and still is the compiler I use most of the time. Well, turns out that although GCC may be a reasonably good companion on the C/C++ development road, there are better alternatives.

Enter Clang: I had heard about Clang a few times in the past but never gave it a real shot. That changed after I watched Chandler Carruth’s talk at GoingNative 2012.

First of all I was stunned by the quote from Richard Stallman about GCC being deliberatly designed to make it hard to use it in non-free software. I always wondered why IDEs like KDevelop keep reinventing the wheel all the time by implementing their own C/C++ parsers instead of using already existing and free GCC code. This was the answer: THEY SIMPLY COULDN’T!!

One main point of Chandler’s talk was the quality of diagnostic messages of Clang. GCC is a friend that although telling you exactly what’s wrong with your code, it often does it with complicated sentences hidden in walls of text.

Clang on the other hand, tries very hard to comprehend what you really wanted to write, it speaks in much more understandable words and shows you the offending code locations with nice graphics.

You could say that compared to Clang, which is empathic, understanding, pragmatic and always tries to be on the same page with you, GCC comes across more like an arrogant, self-pleasing and I’m-more-intelligent-than-you kinda guy.

Where GCC says: “What? That should be a template instantiation? Guess what, you’re doing WRONG!! “, Clang is more like: “Ok my friend, now let’s sit down together and analyse step-by-step what’s the problem here. I’ll make us tea.

You’ll find many examples of Clangs nice diagnostic output in Chandler’s talk. Here is another one, as a little teaser:

struct A
{
std::string _str1;
std::string _str2;
};

struct AHasher
{
std::size_t operator() (const A& a)
{
return std::tr1::hash()(a._str1) ^
std::tr1::hash()(a._str2);
}
};
...
typedef std::tr1::unordered_map<A, int> AMap;
...


What’s wrong with this code? Yes, exactly: the operator in AHasher must be const. Errors with const correctness are typical, easy-to-overlook kind of problems in day-to-day programming. GCCs reaction to something like that is that something discards qualifiers. This may be perfectly right, and after a while you even get used to it. But as you can see with Clang, you can do much better.

The following two screenshots directly compare GCCs and Clangs output compiling the code above. Because there is a template instantiation involved, GCC covers you in its typical wall of text, before it actually tells you what’s wrong (last line).

CLang’s output is much better formated, it shows you the template instantiation steps much more cleanly and in the last line it tells you to the point what is really wrong: …but method is not marked const. Yeah!