BigO Calculator

This BigO Calculator library allows you to calculate the time complexity of a given algorithm. Calculation is performed by generating a series of test cases with increasing argument size, then measuring each test case run time, and determining the probable time complexity based on the gathered durations.

This powers the BigO calculations done on Coderbyte.

Table of contents

• Architecture
• Installation
  • Default code runner
• Initialization
• Analysis
  • Insight
• Extending Calculator Functionality
  • Config
    • Optimal complexities
    • Calculators
    • Repeated samples
    • Default calculator
  • Sample sizes
  • Argument generators
  • Replacement patterns
  • Code transformers

Architecture

This library consists of three essential parts linked together and run by AnalysisService:

• Creator - performs a series of operations to create a runnable sample from the Code you pass to the library in order:
  • generates function arguments for each N
  • creates runnable test sample with injected arguments
• Runner
  • runs each test and returns duration
• Calculator
  • determines BigO based on set of N - duration pairs

Installation

using yarn:

yarn add big-o-calculator

using npm:

npm i big-o-calculator

Default code runner

BigO Calculator includes CBHttpCodeRunner, which is a client for cb-code-runner along with AxiosClient as an HTTP client. If you choose to use those classes as a Runner part of the calculator you need to install the optional axios dependency.

using yarn:

yarn add axios

using npm:

npm i axios

Initialization

import {AxiosClient, CBHttpCodeRunner, AnalysisService} from "big-o-calculator";

// First occurrence of [runnerLanguage] in URI will be replaced with language
const codeRunnerUri = 'http://example.com/code-runner/[runnerLanguage]';
const codeRunner = new CBHttpCodeRunner(codeRunnerUri, new AxiosClient())
const calculator = new AnalysisService(codeRunner);

Analysis

Assume you want to determine the BigO for the following JavaScript code:

function firstLetters(words) {
  return words.split(' ').map(word => {
    return word.substring(0, 1);
  });
}

BigO Calculator needs a way to inject arguments into the tested code, so a function call and {funcArgs} argument placeholder needs to be added.

firstLetters({funcArgs});

Full code will look like this:

function firstLetters(words) {
  return words.split(' ').map(word => {
    return word.substring(0, 1);
  });
}
firstLetters({funcArgs});

Then create a Code object.

import {AlgorithmSpeed, BuiltInArgumentTypes, Language} from "big-o-calculator";

let code: Code = {
  // Language of the tested code
  language: Language.JS,
  // Most languages handle data types differenty (e.g. integers vs strings). 
  // This parameter tells the calculator about type of algorithm tested.
  expectedSpeed: AlgorithmSpeed.SLOW,
  // Tested code with function call and argument placeholder
  content: 'function firstLetters(words) { /*...*/ };firstLetters({funcArgs});',
  // Type of arguments to generate for tested code
  testedFunctionName: BuiltInArgumentTypes.WORDS
};

// AnalysisService.analyze returns a promisified BigO value
calculator.analyze(code)
  .then(analysisResult => {
    console.log(analysisResult.bigO); // O(n)
  });

More details on the meaning of Code parameters can be found in Extending Calculator Functionality section.

Insight

This section describes how the transformation from Code to BigO is done in the calculator. The logic for AnalysisService is the following:

(Code) -> [Creator] -> [Runner] -> [Calculator] -> (BigO)
                          ^              |
                          |______________|

Creator

1. Determine sample sizes N[] essential to calculate time complexity. Defaults are [16, 32, 128, 256, 512, 1024, 2048, 4096]
2. For each N generate the samples based on testedFunctionName. Built-in argument types can be used. Examples of arguments generated for sample size 16:
   • BuiltInArgumentTypes.WORDS:

     "qbrtpygpd xl jmt hhpynvgb cdnsjgofyg fxserr qecaegdcj tfgsleqvis eecuidbg fmx rfqdwldmz rdkrf qsqstb mnkfml qvw rftsinug"

   • BuiltInArgumentTypes.ALPHA_STRING:

     "xrjzvprvxsnqqqcq"

   • BuiltInArgumentTypes.NUMBER_STRING:

     "4223913635625778"

   • BuiltInArgumentTypes.NUMBER:

     16

   • BuiltInArgumentTypes.RANDOM_NUMBERS:

     [16, 11, 2, 11, 12, 9, 9, 2, 9, 3, 3, 1, 4, 14, 11, 6]

   • BuiltInArgumentTypes.ORDERED_NUMBERS:

     [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]

3. Convert each sample to the proper syntax for given language
4. Inject sample into tested function Test set created for example in Analysis section would look similar to this:

let created = {
 code: {
   language: Language.JS,
   expectedSpeed: AlgorithmSpeed.SLOW,
   content: 'function firstLetters(words) { /*...*/ };firstLetters({funcArgs});',
   testedFunctionName: BuiltInArgumentTypes.WORDS
 },
 samples: [
   {
     n: 16,
     code: 'function firstLetters(words) { /*...*/ };firstLetters("qbrtpygpd xl jmt hhpynvgb cdnsjgofyg fxserr qecaegdcj tfgsleqvis eecuidbg fmx rfqdwldmz rdkrf qsqstb mnkfml qvw rftsinug");'
   },
   {
     n: 32,
     code: 'function firstLetters(words) { /*...*/ };firstLetters(/*...*/);'
   },
   //...
 ],
}

Runner

By default cb-code-runner is used. It is able to measure the run time of a tested sample. Samples are passed to the runner one by one. When sample measuring is done, duration is passed to Calculator as a test result.

Calculator

By default GenericCalculator is used. It is designed to determine the BigO based on as few run time durations as possible. It compares durations with each other to see at which N times start to grow and by how much. Based on this information it is returning the BigO. If Calculator is unable to determine the BigO for given test result set AnalysisService runs more samples at the Runner. If there is no more samples to run and Calculator is still not sure about the BigO, optimal complexity is returned (BigO.LINEAR).

Extending Calculator Functionality

AnalysisService config

type AnalysisServiceConfig = {
  optimalComplexities?: Map<string, BigO>,
  calculators?: Map<Language, Calculator>,
  repeatedSamples?: Map<Language, number[]>,
  defaultCalculator?: Calculator,
}

Optimal complexities

If the Calculator is not able to notice any pattern in test results, after duration measuring for each sample, it will return the optimal complexity, which by default is equal to BigO.LINEAR. optimalComplexity config parameter can be used to set different complexity for different tested functions.

import {AnalysisService} from "./AnalysisService";

const optimalComplexities = new Map<string, BigO>([
  [BuiltInArgumentTypes.WORDS, BigO.LOGLINEAR],
  ['someMatrixFunction', BigO.QUADRATIC],
]);
const calculator = new AnalysisService(codeRunner, {optimalComplexities});

Calculators

Since different languages tend to run code in different time, custom calculators can be added for each language by using calculators parameter of the config. All new calculators must implement the Calculator interface.

class ClojureCalculator extends GenericCalculator {
  // implementation of rules specific for clojure run times.
  // ...
}

const calculators = new Map<Language, Calculator>([
  [Language.CLOJURE, new ClojureCalculator()]
]);

const calculator = new AnalysisService(codeRunner, {calculators});

Default calculator

By default, instance of GenericCalculator is used. You can override this by setting defaultCalculator config parameter.

class BetterCalculator implements Calculator {
  // some logic
}
const calculator = new AnalysisService(codeRunner, {defaultCalculator: new BetterCalculator()});

Repeated samples

Sometimes specific samples need to be run several times at Runner to reduce randomness in test results. Samples set in repeatedSamples parameter for chosen language will be run 3 times and average time will be passed to Calculator.

import {Language} from "./Language";

const repeatedSamples = new Map<Language, number[]>([
  [Language.KOTLIN, [128, 256, 512]]
]);
const calculator = new AnalysisService(codeRunner, {repeatedSamples});

Customize sample sizes

Setting sample sizes per language

Our tests show that for some language more sample sizes should be added to determine BigO more reliably. This can be done by calling AnalysisService.addTestSetCreatorDefaultLanguageSet() as in the example below.

GenericCalculator will only handle sample sizes defined in SampleSize class, but any sample sizes can be used for custom calculators.

const calculator = new AnalysisService(codeRunner);
calculator.addTestSetCreatorDefaultLanguageSet(Language.PHP, [16, 128, 1024, 8192, 65536]);
calculator.addTestSetCreatorDefaultLanguageSet(
    Language.JS,
    TestSetCreator.DEFAULT_SAMPLES.concat([SampleSize.n16K, SampleSize.n32K])
);

Sample sizes versus algorithm speed

Code which operates on integers tend to produce lower run times. BigO Calculator can run different sample size for different algorithms, based on expectedSpeed. AnalysisService.addTestSetCreatorSpeedLanguageSet() method can be used to set custom sample set for each algorithm speed.

const calculator = new AnalysisService(codeRunner);
calculator.addTestSetCreatorSpeedLanguageSet(
  Language.JS, 
  AlgorithmSpeed.FAST, 
  [SampleSize.n16, SampleSize.n32, SampleSize.n2K, SampleSize.n4K, SampleSize.n16K, SampleSize.n32K]
);

Argument generators

This library includes some basic generators, which create arguments for tested functions. Some functions might need custom arguments and this can be achieved in two ways:

Custom function name + built-in generator

Calling AnalysisService.useBuiltInGenerator() method allows to set a built-in generator function for any tested function you want to run. Following example shows the possible use case:

const config: AnalysisServiceConfig = {
  optimalComplexities: new Map<string, BigO>([
    ['fancySortingAlgorithm', BigO.LOGLINEAR]
  ])
}

const calculator = new AnalysisService(codeRunner, config);
calcualtor.useBuiltInGenerator('fancySortingAlgorithm', BuiltInArgumentTypes.RANDOM_NUMBERS);

const code: Code = {
  language: Language.JS,
  expectedSpeed: AlgorithmSpeed.FAST,
  content: 'function fancySortingAlgorithm(arrArg) { /*...*/ };fancySortingAlgorithm({funcArgs});',
  testedFunctionName: 'fancySortingAlgorithm'
}
calculator.analyze(code);

Custom generator function

Anything can be generated and injected into the tested function as an argument. AnalysisService.addCustomGenerator() method allows you to add a custom ArgumentGeneratingFunction for specific functions.

const calculator = new AnalysisService(codeRunner);
calcualtor.addCustomGenerator('customObjectTransformingFunction', n => {
  let customObject = {};
  customObject.property = n;
  // ...
  return customObject;
});

const code: Code = {
  language: Language.JS,
  expectedSpeed: AlgorithmSpeed.SLOW,
  content: 'function customObjectTransformingFunction(objArg) { /*...*/ };customObjectTransformingFunction({funcArgs});',
  testedFunctionName: 'customObjectTransformingFunction'
}
calculator.analyze(code);

Replacement patterns

By default, BigO Calculator replaces {funcArgs} with generated arguments for testing. This pattern can be customized for each language by calling AnalysisService.addLanguageReplacePattern() method.

const calculator = new AnalysisService(codeRunner);
calculator.addLanguageReplacePattern(Language.GO, 'input()');

const code: Code = {
  language: Language.GO,
  expectedSpeed: AlgorithmSpeed.SLOW,
  content: 'package main\nfunc reverse(str string) string {\n/*...*/\n}\nfunc main() {\n  reverse(input())\n}',
  testedFunctionName: BuiltInArgumentTypes.ALPHA_STRING
}
calculator.analyze(code);

RegExp can be used as a replacement pattern

const calculator = new AnalysisService(codeRunner);
calculator.addLanguageCodeTransformer(Language.JS, /io\([a-z]*\)/g);
const code: Code = {
  language: Language.JS,
  expectedSpeed: AlgorithmSpeed.SLOW,
  content: 'function reverse(strArg) {/*...*/}; reverse(io(abc));',
  testedFunctionName: BuiltInArgumentTypes.ALPHA_STRING
}
calculator.analyze(code);

Custom code transformers

Code sent to Runner can be transformed by calling AnalysisService.addLanguageCodeTransformer() method with CodeTransformerFunction as a parameter.

const calculator = new AnalysisService(codeRunner);
calculator.addLanguageCodeTransformer(Language.PHP, code => {
  return '<?php\n' + code;
});