Algorithmic Complexity

This project contains a timing framework for measuring the efficiency of algorithms. This timing framework has been applied on in built JS functions and on custom built JS functions I've made myself to test my skills of algorithm desgin.

Each custom built function comes with its own feature test, unit test, JS file for plotting data using Chart.js and a HTML file for displaying the plotted graph. A package.json has also been made for each function in order to use esbuild to generate a script that is passed into the HTML file.

There are a number of helper functions that generate all the necessary data by passing the relevant function in as a callback:

• generateArray(length)
  • Creates an array which has a length equal to the parameter passed in
  • This function is called to create huge arrays which are passed into each function to test the time complexity
• createDataPoint(input, callback, numberOfMeasurements, target)
  • Takes an average of numberOfMeasurements measurements of the time taken for callback to act on input
  • Time is measured by using performance.now()
  • target is another parameter which is exclusively used for subSequenceSum()
• saveData(callbackOne, numberOfMeasurements, increment)
  • Calls generateArray and createDataPoint() 20 times to create an array of data points for timing callbackOne, ready to be plotted on a graph
  • increment is the length of the first array being used to test the timing of callbackOne and is the increase to every subesquent array length afterwards

Custom Functions

• last(array)
  • returns the last element from the array passed in
• reverse(array)
  • reverses the order of the array passed in and returns the updated array
• sort(array)
  • mutates the array passed in into ascending order and returns it
• shuffle(array)
  • returns a new array which contains all the elements of the original in a random order
• duplicate(array)
  • returns an array containing the elements that appeared more than once in the original array passed in
• fibonacci(n)
  • returns an array containing the first n-terms in the fibonacci sequence
• subSequenceSum(array, target)
  • returns true if there exists a sub-sequence in the array passed in that sums up to the target

Note: Due to a couple of slight differences in the input required for each custom function, fibonacci() has its own function to save its data and sort() has its own function to create a single data point

Getting Started

This program is run using Node.js, which is installed using NVM - Node Version Manager. So, if you haven't already, install NVM using:

curl -o- https://raw.githubusercontent.com/nvm-sh/nvm/v0.39.1/install.sh | bash

Now, your ~/.zshrc file will need reloading:

source ~/.zshrc

Next, you can install and start using node by running:

nvm install node
nvm use node

nvm use node will use the latest stable version. Once that is set up, you can now clone this repository and then install the necessary dependencies using:

git clone https://github.com/jmcnally17/algorithmic-complexity
npm install

npm install must be run while in the main directory.

Now you are all set up. Move onto the following section to learn how to use this program.

How To Use

The graphs for each timed funtion can be found below. However, if you wish to run the program yourself, navigate to the folder of the function you wish to time and run npm run build. Then, in the same folder, open the corresponding HTML file to plot the data and view the graph in your browser. E.g. for reverse(), navigate to the reverse folder and run:

npm run build
open reverse.html

Graphs

In Built JS Functions

reverse()

O(n)

sort()

Appears to be O(n) but is actually O(n log n)

Custom JS Functions

last()

O(1)

reverse()

O(n)

sort()

O(n log n)

shuffle()

O(n)

duplicate()

O(n)

fibonacci()

Looks like O(n) but slight uncertainty with the fluctuations

subSequenceSum()

O(n²)

Testing

The Test-Driven Development (TDD) process was followed for creating every function in this project, with Jest being used as the testing framework. In order to run these tests, while in the main directory, simply run npm test. The test coverage can also be viewed by running npm run test:coverage.