Counting Sort

Counting sort – counting sort algorithm. What? Yes! Just like that!

The algorithm involves at least two arrays, the first is a list of integers to be sorted, the second is an array of size = (maximum number – minimum number) + 1, initially containing only zeros. Next, the numbers from the first array are sorted out, the index in the second array is obtained by the element-number, which is incremented by one. After going through the entire list, we will get a completely filled second array with the number of repetitions of numbers from the first. The algorithm has a serious overhead – the second array also contains zeros for numbers that are not in the first list, the so-called. memory overhead.

After getting the second array, iterate over it and write the sorted version of the number by index, decrementing the counter to zero. Initially, the zero counter is ignored.

An unoptimized example of how the counting sort algorithm works:

  1. Input array 1,9,1,4,6,4,4
  2. Then the array to count will be 0,1,2,3,4,5,6,7,8,9 (minimum number 0, maximum 9)
  3. With total counters 0,2,0,0,3,0,1,0,0,1
  4. Total sorted array 1,1,4,4,4,6,9

Algorithm code in Python 3:

print("Counting Sort")

numbers = [42, 89, 69, 777, 22, 35, 42, 69, 42, 90, 777]

minimal = min(numbers)
maximal = max(numbers)
countListRange = maximal - minimal
countListRange += 1
countList = [0] * countListRange

print(f"Minimal number: {minimal}")
print(f"Maximum number: {maximal}")
print(f"Count list size: {countListRange}")

for number in numbers:
    index = number - minimal
    countList[index] += 1

replacingIndex = 0
for index, count in enumerate(countList):
    for i in range(count):
        outputNumber = minimal + index
        numbers[replacingIndex] = outputNumber
        replacingIndex += 1


Due to the use of two arrays, the time complexity of the algorithm is O(n + k)




Pseudo sort or swamp sort, one of the most useless sorting algorithms.

It works like this:
1. Input is an array of numbers
2. An array of numbers is shuffled randomly (shuffle)
3. Checking if the array is sorted
4. If not sorted, then the array is shuffled again
5. All this action is repeated until the array is sorted randomly.

As you can see, the performance of this algorithm is terrible, smart people think that even O(n * n!) there is a chance to get stuck throwing dice for the glory of the god of chaos for many years, the array will not be sorted, or maybe sorted?


For the TypeScript implementation, I needed to implement the following functions:
1. Shuffling an array of objects
2. Comparing arrays
3. Generating a random number between zero and a number (sic!)
4. Seal of progress, as the sorting seems to run indefinitely

Below is the TypeScript implementation code:

const printoutProcess = (numbers: number[], sortedNumbers: number[], numberOfRuns: number) => console.log(`Still trying to sort: ${numbers}, current shuffle ${sortedNumbers}, try number: ${numberOfRuns}`);
const randomInteger = (maximal: number) => Math.floor(Math.random() * maximal);
const isEqual = (lhs: any[], rhs: any[]) => lhs.every((val, index) => val === rhs[index]);
const shuffle = (array: any[]) => {
    for (var i = 0; i < array.length; i++) { var destination = randomInteger(array.length-1); vartemp = array[i]; array[i] = array[destination]; array[destination] = temp; } } let numbers: number[] = Array.from({length: 10}, ()=>randomInteger(10));
const originalNumbers = [...numbers];
const sortedNumbers = [...numbers].sort();

let numberOfRuns = 1;

do {
    if (numberOfRuns % 1000 == 0) {
        printoutProcess(originalNumbers, numbers, numberOfRuns);
} while (isEqual(numbers, sortedNumbers) == false)

console.log(`Run number: ${numberOfRuns}`)
console.log(`Original numbers: ${originalNumbers}`);
console.log(`Current numbers: ${originalNumbers}`);
console.log(`Sorted numbers: ${sortedNumbers}`);

You can use VSCode and kakumei’s TypeScript Debugger plugin for debugging.

How long

Output of the algorithm:

Still trying to sort: 5,4,8,7,5,0,2,9,7,2, current shuffle 2,9,7,8,0,7,4,5,2 ,5, try number: 144000
Still trying to sort: 5,4,8,7,5,0,2,9,7,2, current shuffle 8,7,0,2,4,7,2,5,9,5, try number: 145000
Still trying to sort: 5,4,8,7,5,0,2,9,7,2, current shuffle 7,5,2,4,9,8,0,5,2,7, try number: 146000
Still trying to sort: 5,4,8,7,5,0,2,9,7,2, current shuffle 0,2,7,4,9,5,7,5,8,2, try number: 147000
Still trying to sort: 5,4,8,7,5,0,2,9,7,2, current shuffle 5,9,7,8,5,4,2,7,0,2, try number: 148000
Run number: 148798
Original numbers: 5,4,8,7,5,0,2,9,7,2
Current numbers: 5,4,8,7,5,0,2,9,7,2
Sorted numbers: 0,2,2,4,5,5,7,7,8,9

For an array of 10 numbers, Bogosort shuffled the original array 148798 times, too much right?
The algorithm can be used as a training one, to understand the capabilities of the language with which to work on the market. Personally, I was surprised to learn that vanilla JS and TS still do not have their own algorithm for shuffling arrays, generating an integer in a range, accessing object hashes for quick comparison.

Links /algorithms/-/tree/master/sortAlgorithms/bogosort kakumei.ts-debug


GoF Patterns

List of most important OOP patterns in computer programming aka Gang of Four Design Patterns.

Creational patterns

Structural patterns

Behavioral patterns

Interpreter Pattern

What’s included

The Interpreter Pattern is a Behavioral Design Pattern. This pattern allows you to implement your own programming language by working with an AST tree, the vertices of which are terminal and non-terminal expressions that implement the Interpret method, which provides the functionality of the language.

  • Terminal expression – e.g. string constant – “Hello World”
  • Non-terminal expression – e.g. Print(“Hello World”), contains Print and an argument from the Terminal expression “Hello World”

What’s the difference? The difference is that the interpretation on terminal expressions ends, and for non-terminal expressions it continues deep into all incoming nodes/arguments. If the AST tree consisted only of non-terminal expressions, then the application would never complete, because some end of any process is required, this end is what terminal expressions are, they usually contain data, for example, strings.

An example of an AST tree is below:

Dcoetzee, CC0, via Wikimedia Commons

As you can see, terminal expressions are constant and variable, non-terminal expressions are the rest.

What is not included

The implementation of the Interpreter does not parse the string input of the language into the AST tree. It is enough to implement classes of terminal, non-terminal expressions, Interpret methods with the Context argument at the input, form an AST tree from expressions, run the Interpret method at the root expression. The context can be used to store the state of the application at runtime.


Participants in the pattern:

  • Client – returns AST tree and runs Interpret(context) on root node (Client)
  • Context – contains the state of the application, passed to expressions when interpreted (Context)
  • Abstract expression – an abstract class containing the method Interpret(context) (Expression)
  • Terminal expression is a final expression, a descendant of an abstract expression (TerminalExpression)
  • A non-terminal expression is not a final expression, contains pointers to nodes deep into the AST tree, subordinate nodes usually affect the result of interpreting a non-terminal expression (NonTerminalExpression)

C# Client Example

class Application {
        static void Main(string[] args)
            var context = new Context();
            var initialProgram = new PerformExpression(
                new IExpression[] {
                    new SetExpression("alpha", "1"),
                    new GetExpression("alpha"),
                    new PrintExpression(
                        new IExpression[] {
                            new ConstantExpression("Hello Interpreter Pattern")

Example of an Abstract Expression in C#

interface IExpression
    String interpret(Context context);

C# Terminal Expression Example (String Constant)

class ConstantExpression : TerminalExpression
    private String constant;

    public ConstantExpression(String constant) {
        this.constant = constant;

    override public String interpret(Context context) {
        return constant;

Example of a Non-Terminal Expression in C# (Launching and concatenating the results of subordinate nodes, using the delimiter “;”

class PerformExpression : NonTerminalExpression
    public PerformExpression(IExpression[] leaves) : base(leafs) {
        this.leafs = leaves;
    override public String interpret(Context context) {
        var output = "";
        foreach (var leaf in leaves) {
            output += leaf.interpret(context) + ";";
        return output;

Functionally, can you?

As you know, all Turing-complete languages ​​are equivalent. Can the Object-Oriented pattern be transferred to a Functional Programming language?

You can, for the experiment, let’s take the FP language for the web called Elm. There are no classes in Elm, but there are Records and Types, so the following records and types are involved in the implementation:

  • Expression – enumeration of all possible language expressions (Expression)
  • Subordinate expression – an expression that is subordinate to a non-terminal expression (ExpressionLeaf)
  • Context – a record that stores the state of the application (Context)
  • Functions that implement the Interpret(context) methods – all the necessary functions that implement the functionality of Terminal, Non-Terminal expressions
  • Auxiliary records of the Interpreter state – necessary for the correct operation of the Interpreter, store the state of the Interpreter, the context

For example function that implements the interpretation for the entire set of possible expressions on Elm:

run input =
  case input.expression of
    Constant text ->
        output = text
        context = input.context
    Perform leafs ->
      let inputs = (\leaf -> { expressionLeaf = leaf, context = input.context } ) leafs in
        let startLeaf = { expressionLeaf = (Node (Constant "")), context = { variables = Dict.empty } } in
          let outputExpressionInput = List.foldl mergeContextsAndRunLeafs startLeaf inputs in
              output = (runExpressionLeaf outputExpressionInput).output,
              context = input.context
    Print printExpression ->
        expression = printExpression,
        context = input.context
    Set key value ->
      let variables = Dict.insert key value input.context.variables in
        context = { variables = variables }
    get key ->
        output = Maybe.withDefault("No value for key: " ++ key)(Dict.get key input.context.variables),
        context = input.context

What about parsing?

Parsing source code into an AST tree is not part of the Interpreter pattern, there are several approaches to parsing source code, but more on that some other time.
In the implementation of the Interpreter for Elm, I wrote the simplest parser into the AST tree, consisting of two functions – parsing a vertex, parsing subordinate vertices.

parseLeafs: ParseLeafsState -> ParseLeafsState
parseLeafs state =
    let tokensQueue = state.tokensQueue in
        let popped = pop state.tokensQueue in
            let tokensQueueTail = tail state.tokensQueue in
                if popped == "Nothing" then
                else if popped == "Perform(" then
                        tokensQueue = tokensQueue,
                        result = (state.result++[Node(parse tokensQueue)])
                else if popped == ")" then
                    parseLeafs {
                        tokensQueue = tokensQueueTail,
                        result = state.result
                else if popped == "Set" then
                    let key = pop tokensQueueTail in
                        let value = pop(tail tokensQueueTail) in
                            parseLeafs {
                                tokensQueue = tail(tail tokensQueueTail),
                                result = (state.result++[Node(Set key value)])
                else if popped == "Get" then
                    let key = pop tokensQueueTail in
                        parseLeafs {
                            tokensQueue = tail tokensQueueTail,
                            result = (state.result++[Node(Get key)])
                    parseLeafs {
                        tokensQueue = tokensQueueTail,
                        result = (state.result++[Node(Constant popped)])

parse tokensQueue =
    let popped = pop tokensQueue in
        let tokensQueueTail = tail tokensQueue in
            if popped == "Perform(" then
                    parseLeafs {
                        tokensQueue = tokensQueueTail,
                        result = []
            else if popped == "Set" then
                let key = pop tokensQueueTail in
                    let value = pop(tail tokensQueueTail) in
                        set key value
            else if popped == "Print" then
                Print(parse tokensQueueTail)
                Constant popped

Links /patterns/-/tree/master/interpreter/elm -/tree/master/interpreter/csharp

Sources /csharp/

RGB Image to Grayscale

In this article I will describe algorithm of converting RGB image buffer to Grayscale
And this is done quite simply, each pixel of the color channel of the buffer is converted according to a certain formula, and the output is a gray image.
Average method:

const average = (red + green + blue) / 3;
red = average;
green = average;
blue = average;

Add the 3 color channels and divide by 3.

However, there is another method – the weighted average method, it takes into account the human color perception:

const luminance = 0.2126 * red + 0.7152 * green + 0.0722 * blue;
red = luminance;
green = luminance;
blue = luminance;

What is the best method to use? Choose one that suits you better for a particular task. Next, a comparison of methods using a test color grid:

Example JavaScript + HTML 5

function rgb2grayscale(
) {
    const context = canvas.getContext('2d');

    const imageWeight = image.width;
    const imageHeight = image.height;

    canvas.width = imageWeight;
    canvas.height = imageHeight;

    context.drawImage(image, 0, 0);

    let pixels = context

    for (let y = 0; y & lt; pixels.height; y++) {
        for (let x = 0; x & lt; pixels.width; x++) {
            const i = (y * 4) * pixels.width + x * 4;

            let red =[i];
            let green =[i + 1];
            let blue =[i + 2]

            const average = (red + green + blue) / 3;
            const luminance = 0.2126 * red +
                0.7152 * green +
                0.0722 * blue;

            red = weightedAverage ? luminance : average;
            green = weightedAverage ? luminance : average;
            blue = weightedAverage ? luminance : average;

  [i] = red;
  [i + 1] = green;
  [i + 2] = blue;




Thanks to Aleksei Matiushkin ( for showing Rosetta Code

Turing Bombe

In 1936, the scientist Alan Turing in his publication “On Computable Numbers, With An Application to Entscheidungsproblem”describes the use of a universal computing machine that could put an end to the problem of decidability in mathematics. As a result, he comes to the conclusion that such a machine would be nothing could solve correctly, if the result of her work would be inverted and looped on itself.It turns out that * ideal * antivirus cannot be created, * ideal * tile layer too, a program that suggests ideal phrases for your crash, etc. Paradox, sir!

However, this universal computing machine can be used to implement any algorithm, which was used by British intelligence, hiring Turing and allowing to create a “Bombe” machine for decrypting German messages during the Second World War.

The following is an example of OOP modeling a single-tape calculator in Dart, based on the original document.

The Turing machine consists of a tape divided into sections, each section contains a symbol, symbols can be read or written. Film class example:

class MapInfiniteTape implements InfiniteTape { 
final _map = Map<int, String>(); 

  String read({required int at}) { 
    return _map[at] ?? ""; 

  void write({required String symbol, required int at}) { 
    _map[at] = symbol; 

There is also a “scanning square”, it can move along the film, read or write information, in modern language – a magnetic head. Magnetic head class example:

class TapeHead { 
  int _index = 0; 
  InfiniteTape _infiniteTape; 
  TapeHead(this._infiniteTape) {} 

  String next() { 
    _index += 1; 
    move(to: _index); 
    final output = read(); 
    return output; 

  String previous() { 
    _index -= 1; 
    move(to: _index); 
    final output = read(); 
    return output; 

  void move({required int to}) { 
    this._index = to; 

  String read() { 
    return this._index); 

  void write(String symbol) { 
    _infiniteTape.write(symbol: symbol, at: this._index); 

  int index() { 
    return _index; 

The machine contains “m-configurations” by which it can decide what to do next. In modern parlance, states and state handlers. State handler example:

class FiniteStateControl { 
  FiniteStateControlDelegate? delegate = null; 

  void handle({required String symbol}) { 
    if (symbol == OPCODE_PRINT) { 
      final argument = delegate?.nextSymbol(); 
      final to = int.tryParse(delegate!.nextSymbol())!; 
      final value = new Random().nextInt(to); 
    else if (symbol == OPCODE_INPUT_TO_NEXT) { 
      final input = stdin.readLineSync()!; 
    else if (symbol == OPCODE_COPY_FROM_TO) { 
      final currentIndex = delegate!.index(); 

и т.д. 

After that, you need to create “configurations”, in modern language these are operation codes (opcodes), their handlers. Example opcodes:

const OPCODE_STOP = "stop"; 
const OPCODE_PRINT = "print"; 
const OPCODE_INCREMENT_NEXT = "increment next"; 
const OPCODE_DECREMENT_NEXT = "decrement next"; 
const OPCODE_IF_PREVIOUS_NOT_EQUAL = "if previous not equal"; 
const OPCODE_MOVE_TO_INDEX = "move to index"; 
const OPCODE_COPY_FROM_TO = "copy from index to index"; 
const OPCODE_INPUT_TO_NEXT = "input to next"; 
const OPCODE_GENERATE_RANDOM_NUMBER_FROM_ZERO_TO_AND_WRITE_AFTER = "generate random number from zero to next and write after"; 

Don’t forget to create an opcode and a breakpoint handler, otherwise you won’t be able to prove or not prove (sic!) The resolution problem.

Now, using the “mediator” pattern, we connect all the classes in the Turing Machine class, create an instance of the class, record the programs through the tape recorder, load the cassette and you can use it!

For me personally, the question remained interesting, what was primary – the creation of a universal calculator or the proof of the “Entscheidungsproblem” as a result of which, as a by-product, a calculator appeared.


For the sake of entertainment, I recorded several cassette programs for my version of the car.

Hello World

hello world 

Считаем до 16-ти

increment next
if previous not equal
copy from index to index
move to index
copy from index to index

The most interesting challenge was writing Quine a program that prints its source code for a single tape machine. For the first 8 hours it seemed to me that this problem could not be solved with such a small number of opcodes, but after only 16 hours it turned out that I was wrong.

Implementation and examples of cassettes, sources below.



Writing stuff in Assembly for Sega Genesis #5

In this post I will describe the process of reading the joystick, changing the position of the sprite, horizontal flip, the Sega Genesis emulator and potentially the console itself.

Reading of clicks, processing of “events” of the shogi joystick is carried out according to the following scheme:

  1. Request a combination of bits of pressed buttons
  2. Reading the bits of pressed buttons
  3. Processing at the level of game logic

To move the skeleton sprite, we need to store the variables of the current position.


The variables of the game logic are stored in RAM, so far people have not come up with anything better. Let’s declare the addresses of the variables, change the rendering code:

skeletonXpos = $FF0000
skeletonYpos = $FF0002 
frameCounter = $FF0004 
skeletonHorizontalFlip = $FF0006

    move.w #$0100,skeletonXpos 
    move.w #$0100,skeletonYpos 
    move.w #$0001,skeletonHorizontalFlip 

    move.l #$70000003,vdp_control_port 
    move.w skeletonYpos,vdp_data_port  
    move.w #$0F00,vdp_data_port 
    move.w skeletonHorizontalFlip,vdp_data_port 
    move.w skeletonXpos,vdp_data_port 

As you can see, the address available for work starts with 0xFF0000, and ends at 0xFFFFFF, in total we have 64 KB of memory available. Skeleton positions are declared at skeletonXpos, skeletonYpos, horizontal flip at skeletonHorizontalFlip.


By analogy with VDP, work with joypads occurs through two ports separately – the control port and the data port, for the first it is 0xA10009 and 0xA10003 so-but. When working with a joypad, there is one interesting feature – first you need to request a combination of buttons for polling, and then, after waiting for the update via the bus, read the necessary clicks. For the C / B buttons and the cross, this is 0x40, an example is below:

  move.b #$40,joypad_one_control_port; C/B/Dpad 
  nop ; bus sync 
  nop ; bus sync 
  move.b joypad_one_data_port,d2 

In register d2, the state of the buttons pressed, or not pressed, in general, what was requested through the date port, will remain. After that, go to the Motorola 68000 register viewer of your favorite emulator, see what the d2 register is, depending on the keystrokes. In a smart way, you can find out in the manual, but we do not believe a word. Further processing of pressed buttons in register d2

    cmp #$FFFFFF7B,d2; handle left 
    beq MoveLeft  
    cmp #$FFFFFF77,d2; handle right  
    beq MoveRight  
    cmp #$FFFFFF7E,d2; handle up  
    beq MoveUp  
    cmp #$FFFFFF7D,d2; handle down  
    beq MoveDown  

Of course, you need to check individual bits, not whole words, but for now it will do. Now the simplest thing is left – to write handlers for all events of movement in 4 directions. To do this, we change the variables in RAM, and start the repainting procedure.

Example for moving left + changing horizontal flip:

    move.w skeletonXpos,d0 
    sub.w #1,d0 
    move.w d0,skeletonXpos 
    move.w #$0801,skeletonHorizontalFlip 
    jmp FillSpriteTable

After adding all the handlers and assemblies, you will see how the skeleton moves and rotates around the screen, but too fast, faster than Sonic the hedgehog itself.

Not so fast!

To slow down the speed of the game loop, there are several techniques, I chose the simplest and not affecting work with external ports – counting a digit through a register until it becomes zero.

An example of a slowing loop and a game loop:

  move.w #512,frameCounter 
  move.w frameCounter,d0 
  sub.w #1,d0 
  move.w d0,frameCounter 
  dbra d0,WaitFrame 
  jsr ReadJoypad 
  jsr HandleJoypad 
  jmp GameLoop 

After that, the skeleton runs slower, which is required. As far as I know, the most common variant of “slowing down” is counting the vertical sync flag, you can count how many times the screen has been rendered, thus binding to a specific fps.