*
   * <p><i>Notes:</i> This is an implementation of the algorithm for Lexicographical Permutations
   * Generation, described in Knuth's "The Art of Computer Programming", Volume 4, Chapter 7,
   * Section 7.2.1.2. The iteration order follows the lexicographical order. This means that the
   * first permutation will be in ascending order, and the last will be in descending order.
   *

  /** Adds the given pair of values to the dataset. */
  public void add(double x, double y) {
    // We extend the recursive expression for the one-variable case at Art of Computer Programming
    // vol. 2, Knuth, 4.2.2, (16) to the two-variable case. We have two value series x_i and y_i.
    // We define the arithmetic means X_n = 1/n \sum_{i=1}^n x_i, and Y_n = 1/n \sum_{i=1}^n y_i.

Ama yine de, FastAPI, Requests'ten oldukça ilham aldı.

**Requests**, <abbr title="API (Application Programming Interface): Uygulama Programlama Arayüzü">API'lar</abbr> ile bir istemci olarak *etkileşime geçmeyi* sağlayan bir kütüphaneyken **FastAPI** bir sunucu olarak <abbr title="API (Application Programming Interface): Uygulama Programlama Arayüzü">API'lar</abbr> oluşturmaya yarar.

One particular advantage that is not necessarily obvious is that you can **generate clients** (sometimes called <abbr title="Software Development Kits">**SDKs**</abbr> ) for your API, for many different **programming languages**.

## OpenAPI Client Generators

There are many tools to generate clients from **OpenAPI**.

A common tool is <a href="https://openapi-generator.tech/" class="external-link" target="_blank">OpenAPI Generator</a>.

It is designed to be very simple to use, and to make it very easy for any developer to integrate other components with **FastAPI**.

## What is "Dependency Injection"

**"Dependency Injection"** means, in programming, that there is a way for your code (in this case, your *path operation functions*) to declare things that it requires to work and use: "dependencies".

  /** Adds the given pair of values to the dataset. */
  public void add(double x, double y) {
    // We extend the recursive expression for the one-variable case at Art of Computer Programming
    // vol. 2, Knuth, 4.2.2, (16) to the two-variable case. We have two value series x_i and y_i.
    // We define the arithmetic means X_n = 1/n \sum_{i=1}^n x_i, and Y_n = 1/n \sum_{i=1}^n y_i.

 * href="http://en.wikipedia.org/wiki/Null_Object_pattern">null object</a> for the type in question.
 *
 * <p>This class is not intended as a direct analogue of any existing "option" or "maybe" construct
 * from other programming environments, though it may bear some similarities.
 *
 * <p>An instance of this class is serializable if its reference is absent or is a serializable
 * object.
 *

      max = value;
      if (!isFinite(value)) {
        sumOfSquaresOfDeltas = NaN;
      }
    } else {
      count++;
      if (isFinite(value) && isFinite(mean)) {
        // Art of Computer Programming vol. 2, Knuth, 4.2.2, (15) and (16)
        double delta = value - mean;
        mean += delta / count;
        sumOfSquaresOfDeltas += delta * (value - mean);
      } else {

That's why it makes a lot of sense to use asynchronous ⏸🔀⏯ code for web APIs.

This kind of asynchronicity is what made NodeJS popular (even though NodeJS is not parallel) and that's the strength of Go as a programming language.

And that's the same level of performance you get with **FastAPI**.

  public static final MediaType BZIP2 = createConstant(APPLICATION_TYPE, "x-bzip2");

  /**
   * Files in the <a href="https://www.dartlang.org/articles/embedding-in-html/">dart</a>
   * programming language.
   *
   * @since 19.0
   */
  public static final MediaType DART_UTF_8 = createConstantUtf8(APPLICATION_TYPE, "dart");

  /**
   * <a