@ParametricNullness E key,
          List<? extends E> list,
          int foundIndex) {
        // Of course, we have to use binary search to find the precise
        // breakpoint...
        int lower = 0;
        int upper = foundIndex;
        // Of course, we have to use binary search to find the precise breakpoint...
        // Everything between lower and upper inclusive compares at <= 0.

## External Courses

Although the [Tutorial - User Guide](../tutorial/index.md){.internal-link target=_blank} and this **Advanced User Guide** are written as a guided tutorial (like a book) and should be enough for you to **learn FastAPI**, you might want to complement it with additional courses.

Or it might be the case that you just prefer to take other courses because they adapt better to your learning style.

  }

  /**
   * The version of this test supplied by {@link MapInterfaceTest} fails for this particular Map
   * implementation, because {@code map.get()} returns a view collection that changes in the course
   * of a call to {@code remove()}. Thus, the expectation doesn't hold that {@code map.remove(x)}
   * returns the same value which {@code map.get(x)} did immediately beforehand.
   */
  @Override
  public void testRemove() {

So, even with the code above that doesn't use Pydantic explicitly, FastAPI is using Pydantic to convert those standard dataclasses to Pydantic's own flavor of dataclasses.

And of course, it supports the same:

* data validation
* data serialization
* data documentation, etc.

This works the same way as with Pydantic models. And it is actually achieved in the same way underneath, using Pydantic.

| `Forwarded`   | For outgoing requests, the original source IP. Note that since we spoof IPs in most cases, this usually is the same as the actual IP seen. For incoming requests, this is used only for traffic from waypoints (which are trusted and cannot spoof IPs) |

  }

  /**
   * The version of this test supplied by {@link MapInterfaceTest} fails for this particular Map
   * implementation, because {@code map.get()} returns a view collection that changes in the course
   * of a call to {@code remove()}. Thus, the expectation doesn't hold that {@code map.remove(x)}
   * returns the same value which {@code map.get(x)} did immediately beforehand.
   */
  @Override
  public void testRemove() {

## Running on Startup

In most cases, when you create a web API, you want it to be **always running**, uninterrupted, so that your clients can always access it. This is of course, unless you have a specific reason why you want it to run only in certain situations, but most of the time you want it constantly running and **available**.

### In a Remote Server

    A `Response` returned directly by your *path operation function* won't be documented in OpenAPI (for example, the `Content-Type` won't be documented) and won't be visible in the automatic interactive docs.

!!! info
    Of course, the actual `Content-Type` header, status code, etc, will come from the `Response` object you returned.

### Document in OpenAPI and override `Response`

 *
 * <p>The multimap does not store duplicate key-value pairs. Adding a new key-value pair equal to an
 * existing key-value pair has no effect.
 *
 * <p>Null keys and values are permitted (provided, of course, that the respective comparators
 * support them). All optional multimap methods are supported, and all returned views are
 * modifiable.
 *

  public static void assertEqualIgnoringOrder(Iterable<?> expected, Iterable<?> actual) {
    List<?> exp = copyToList(expected);
    List<?> act = copyToList(actual);
    String actString = act.toString();

    // Of course we could take pains to give the complete description of the
    // problem on any failure.

    // Yeah it's n^2.
    for (Object object : exp) {
      if (!act.remove(object)) {
        Assert.fail(