* including navigation controls and search/filter parameters.
 *
 * <p>Duplicate hosts allow administrators to define hostname patterns that should
 * be treated as equivalent during crawling, helping to avoid duplicate content
 * from the same logical site accessed via different hostnames.</p>
 */
public class DuplicateHostPager implements Serializable {

`Optional[Something]` is actually a shortcut for `Union[Something, None]`, they are equivalent.

This also means that in Python 3.10, you can use `Something | None`:

//// tab | Python 3.10+

```Python hl_lines="1"
{!> ../../docs_src/python_types/tutorial009_py310.py!}
```

////

Alternativamente, se você não tiver uma maneira de fornecer uma opção de linha de comando como `--root-path` ou equivalente, você pode definir o parâmetro `root_path` ao criar sua aplicação FastAPI:

{* ../../docs_src/behind_a_proxy/tutorial002_py39.py hl[3] *}

Passar o `root_path` para `FastAPI` seria o equivalente a passar a opção de linha de comando `--root-path` para Uvicorn ou Hypercorn.

### Sobre `root_path` { #about-root-path }

</div>

/// note

The command `uvicorn main:app` refers to:

* `main`: the file `main.py` (the Python "module").
* `app`: the object created inside of `main.py` with the line `app = FastAPI()`.

It is equivalent to:

```Python
from main import app
```

///

Each alternative ASGI server program would have a similar command, you can read more in their respective documentation.

/// warning

   * evaluate the integral of the function from 7.0 to 10.0.
   *
   * Using integrals guarantees that the effect of a single acquire(3) is equivalent to {
   * acquire(1); acquire(1); acquire(1); }, or { acquire(2); acquire(1); }, etc, since the integral
   * of the function in [7.0, 10.0] is equivalent to the sum of the integrals of [7.0, 8.0], [8.0,
   * 9.0], [9.0, 10.0] (and so on), no matter what the function is. This guarantees that we handle

* Construa sua imagem FastAPI:

<div class="termy">

```console
$ docker build -t myimage .

---> 100%
```

</div>

/// tip | Dica

Note o `.` no final, é equivalente a `./`, ele diz ao Docker o diretório a ser usado para construir a imagem do contêiner.

Nesse caso, é o mesmo diretório atual (`.`).

///

### Inicie o Contêiner Docker { #start-the-docker-container }

  RangeMap<K, V> subRangeMap(Range<K> range);

  /**
   * Returns {@code true} if {@code obj} is another {@code RangeMap} that has an equivalent {@link
   * #asMapOfRanges()}.
   */
  @Override
  boolean equals(@Nullable Object o);

  /** Returns {@code asMapOfRanges().hashCode()}. */
  @Override
  int hashCode();

  private static int[] createFilledWithAbsent(int size) {
    int[] array = new int[size];
    Arrays.fill(array, ABSENT);
    return array;
  }

  /** Equivalent to {@code Arrays.copyOf(array, newSize)}, save that the new elements are ABSENT. */
  private static int[] expandAndFillWithAbsent(int[] array, int newSize) {
    int oldSize = array.length;

   * note that the execution order of all listeners is ultimately chosen by the implementations of
   * the supplied executors.
   *
   * <p>This method is idempotent. Calling it several times in parallel is semantically equivalent
   * to calling it exactly once.
   *
   * @since 10.0 (present in 1.0 as {@code run})
   */
  public void execute() {
    // Lock while we update our state so the add method above will finish adding any listeners

   */
  public abstract ContiguousSet<C> intersection(ContiguousSet<C> other);

  /**
   * Returns a range, closed on both ends, whose endpoints are the minimum and maximum values
   * contained in this set. This is equivalent to {@code range(CLOSED, CLOSED)}.
   *
   * @throws NoSuchElementException if this set is empty
   */
  public abstract Range<C> range();

  /**