### Top-level application { #top-level-application }

First, create the main, top-level, **FastAPI** application, and its *path operations*:

{* ../../docs_src/sub_applications/tutorial001.py hl[3, 6:8] *}

### Sub-application { #sub-application }

Then, create your sub-application, and its *path operations*.

This sub-application is just another standard FastAPI application, but this is the one that will be "mounted":

     */
    @Override
    public Iterator<E> iterator() {
        return map.keySet().iterator();
    }

    /**
     * Returns the number of elements in this set (its cardinality).
     *
     * @return the number of elements in this set (its cardinality).
     */
    @Override
    public int size() {
        return map.size();
    }

    /**
     * Returns true if this set contains no elements.
     *

        return new RegularImmutableAsList<E>(this, toArray());
    }
  }

  /** If this collection is backed by an array of its elements in insertion order, returns it. */
  Object @Nullable [] internalArray() {
    return null;
  }

  /**
   * If this collection is backed by an array of its elements in insertion order, returns the offset
   * where this collection's elements start.
   */
  int internalArrayStart() {

    /**
     * Validate that the constructor masks the supplied value to its
     * lowest 8 bits (NdrShort incorrectly masks to 8 bits even though it's a short).
     */
    @ParameterizedTest
    @ValueSource(ints = { 0, 1, 255, -1, 256, 65535 })
    void constructorMasksValue(int input) {
        NdrShort ns = new NdrShort(input);
        // NdrShort masks to 0xFF (8 bits) in its constructor
        int expected = input & 0xFF;

     * <li>If <code>type</code> is a parameterized type, its raw type is returned.</li>
     * <li>If <code>type</code> is a wildcard type, its (first) upper bound is returned.</li>
     * <li>If <code>type</code> is a type variable and is a key in the given map, its actual type argument is returned.</li>
     * <li>If <code>type</code> is a type variable and is not a key in the given map, its (first) upper bound is returned.</li>

            op.rangeSize(fessConfig.getPagingPageRangeSizeAsInteger());
        }).createPageNumberList());

        return fileConfigList;
    }

    /**
     * Deletes a file configuration and its associated authentication records.
     * This method removes the file configuration from the database and also
     * deletes all related file authentication entries.
     *

The history of **FastAPI** is in great part the history of its predecessors.

As said in the section [Alternatives](alternatives.md){.internal-link target=_blank}:

<blockquote markdown="1">

**FastAPI** wouldn't exist if not for the previous work of others.

There have been many tools created before that have helped inspire its creation.

    }

    /**
     * Returns {@literal true} if the array is not {@literal null} and its length is not 0.
     *
     * @param <T>
     *            the type of the array elements
     * @param arrays
     *            the array
     * @return {@literal true} if the array is not {@literal null} and its length is not 0
     */
    public static <T> boolean isNotEmpty(final T[] arrays) {

  // implementations.

  private Futures() {}

  /**
   * Creates a {@code ListenableFuture} which has its value set immediately upon construction. The
   * getters just return the value. This {@code Future} can't be canceled or timed out and its
   * {@code isDone()} method always returns {@code true}.
   */
  public static <V extends @Nullable Object> ListenableFuture<V> immediateFuture(

  /** Maps a bucket to the "entry" of its first element. */
  private transient int[] hashTableKToV;

  /** Maps a bucket to the "entry" of its first element. */
  private transient int[] hashTableVToK;

  /** Maps an "entry" to the "entry" that follows it in its bucket. */
  private transient int[] nextInBucketKToV;

  /** Maps an "entry" to the "entry" that follows it in its bucket. */