from datetime import datetime
from typing import Union

from fastapi import FastAPI
from fastapi.encoders import jsonable_encoder
from pydantic import BaseModel

fake_db = {}


class Item(BaseModel):
    title: str
    timestamp: datetime
    description: Union[str, None] = None


app = FastAPI()


@app.put("/items/{id}")
def update_item(id: str, item: Item):
    json_compatible_item_data = jsonable_encoder(item)

from datetime import datetime, time, timedelta
from typing import Annotated, Union
from uuid import UUID

from fastapi import Body, FastAPI

app = FastAPI()


@app.put("/items/{item_id}")
async def read_items(
    item_id: UUID,
    start_datetime: Annotated[datetime, Body()],
    end_datetime: Annotated[datetime, Body()],
    process_after: Annotated[timedelta, Body()],
    repeat_at: Annotated[Union[time, None], Body()] = None,
):

    }

    void addEdge(Vertex from, Vertex to) throws CycleDetectedException {
        from.children.add(to);
        to.parents.add(from);
        List<String> cycle = findCycle(to);
        if (cycle != null) {
            // remove edge which introduced cycle
            removeEdge(from, to);
            throw new CycleDetectedException(

import datetime
from collections import defaultdict, deque
from decimal import Decimal
from enum import Enum
from ipaddress import (
    IPv4Address,
    IPv4Interface,
    IPv4Network,
    IPv6Address,
    IPv6Interface,
    IPv6Network,
)
from pathlib import Path, PurePath
from re import Pattern
from types import GeneratorType
from typing import Annotated, Any, Callable, Optional, Union
from uuid import UUID

import inspect
import sys
from dataclasses import dataclass, field
from functools import cached_property, partial
from typing import Any, Callable, Optional, Union

from fastapi._compat import ModelField
from fastapi.security.base import SecurityBase
from fastapi.types import DependencyCacheKey
from typing_extensions import Literal

if sys.version_info >= (3, 13):  # pragma: no cover
    from inspect import iscoroutinefunction

from typing import Optional

from fastapi import FastAPI
from fastapi.params import Param
from fastapi.testclient import TestClient

app = FastAPI()


@app.get("/items/")
def read_items(q: Optional[str] = Param(default=None)):  # type: ignore
    return {"q": q}


client = TestClient(app)


def test_default_param_query_none():
    response = client.get("/items/")
    assert response.status_code == 200, response.text

# WebSockets

When defining WebSockets, you normally declare a parameter of type `WebSocket` and with it you can read data from the client and send data to it.

It is provided directly by Starlette, but you can import it from `fastapi`:

```python
from fastapi import WebSocket
```

/// tip

	if !reflect.DeepEqual(lc.Keys(), []string{"key1"}) {
		t.Fatalf("value differs from expected")
	}

	if lc.Resize(0) != 0 {
		t.Fatalf("evicted count differs from expected")
	}
	if lc.Resize(2) != 0 {
		t.Fatalf("evicted count differs from expected")
	}
	lc.Add("key2", "val2")
	if lc.Resize(1) != 1 {
		t.Fatalf("evicted count differs from expected")
	}
}

func TestLRUEdgeCases(t *testing.T) {

  }

  ImmutableSortedMultiset<E> getSubMultiset(int from, int to) {
    checkPositionIndexes(from, to, length);
    if (from == to) {
      return emptyMultiset(comparator());
    } else if (from == 0 && to == length) {
      return this;
    } else {
      RegularImmutableSortedSet<E> subElementSet = elementSet.getSubSet(from, to);
      return new RegularImmutableSortedMultiset<>(

 * Negotiation Protocol) authentication. It contains the username extracted from the
 * SPNEGO authentication process, typically from a Kerberos ticket.
 */
public class SpnegoCredential implements LoginCredential, FessCredential {

    /** The username extracted from SPNEGO authentication. */
    private final String username;

    /**