What is FastAPI's dependency injection system and how do you use it?

from fastapi import FastAPI, Depends, HTTPException
from typing import Annotated

app = FastAPI()

# Simple dependency — shared pagination logic
def pagination(skip: int = 0, limit: int = 10):
    return {"skip": skip, "limit": limit}

@app.get("/items")
def list_items(pagination: Annotated[dict, Depends(pagination)]):
    return {"pagination": pagination}

@app.get("/users")
def list_users(pagination: Annotated[dict, Depends(pagination)]):
    return {"pagination": pagination}

# Class-based dependency
class DBSession:
    def __init__(self):
        self.db = "fake_db_connection"  # in real code: create session

    def close(self):
        pass  # close connection

# Generator dependency — enables cleanup with finally
def get_db():
    db = DBSession()
    try:
        yield db.db   # yield makes it a context-managed dependency
    finally:
        db.close()    # runs after request completes, even on error

@app.get("/data")
def get_data(db: Annotated[str, Depends(get_db)]):
    return {"db": db}

# Nested dependencies
def verify_token(token: str) -> str:
    if token != "secret":
        raise HTTPException(status_code=401, detail="Invalid token")
    return token

def get_current_user(token: Annotated[str, Depends(verify_token)]):
    return {"user": "alice", "token": token}