⚡ Live Sandbox: AI Dev Tool: FastAPI Pydantic v2 (i3dr)

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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Boilerplate with PostgreSQL Vector Search Extension
# =================================================================================================

from fastapi import FastAPI, Depends
from fastapi.responses import JSONResponse
from pydantic import BaseModel
from typing import List, Optional
from sqlalchemy import create_engine, Column, Integer, String
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.orm import sessionmaker, Session
from psycopg2.extras import Json

# Initialize FastAPI App
app = FastAPI()

# Initialize PostgreSQL Database Connection
SQLALCHEMY_DATABASE_URL = "postgresql://user:password@host:port/dbname"
engine = create_engine(SQLALCHEMY_DATABASE_URL)
SessionLocal = sessionmaker(autocommit=False, autoflush=False, bind=engine)

Base = declarative_base()

# Define PostgreSQL Vector Search Extension Model
class VectorSearchModel(Base):
    __tablename__ = "vector_search"
    id = Column(Integer, primary_key=True)
    vector = Column(Json)

# Create PostgreSQL Vector Search Extension Table
Base.metadata.create_all(bind=engine)

# Define Pydantic Model for Vector Search Request
class VectorSearchRequest(BaseModel):
    query: str
    limit: int = 10

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