⚡ Live Sandbox: AI Dev Tool: PostgreSQL Vector Search Extension

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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Boilerplate with PostgreSQL Vector Search Extension
# =============================================================================================
# This is a production-ready developer code asset for building high-performance micro-SaaS applications.
# It combines the power of FastAPI, Pydantic v2, and PostgreSQL Vector Search Extension.

from fastapi import FastAPI, Depends
from fastapi.responses import JSONResponse
from pydantic import BaseModel
from sqlalchemy import create_engine, Column, Integer, String
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.orm import sessionmaker
from sqlalchemy.exc import SQLAlchemyError
from typing import List
import psycopg2
import logging

# Initialize the logger
logging.basicConfig(level=logging.INFO)
logger = logging.getLogger(__name__)

# Define the database connection parameters
DB_HOST = "localhost"
DB_PORT = 5432
DB_USER = "postgres"
DB_PASSWORD = "postgres"
DB_NAME = "micro_saaS"

# Create a PostgreSQL database engine
engine = create_engine(f"postgresql://{DB_USER}:{DB_PASSWORD}@{DB_HOST}:{DB_PORT}/{DB_NAME}")

# Create a configured "Session" class
Session = sessionmaker(bind=engine)

# Create a base class for declarative class

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