⚡ Live Sandbox: AI Dev Tool: Humazon

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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS with PostgreSQL Vector Search Extension
# Description: A production-ready FastAPI boilerplate with Pydantic v2 and PostgreSQL Vector Search Extension
# Author: [Your Name]

from fastapi import FastAPI, Depends
from fastapi.responses import JSONResponse
from fastapi.requests import Request
from pydantic import BaseModel
from typing import List, Optional
import psycopg2
from psycopg2 import Error
import logging

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

# Define the FastAPI app
app = FastAPI()

# Define the Pydantic model for the search query
class SearchQuery(BaseModel):
    query: str
    limit: Optional[int] = 10

# Define the Pydantic model for the search result
class SearchResult(BaseModel):
    id: int
    title: str
    description: str

# Define the PostgreSQL connection settings
POSTGRES_HOST = "localhost"
POSTGRES_DB = "mydb"
POSTGRES_USER = "myuser"
POSTGRES_PASSWORD = "mypassword"

# Establish a connection to the PostgreSQL database
def get_db_connection():
    try:
        connection

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