from typing import List, Dict, Optional, Union, Any
from datetime import datetime
import math

def calculate_distance(point1: tuple, point2: tuple) -> float:
    """
    Calculate the Euclidean distance between two points.

    Args:
        point1 (tuple): A tuple representing the coordinates (x, y) of the first point.
        point2 (tuple): A tuple representing the coordinates (x, y) of the second point.

    Returns:
        float: The Euclidean distance between the two points.
    """
    x1, y1 = point1
    x2, y2 = point2
    return math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)

def optimize_route(points: List[tuple]) -> List[tuple]:
    """
    Optimize a route by finding the shortest path that visits all points.

    Args:
        points (List[tuple]): A list of tuples representing the coordinates (x, y) of the points to visit.

    Returns:
        List[tuple]: The optimized route as a list of tuples representing the coordinates (x, y) of the points.
    """
    if not points:
        return []

    num_points = len(points)
    distances = [[0] * num_points for _ in range(num_points)]

    # Calculate the distance matrix
    for i in range(num_points):
        for j in range(i + 1, num_points):
            distances[i][j] = distances[j][i] = calculate_distance(points[i], points[j])

    # Implement your route optimization algorithm here
    # For example, you could use a greedy algorithm or a more sophisticated technique like the Traveling Salesman Problem solver

    return [points[0], points[1], points[2]]  # Replace with the optimized route

def calculate_route_distance(route: List[tuple]) -> float:
    """
    Calculate the total distance of a given route.

    Args:
        route (List[tuple]): A list of tuples representing the coordinates (x, y) of the points in the route.

    Returns:
        float: The total distance of the route.
    """
    total_distance = 0.0
    for i in range(len(route) - 1):
        total_distance += calculate_distance(route[i], route[i + 1])
    return total_distance

def format_route(route: List[tuple]) -> str:
    """
    Format a route as a string for display or output.

    Args:
        route (List[tuple]): A list of tuples representing the coordinates (x, y) of the points in the route.

    Returns:
        str: The formatted route as a string.
    """
    formatted_route = "Route: "
    for point in route:
        formatted_route += f"({point[0]}, {point[1]}) -> "
    formatted_route = formatted_route[:-4]  # Remove the last " -> "
    return formatted_route