import math
from typing import Tuple

import haversine

mean_earth_radius_km = (6378 + 6357) / 2

# if you're more than 1/4 of the Earth's circumfrence away, you get 0
max_dist_km = (math.pi * mean_earth_radius_km) / 2 # this is about 10,000 km

# if you're within 1/16 of the Earth's circumfrence away, you get at least 1000 points
quarter_of_max_km = max_dist_km / 4 # this is about 2,500 km

# https://www.wolframalpha.com/input/?i=sqrt%28%28%28land+mass+of+earth%29+%2F+7%29%29+%2F+pi%29+in+kilometers
# this is the average "radius" of a continent
# within this radius, you get at least 2000 points
avg_continental_rad_km = 1468.0

# somewhat arbitrarily, if you're within 1000 km, you get at least 3000 points
one_thousand = 1000.0

# https://www.wolframalpha.com/input/?i=sqrt%28%28%28land+mass+of+earth%29+%2F+%28number+of+countries+on+earth%29%29+%2F+pi%29+in+kilometers
# this is the average "radius" of a country
# within this radius, you get at least 4000 points
avg_country_rad_km = 479.7

# if you're within 150m, you get a perfect score of 5000
min_dist_km = 0.15  


def score_within(raw_dist: float, min_dist: float, max_dist: float) -> int:
    """
    Gives a score between 0 and 1000, with 1000 for the min_dist and 0 for the max_dist
    """
    # scale the distance down to [0.0, 1.0], then multiply it by 2 for easing
    pd2 = 2 * (raw_dist - min_dist) / (max_dist - min_dist)
    # perform a quadratic ease-in-out on pd2
    r = (pd2 ** 2) / 2 if pd2 < 1 else 1 - (((2 - pd2) ** 2) / 2)
    # use this to ease between 1000 and 0
    return int(1000 * (1 - r))


def score(target: Tuple[float, float], guess: Tuple[float, float]) -> Tuple[int, float]:
    """
    Takes in two (latitude, longitude) pairs and produces an int score.
    Score is in the (inclusive) range [0, 5000]
    Higher scores are closer.

    Returns (score, distance in km)
    """
    dist_km = haversine.haversine(target, guess)

    if dist_km <= min_dist_km:
        point_score = 5000
    elif dist_km <= avg_country_rad_km:
        point_score = 4000 + score_within(dist_km, min_dist_km, avg_country_rad_km)
    elif dist_km <= one_thousand:
        point_score = 3000 + score_within(dist_km, avg_country_rad_km, one_thousand)
    elif dist_km <= avg_continental_rad_km:
        point_score = 2000 + score_within(dist_km, one_thousand, avg_continental_rad_km)
    elif dist_km <= quarter_of_max_km:
        point_score = 1000 + score_within(dist_km, avg_continental_rad_km, quarter_of_max_km)
    elif dist_km <= max_dist_km:
        point_score = score_within(dist_km, quarter_of_max_km, max_dist_km)
    else: # dist_km > max_dist_km
        point_score = 0

    return point_score, dist_km