# How Voting Systems Work 7, Exercise 2: search seeded random profiles for a case where Jefferson gives a state more than its
# upper quota (the quota rounded up). Populations are drawn at random: an assumed model.
import random
from math import ceil

def jefferson(pops, seats):
    alloc = {s: 0 for s in pops}
    for _ in range(seats):
        best = max(sorted(pops), key=lambda s: pops[s] / (alloc[s] + 1))
        alloc[best] += 1
    return alloc

random.seed(31)
for attempt in range(1, 10001):
    pops = {name: random.randint(100, 3000) for name in ("Ardan", "Brex", "Cole", "Dunn")}
    pops["Eld"] = random.randint(10, 100) * 100
    seats = 10
    total = sum(pops.values())
    alloc = jefferson(pops, seats)
    for s in pops:
        quota = seats * pops[s] / total
        if alloc[s] > ceil(quota):
            print("attempt", attempt, "populations", pops)
            print(f"{s}: quota {quota:.2f}, Jefferson gives {alloc[s]} (upper quota {ceil(quota)})")
            print("allocation", alloc)
            raise SystemExit
print("none found")
# attempt 2 populations {'Ardan': 2901, 'Brex': 277, 'Cole': 668, 'Dunn': 560, 'Eld': 7800}
# Eld: quota 6.39, Jefferson gives 8 (upper quota 7)
# allocation {'Ardan': 2, 'Brex': 0, 'Cole': 0, 'Dunn': 0, 'Eld': 8}