# How Voting Systems Work 7, Exercise 1 (assumed, invented numbers): five states share 12 seats under Huntington-Hill.
# Every state starts with 1 seat; each remaining seat goes to the highest priority p / sqrt(n * (n + 1)),
# where n is the number of seats the state already holds.
from math import sqrt

pops = {"Ardan": 9100, "Brex": 5400, "Cole": 3300, "Dunn": 1900, "Eld": 900}
seats = 12
alloc = {s: 1 for s in pops}
gaps = {}
for number in range(len(pops) + 1, seats + 1):
    priority = {s: pops[s] / sqrt(alloc[s] * (alloc[s] + 1)) for s in pops}
    best = max(sorted(priority), key=priority.get)
    print(f"seat {number:>2}: {best:<6} priority {priority[best]:8.1f}  (runner-up {sorted(priority.values())[-2]:8.1f})")
    gaps[number] = priority[best] - sorted(priority.values())[-2]
    alloc[best] += 1
print(alloc)
closest = min(gaps, key=gaps.get)
print("closest call: seat", closest, "decided by a margin of", round(gaps[closest], 1))
# seat  6: Ardan  priority   6434.7  (runner-up   3818.4)
# seat  7: Brex   priority   3818.4  (runner-up   3715.1)
# seat  8: Ardan  priority   3715.1  (runner-up   2333.5)
# seat  9: Ardan  priority   2626.9  (runner-up   2333.5)
# seat 10: Cole   priority   2333.5  (runner-up   2204.5)
# seat 11: Brex   priority   2204.5  (runner-up   2034.8)
# seat 12: Ardan  priority   2034.8  (runner-up   1558.8)
# {'Ardan': 5, 'Brex': 3, 'Cole': 2, 'Dunn': 1, 'Eld': 1}
# closest call: seat 7 decided by a margin of 103.3