Advent of code, day 6, O(1) solution

part1.py

import sys
import math

def get_integer_roots(a, b, c):
  delta = b * b - 4 * a * c
  x1 = (-b + math.sqrt(delta)) / 2 * a
  x2 = (-b - math.sqrt(delta)) / 2 * a
  return (x1, x2)

def get_number_of_better_solutions(total_time, max_distance_so_far):
  roots = get_integer_roots(-1, total_time, -max_distance_so_far)

  start  = math.ceil(roots[0])
  finish = math.floor(roots[1])

  if float(start)  == roots[0]: start  += 1
  if float(finish) != roots[1]: finish += 1

  return finish - start

if __name__ == '__main__':
  times     = list(map(int, sys.stdin.readline().strip().split(':')[1].split()))
  distances = list(map(int, sys.stdin.readline().strip().split(':')[1].split()))

  prod = 1
  for t, d in zip(times, distances):
    prod *= get_number_of_better_solutions(t, d)
    
  print(prod)