# INT-INTERVALS LIBRARY

from math import floor, ceil
from tools import min_max

def reunion_inter(inter, a, b):
  a, b = min_max(a, b)
  a, b = floor(a), ceil(b)
  for i in range(0, len(inter), 2):
    if a <= inter[i+1] + 1:
      return inter[:i] + (b >= inter[i] - 1 and reunion_inter(inter[i+2:], min(a, inter[i]), max(b, inter[i+1])) or [a, b] + inter[i:])
  return inter + [a, b]

def inclus_inter(inter, a, b):
  a, b = min_max(a, b)
  for i in range(0, len(inter), 2):
    if a <= inter[i+1]:
      return a >= inter[i] and b <= inter[i+1]
  return 0

def remove_hidden_by_inter(a, b, inter):
  a, b = min_max(a, b)
  for i in range(0, len(inter), 2):
    if a < inter[i] and b >= inter[i] and b <= inter[i+1]: b = inter[i]
  for i in range(len(inter) - 2, -2, -2):
    if a >= inter[i] and a <= inter[i+1] and b > inter[i+1]: a = inter[i+1]
  return a, b