import collections
import math
import sys

def read_edge_distortions(filename):
  vertices = set()
  distortions = {}
  with open(filename, 'r') as edge_file:
    while edge_line := edge_file.readline():
      line_parts = edge_line.rstrip().split(': ')
      endpoints = tuple(sorted(line_parts[0].split(', ')))
      vertices.update(endpoints)
      if len(line_parts) > 1:
        distortions[endpoints] = float(line_parts[1])
      else:
        distortions[endpoints] = 0
  return (vertices, distortions)

def find_triangles(vertices, edges):
  triangles = []
  for e in edges:
    for v in vertices:
      if e[1] < v:
        if (e[0], v) in edges and (e[1], v) in edges:
          triangles.append((e[0], e[1], v))
  return triangles

# use the law of cosines to get the angle distortion
def angle_distortion(edge_distortions):
  a, b, c = list(edge_distortions)
  cos_angle_a = (1 + 2*(b + c - a) + b*b + c*c - a*a) / (2*(1 + b)*(1 + c))
  return math.degrees(math.acos(cos_angle_a)) - 60

if __name__ == '__main__':
  if len(sys.argv) <= 1:
    print('Pass the path to the file that lists the edge distortions')
  else:
    vertices, distortions = read_edge_distortions(sys.argv[1])
    triangles = find_triangles(vertices, distortions.keys())
    total_angle_distortion = 0
    highest_angle_distortion = -math.inf
    lowest_angle_distortion = math.inf
    print('{} triangles\n'.format(len(triangles)))
    for t in triangles:
      print('Triangle {0}, {1}, {2}'.format(t[0], t[1], t[2]))
      edge_distortions = collections.deque(
        [distortions[(t[j], t[k])] for (j, k) in [(1, 2), (0, 2), (0, 1)]]
      )
      for k in range(3):
        ang_distort = angle_distortion(edge_distortions)
        total_angle_distortion += abs(ang_distort)
        highest_angle_distortion = max(highest_angle_distortion, ang_distort)
        lowest_angle_distortion = min(lowest_angle_distortion, ang_distort)
        print('  {0}: {1}°'.format(t[k], ang_distort))
        edge_distortions.rotate()
      print()
    print('Total angle distortion: {}°'.format(total_angle_distortion))
    print('Highest angle distortion: {}°'.format(highest_angle_distortion))
    print('Lowest angle distortion: {}°'.format(lowest_angle_distortion))