MA0301/exam_template/python/Hasse.py

from sys import argv
from pathlib import Path

from common import printc, replaceContent

# Increase if the diagram becomes too clobbered
HEIGHT_SEPARATOR = 1

# For manual usage via stdin
def getRels(relations=None):
  if relations == None:
    relations = input("Write the relations in the following format: ab ac ad bc cd ...\n")
  relations = (tuple(list(x)) for x in relations.split(' '))
  return set(relations)

# Generate divisibility graph by range
def divisibility_graph(n):
  E = set()
  for dst in range(n):
    for src in range( 1, dst ):
      if dst % src == 0:
        E.add( ( src, dst ) )
  return E

def hasse_diagram(E):
  E2 = set()
  for e0 in E:
    for e1 in E:
      if e0[1] == e1[0]:
        E2.add( ( e0[0], e1[1] ) )
  return E - E2

def latex_hasse(hasse):
  min_el = set(a for a,b in hasse if a not in list(zip(*hasse))[1])
  keys = set(item for tup in hasse for item in tup)
  y_pos = dict.fromkeys(keys, 0)

  i = 0
  while len(next_row := [val for key,val in hasse if key in [x for x,y in y_pos.items() if y == i] ]) != 0:
    for item in next_row:
      y_pos[item] = i + 1
    i += 1

  inv_ypos = dict()
  for key in set(y_pos.values()):
    inv_ypos[key] = [x for x,y in y_pos.items() if y == key]

  output = []
  
  for y in inv_ypos.keys():
    for i, n in enumerate(inv_ypos[y]):
      output.append(f'\\node ({n}) at ({i - len(inv_ypos[y])/2}, {y * HEIGHT_SEPARATOR}) {{${n}$}};')
  
  output.append('')

  for x,y in hasse:
    output.append(f'\\draw ({x}) -- ({y});')


  printc(f"Minimal elements: $\{{ {', '.join(str(e) for e in min_el)} \}}$ \\\\")

  max_el = set(v for k,v in hasse if v not in (x for x,_ in hasse))
  printc(f"Maximal elements: $\{{ {', '.join(str(e) for e in max_el)} \}}$" )

  return '\n'.join(output)

def processFileContent(raw):
  rels = getRels(raw)
  content = latex_hasse(hasse_diagram(rels))
  return replaceContent(content, 'Hasse')


if __name__ == '__main__':
  pass