MA0301/exam_template/python/Relations.py

from sys import argv
from pathlib import Path

from common import printc, printerr
from Graph import Graph

# Increase if hasse diagram becomes too clobbered
HEIGHT_SEPARATOR = 1

def pairToString(pair):
  if str(pair[0]).isdigit() or str(pair[1]).isdigit():
    return f'({pair[0]},{pair[1]})'
  else:
    return pair[0] + pair[1]

def stringToPair(string):
  if string[0] == '(':
    return tuple(string.split(',')[0][1:], string.split(',')[0][:-1])
  else:
    return tuple(list(string))


class Relation:
  def __init__(self, pairs): # pair = (str,str)
    self.pairs = set(pairs)
  
  def __str__(self):
    return f'\\{{ {", ".join(x + y for x,y in self.pairs)} \}}'

  @classmethod
  def fromString(cls, string):
    relations = (stringToPair(x) for x in relations.split(' '))
    return cls(relations)

  @classmethod
  def fromDivisibilityPosetTo(cls, n):
    pairs = set()
    for dst in range(n):
      pairs.add((dst, dst))
      for src in range(1, dst):
        if dst % src == 0:
          pairs.add((src, dst))
    return cls(pairs)


  def isReflexive(self):
    elements = set(list(sum(self.pairs, ())))
    result = all((x,x) in self.pairs for x in elements)

    if not result:
      printc('Not reflexive, missing following pairs:', color='green')
      missingPairs = [(x,x) for x in elements if (x,x) not in self.pairs]
      print(f'\\[ {", ".join(pairToString(p) for p in missingPairs)} \\]')
    
    return result

  def isSymmetric(self):
    result = all((y,x) in self.pairs for x,y in self.pairs)

    if not result:
      printc('Not symmetric, missing following pairs:', color='green')
      missingPairs = [(x,y) for x,y in self.pairs if (y,x) not in self.pairs]
      print(f'\\[ {", ".join(pairToString(p) for p in missingPairs)} \\]')
  
    return result

  def isAntiSymmetric(self):
    result = not any((y,x) in self.pairs and y != x for x,y in self.pairs)

    if not result:
      printc('Not antisymmetric, following pairs are symmetric:', color='green')
      symmetricPairs = [((x,y), (y,x)) for x,y in self.pairs if (y,x) in self.pairs and y > x]
      print(f'\\[ {", ".join(f"{pairToString(p)} and {pairToString(q)}" for p,q in symmetricPairs)} \\]')

    return result

  def isTransitive(self):
    result = True
    nonTransitivePairs = []

    for x,y in self.pairs:
      for z,w in self.pairs:
        if not (y != z or ((x,w) in self.pairs)):
          nonTransitivePairs.append(((x,y), (z,w)))
          result = False
    
    if not result:
      printc('Not transitive, following pairs are missing its transitive counterpart:', color='green')
      print(f'\\[ {", ".join(f"{pairToString(p)} and {pairToString(q)} without {pairToString((p[0], q[1]))}" for p,q in nonTransitivePairs)} \\]')

    return result

  def isEquivalenceRelation(self):
    return self.isReflexive() and self.isSymmetric() and self.isTransitive()

  def isPartialOrder(self):
    return self.isReflexive() and self.isAntiSymmetric() and self.isTransitive()
  
  def getHassePairs(self):
    if not self.isPartialOrder():
      printerr('This is not a partial order')
      return
    hassePairs = set()
    for x1, y1 in self.pairs:
      for x2, y2 in self.pairs:
        if y1 == x2:
          hassePairs.add((x1, y2))
    return self.pairs - hassePairs
  
  def latexifyHasseDiagram(self):
    hasse = self.getHassePairs()
    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 latexifyGraph(self):
    if self.isEquivalenceRelation():
      graphType = 'undirected'
      pairs = [(x,y) for x,y in self.pairs if x != y]
    else:
      graphType = 'directed'
      pairs = self.pairs
    
    pass
    

def processFileContent(raw, template):
  outputType, inp =  raw.split('\n\n')

  if inp.startsWith('divisibilityPosetTo'):
    n = int(inp.split(' ')[1])
    relation = Relation.fromDivisibilityPosetTo(n)
  else: 
    relation = Relation.fromString(inp)

  if outputType == 'proveEquivalence':
    content = relation.isEquivalenceRelation()
  elif outputType == 'provePoset':
    content = relation.isPartialOrder()
  elif outputType == 'hasseDiagram':
    content = relation.latexifyHasseDiagram()
  elif outputType == 'graph':
    content = relation.latexifyGraph()

  content = Relation.fromString(raw).latexifyHasseDiagram()
  return template.replace("%CONTENT", content)

if __name__ == '__main__':
  inp = 'AA BB CC DD AB AC AD BC BD CD'
  relations = [stringToPair(p) for p in inp.split(' ')]
  # print(Relation(relations).isEquivalenceRelation())
  print(Relation(relations).isPartialOrder())
  print(Relation.fromDivisibilityPosetTo(30).isPartialOrder())