S2T2

Jim Randell 8:37 am on 18 August 2020 Permalink Reply
Tags: by: Nick MacKinnon ( 43 )   

• 

  Jim Randell 8:39 am on 18 August 2020 Permalink | Reply

  This Python program uses the [[ Football() ]] helper class from the enigma.py library.

  It runs in 452ms.

  Run: [ @repl.it ]

  from enigma import Football, printf
  
  # scoring system
  football = Football(games="wdl", points=dict(w=3, d=1))
  
  # check home matches have more points and more goals than away matches
  def check(Hs, As):
    for (H, A) in zip(Hs, As):
      if not(H[0] > A[1]): return False
      (h, a) = football.outcomes([H, A], [0, 1])
      if not(football.points(h) > football.points(a)): return False
    return True
  
  # choose C's six games (home, away)
  for (CA, CB, CD, AC, BC, DC) in football.games(repeat=6):
    # table for C
    tC = football.table([CA, CB, CD, AC, BC, DC], [0, 0, 0, 1, 1, 1])
    if not(tC.points == 7): continue
  
    # remaining matches for D
    for (DA, DB, AD, BD) in football.games(repeat=4):
      # table for D
      tD = football.table([DA, DB, DC, AD, BD, CD], [0, 0, 0, 1, 1, 1])
      if not(tD.points == 5): continue
  
      # remaining matches (for A and B)
      for (AB, BA) in football.games(repeat=2):
        # table for A, B
        tA = football.table([AB, AC, AD, BA, CA, DA], [0, 0, 0, 1, 1, 1])
        tB = football.table([BA, BC, BD, AB, CB, DB], [0, 0, 0, 1, 1, 1])
        if not(tA.points == 12 and tB.points == 8): continue
  
        # make possible scores (for C)
        for (sCA, sCB, sCD, sAC, sBC, sDC) in football.scores([CA, CB, CD, AC, BC, DC], [0, 0, 0, 1, 1, 1], 3, 5):
          # check the home matches were better than the away matches
          if not check([sCA, sCB, sCD], [sAC, sBC, sDC]): continue
  
          # remaining scores (for D)
          for (sDA, sDB, sAD, sBD) in football.scores([DA, DB, AD, BD], [0, 0, 1, 1], 9, 13, [sCD, sDC], [1, 0]):
            # check home matches were better than away matches
            if not check([sDA, sDB, sDC], [sAD, sBD, sCD]): continue
  
            # remaining scores (for A)
            for (sAB, sBA) in football.scores([AB, BA], [0, 1], 15, 8, [sAC, sAD, sCA, sDA], [0, 0, 1, 1]):
              # check for/against B
              (fB, aB) = football.goals([sBA, sBC, sBD, sAB, sCB, sDB], [0, 0, 0, 1, 1, 1])
              if not(fB == 12 and aB == 13): continue
              # check home matches were better than away matches
              if not check([sAB, sAC, sAD], [sBA, sCA, sDA]): continue
              if not check([sBA, sBC, sBD], [sAB, sCB, sDB]): continue
  
              printf("AB={AB}:{sAB} AC={AC}:{sAC} AD={AD}:{sAD} / BA={BA}:{sBA} CA={CA}:{sCA} DA={DA}:{sDA}")
              printf("BA={BA}:{sBA} BC={BC}:{sBC} BD={BD}:{sBD} / AB={AB}:{sAB} CB={CB}:{sCB} DB={DB}:{sDB}")
              printf("CA={CA}:{sCA} CB={CB}:{sCB} CD={CD}:{sCD} / AC={AC}:{sAC} BC={BC}:{sBC} DC={DC}:{sDC}")
              printf("DA={DA}:{sDA} DB={DB}:{sDB} DC={DC}:{sDC} / AD={AD}:{sAD} BD={BD}:{sBD} CD={CD}:{sCD}")
              printf()
  

  Solution: The scores in the Borough vs. District matches were: B (home) vs. D (away) = 4 – 2; D (home) vs. B (away) = 3 – 3.

  The scores in the matches are: (home vs. away)

  A vs B = 4 – 1; A vs C = 2 – 0; A vs D = 3 – 1
  B vs A = 3 – 3; B vs C = 1 – 0; B vs D = 4 – 2
  C vs A = 1 – 1; C vs B = 1 – 0; C vs D = 1 – 0
  D vs A = 2 – 2; D vs B = 3 – 3; D vs C = 1 – 0

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