S2T2

Jim Randell 9:24 am on 8 March 2022 Permalink Reply
Tags: by: Ian Gilchrist ( 2 )   

• 

  Jim Randell 9:26 am on 8 March 2022 Permalink | Reply

  We can look for viable 12-seat layouts, and then remove Ari and Ira to give a 10-seat layout, which we can check is viable.

  This Python program runs in 88ms.

  Run: [ @replit ]

  from enigma import (update, ordered, diff, join, printf)
  
  # implement a circular list (see Tantalizer 496)
  class CircularList(list):
  
    def __getitem__(self, i):
      return list.__getitem__(self, i % len(self))
  
    def copy(self):
      # list.copy() returns a list(), so re-wrap it
      return self.__class__(list.copy(self))
  
  # find names in <ns> that can be opposite/adjacent to <ps>
  def valid(ns, ps):
    # find disallowed initials and anagrams
    xis = set(p[0] for p in ps if p is not None)
    xas = set(ordered(*p) for p in ps if p is not None)
    for n in ns:
      if n[0] in xis or ordered(*n) in xas: continue
      yield n
  
  # place names <ns> in table <t>
  def place(t, ns):
    # are we done?
    if not ns:
      if t[1] < t[-1]:
        yield t
    else:
      # find the next unoccupied place
      i = t.index(None)
      # choose someone to occupy it
      for n in valid(ns, {t[i + 6], t[i - 1], t[i + 1], t[i - 2], t[i + 2]}):
        yield from place(update(t, [(i, n)]), ns.difference([n]))
  
  # create a 12-place table
  t = CircularList([None] * 12)
  
  # place IAN at position 0 and ROLAND in position 6
  t[0] = "IAN"
  t[6] = "ROLAND"
  
  # the remaining people
  people = { "ALICE", "ARNOLD", "CARLA", "CELIA", "CLARA", "INA", "RONA", "RONALD", "ARI", "IRA" }
  
  # find possible 12 place tables
  for t12 in place(t, people):
    # now remove ARI and IRA to give a 10 place table
    t = CircularList(diff(t12, {"ARI", "IRA"}))
    # check ROLAND is no longer opposite IAN
    if t[5] == "ROLAND": continue
    # check t is a valid table
    if not all(n in valid([n], {t[i + 5], t[i - 1], t[i + 1], t[i - 2], t[i + 2]}) for (i, n) in enumerate(t)): continue
    
    # output solution
    printf("{t12} <- {t10}", t12=join(t12, sep=" ", enc="[]"), t10=join(t, sep=" ", enc="[]"))
    for x in ["ALICE", "CELIA"]:
      opp = t[t.index(x) + 5]
      printf("-> ({x} <-> {opp})")
    printf()
  

  Solution: Rona ended up opposite Alice. Ira ended up opposite Celia.

  Here is a possible layout of the 12 seats (going round the table, listing opposites):

  IAN = 0; ROLAND = 6
  ARI = 1; CLARA = 7
  RONALD = 2; INA = 8
  CARLA = 3; ARNOLD = 9
  ALICE = 4; RONA = 10
  IRA = 5; CELIA = 11

  CARLA and CLARA can swap positions to give a second layout.

  And the tables can be mirrored (go round the table anti-clockwise, instead of clockwise) to give further viable layouts.

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