[Tutor] Creating lists with 3 (later4) items occuring only once

[Martin A. Brown]

Marcus,

I have more questions for you, as well as a possible solution 
(though it's a bit more verbose than I would have liked to offer).

Question:

   Problem A:  Are you looking to identify the complete set of
   possible options for constructing the triples of pairs?

   Problem B: Are you looking only to construct one set that
   satisfies the problem? [see my lousy solution]

You may observe that the question I ask is quite similar to the 
question asked by Francesco [0].

If you are asking about the complete set of possible options 
(Problem A), then I submit to you that you are asking a mathematical 
question, not a Python question.  If that's the case, perhaps you 
should look further into the Steiner system and/or ask again on the 
list.

If you are asking about finding an individual solution satisfying 
the constraints, I submit to you that either my approach or 
Francesco's approach could work for you.  If that's the case, then 
using random.sample may offer you some help.  See my sample, 
below--it should work on Python 2.x or Python 3.x.

Comments:

   * There are rules in your system about when a player can play
     again.  The rules were not fully clear to me, so I allowed
     players to be selecteda second time, if there were no more
     players who had not already been chosen.

   * This program produces only one possible scenario for 7
     rounds of 3 distinct, simultaneously played 2-player games.
     No player can play twice in the same round.  (Simple arithmetic
     determines the minimum number of players.)

If your question is Problem A, then I wonder if you know anybody who 
knows combinatorics?  I do not.

-Martin

  [0] https://mail.python.org/pipermail/tutor/2015-September/106820.html


#! /usr/bin/python

from __future__ import print_function

import sys
import string
import random
import logging

logging.basicConfig(stream=sys.stderr, level=logging.INFO)
logger = logging.getLogger()


class NotEnoughPlayers(Exception):
     pass


def choose_game_participants(players, pcount=2):
     '''returns a tuple of players for a single game
     '''
     if len(players) < pcount:
         raise NotEnoughPlayers("not enough players, need %d, have only %d: %r" %
                                (pcount, len(players), players))
     game = tuple(sorted(random.sample(players, pcount)))
     return game


def choose_match_games(players, pcount=2, gcount=3):
     '''returns a list of games where no player is duplicated
     '''
     mcount = pcount * gcount
     if len(players) < mcount:
         raise NotEnoughPlayers("not enough players, need %d, have only %d: %r" %
                                (mcount, len(players), players))
     eligible_players = random.sample(players, mcount)
     match = list()
     while eligible_players:
         m = choose_game_participants(eligible_players, pcount)
         for x in m:
             eligible_players.remove(x)
         match.append(m)
     match.sort()  # optional
     return match


def generate_rounds(players, pcount, gcount, rcount):
     games = set()
     matches = list()
     mcount = pcount * gcount
     eligible_players = list(players)
     if mcount > len(eligible_players):
         raise NotEnoughPlayers("not enough players (%d) to guarantee %d %d-player games per match" %
                                (len(eligible_players), gcount, pcount))
     r = 1
     while r <= rcount:
         try:
             proposed_match = choose_match_games(eligible_players, pcount, gcount)
         except NotEnoughPlayers:
             logger.info("adding %d additional players in round %d to meet minimum pool requirements",
                         mcount, r)
             how_many = mcount - len(eligible_players)
             eligible_players.extend(random.sample(players, how_many))
             continue
         already_played = games.intersection(set(proposed_match))
         if already_played:
             logger.info("discarding %d %r because %r have already played",
                         r, proposed_match, list(already_played))
             continue
         else:
             games.update(proposed_match)
             matches.append(proposed_match)
             logger.info('Proposed match %r', proposed_match)
             for game in proposed_match:
                 for player in game:
                     eligible_players.remove(player)
         r = r + 1
     return matches


def log_match_info(matches, detail=False):
     for mnum, match in enumerate(matches, 1):
         logger.info("match summary %d: %r", mnum, match)
         for gnum, game in enumerate(match, 1):
             if not detail:
                 continue
             logger.info("match detail %d, game %d: players %r",
                         mnum, gnum, game)


def log_match_summary(matches):
     log_match_info(matches, detail=False)


def log_match_detail(matches):
     log_match_info(matches, detail=True)


if __name__ == '__main__':
     players = list(string.ascii_uppercase)
     random.shuffle(players)
     # players = set('ABCDEFGHIJ')
     pcount = 2                              # players per game
     gcount = 3                              # games per match
     rcount = 7                              # rounds (of matches)
     matches = generate_rounds(players, pcount, gcount, rcount)
     log_match_detail(matches)

# -- end of file


-- 
Martin A. Brown
http://linux-ip.net/