Select teams in competition with random drawing and non-trivial matching

select_teams.py

# A script to find plays in a group of N people where in one game k players plays
# To be executed in python 3
# Written by Luca Naterop and Philippe frei
# January, 2019

from itertools import combinations 
import numpy as np
from random import randint
from operator import itemgetter

def fact(n, total=1):
    while True:
        if n == 1:
            return total
        n, total = n - 1, total * n

def get_all_combinations(N,k):
  combs = combinations(np.linspace(1,N,N), k)
  amount_combinations = fact(N)/(fact(k)*fact(N-k))
  M = np.zeros([amount_combinations,k])
  i = 0
  for combination in combs:
    combination_as_array = np.asarray(combination)
    M[i,:] = combination_as_array
    i = i+1
  return M

def games_match(game1,game2):
  amount_shared = 0
  for i in range(0,len(game1)):
    for j in range(i,len(game2)):
      if game1[i] == game2[j]:
        amount_shared = amount_shared + 1
  if amount_shared >= 2:
    return True
  return False

def want_this_game(M,game,amount_for_each):
  # returns true if we want that new game otherwise false

  # kommt spieler mit am wenigsten vor im kandidat?
  index_of_player_with_least = min(enumerate(amount_for_each), key=itemgetter(1))[0]
  player_with_least = index_of_player_with_least + 1
  if not (player_with_least in game):
    return False

  for i in range(0,len(M)):
    if games_match(game, M[i]):
      return False
  return True

def amount_games_for_each_player(games,N):
  want = False
  amount_games = np.zeros([N+1])
  for game in games:
    for player in game:
      amount_games[int(player-1)] += 1
  return amount_games

N = 8
k = 3
tries = 1000
j = 0

M = get_all_combinations(N,k)
games = np.zeros([10,k])

for i in range(0,tries):
  random_index = randint(0,len(M)-1)
  next_candidate = M[random_index,:]
  amount_for_each = amount_games_for_each_player(games,N)
  if(want_this_game(games,next_candidate,amount_for_each)):
    games[j,:] = next_candidate
    j += 1

  amount_for_each = amount_games_for_each_player(games,N)
  print(games)
  print(amount_for_each)
  print('amount games', j)
  print('----------------')