"""
A set partitioning model of a wedding seating problem

Authors: Stuart Mitchell 2009
"""

import pulp

max_tables = 5
max_table_size = 4
guests = 'A B C D E F G I J K L M N O P Q R'.split()

def happiness(table):
    """
    Find the happiness of the table
    - by calculating the maximum distance between the letters
    """
    return abs(ord(table[0]) - ord(table[-1]))
                
#create list of all possible tables
possible_tables = [tuple(c) for c in pulp.allcombinations(guests, 
                                        max_table_size)]

#create a binary variable to state that a table setting is used
x = pulp.LpVariable.dicts('table', possible_tables, 
                            lowBound = 0,
                            upBound = 1,
                            cat = pulp.LpInteger)

seating_model = pulp.LpProblem("Wedding Seating Model", pulp.LpMinimize)

seating_model += sum([happiness(table) * x[table] for table in possible_tables])

#specify the maximum number of tables
seating_model += sum([x[table] for table in possible_tables]) <= max_tables, \
                            "Maximum_number_of_tables"

#A guest must seated at one and only one table
for guest in guests:
    seating_model += sum([x[table] for table in possible_tables
                                if guest in table]) == 1, "Must_seat_%s"%guest

seating_model.solve()

print("The choosen tables are out of a total of %s:"%len(possible_tables))
for table in possible_tables:
    if x[table].value() == 1.0:
        print(table)