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"""

Matching games.

This module implements a class for matching games (stable marriage problems)

[DI1989]_. At present the extended Gale-Shapley algorithm is implemented

which can be used to obtain stable matchings.

AUTHORS:

- James Campbell and Vince Knight 06-2014: Original version

"""

#*****************************************************************************

# This program is free software: you can redistribute it and/or modify

# it under the terms of the GNU General Public License as published by

# the Free Software Foundation, either version 3 of the License, or

# (at your option) any later version.

# http://www.gnu.org/licenses/

#*****************************************************************************

from sage.structure.sage_object import SageObject

from sage.rings.all import ZZ

from copy import deepcopy

from sage.graphs.bipartite_graph import BipartiteGraph

class MatchingGame(SageObject):

r"""

A matching game.

A matching game (also called a stable matching problem) models a situation

in a population of `N` suitors and `N` reviewers. Suitors and reviewers

rank their preferences and attempt to find a match.

Formally, a matching game of size `N` is defined by two disjoint sets `S`

and `R` of size `N`. Associated to each element of `S` and `R` is a

preference list:

.. MATH::

f : S \to R^N

\text{ and }

g : R \to S^N.

Here is an example of matching game on 4 players:

.. MATH::

S = \{J, K, L, M\}, \\

R = \{A, B, C, D\}.

With preference functions:

.. MATH::

f(s) = \begin{cases}

(A, D, C, B) & \text{ if } s=J,\\

(A, B, C, D) & \text{ if } s=K,\\

(B, D, C, A) & \text{ if } s=L,\\

(C, A, B, D) & \text{ if } s=M,\\

\end{cases}

g(s) = \begin{cases}

(L, J, K, M) & \text{ if } s=A,\\

(J, M, L, K) & \text{ if } s=B,\\

(K, M, L, J) & \text{ if } s=C,\\

(M, K, J, L) & \text{ if } s=D.\\

\end{cases}

INPUT:

Two potential inputs are accepted (see below to see the effect of each):

- ``reviewer/suitors_preferences`` -- a dictionary containing the

preferences of all players:

* key - each reviewer/suitors

* value - a tuple of suitors/reviewers

OR:

- ``integer`` -- an integer simply representing the number of reviewers

and suitors.

To implement the above game in Sage::

sage: suitr_pref = {'J': ('A', 'D', 'C', 'B'),

....: 'K': ('A', 'B', 'C', 'D'),

....: 'L': ('B', 'D', 'C', 'A'),

....: 'M': ('C', 'A', 'B', 'D')}

sage: reviewr_pref = {'A': ('L', 'J', 'K', 'M'),

....: 'B': ('J', 'M', 'L', 'K'),

....: 'C': ('K', 'M', 'L', 'J'),

....: 'D': ('M', 'K', 'J', 'L')}

sage: m = MatchingGame([suitr_pref, reviewr_pref])

sage: m

A matching game with 4 suitors and 4 reviewers

sage: m.suitors()

('K', 'J', 'M', 'L')

sage: m.reviewers()

('A', 'C', 'B', 'D')

A matching `M` is any bijection between `S` and `R`. If `s \in S` and

`r \in R` are matched by `M` we denote:

.. MATH::

M(s) = r.

On any given matching game, one intends to find a matching that is stable.

In other words, so that no one individual has an incentive to break their

current match.

Formally, a stable matching is a matching that has no blocking pairs.

A blocking pair is any pair `(s, r)` such that `M(s) \neq r` but `s`

prefers `r` to `M(r)` and `r` prefers `s` to `M^{-1}(r)`.

To obtain the stable matching in Sage we use the ``solve`` method which

uses the extended Gale-Shapley algorithm [DI1989]_::

sage: m.solve()

{'J': 'A', 'K': 'C', 'L': 'D', 'M': 'B'}

Matchings have a natural representations as bipartite graphs::

sage: plot(m)

Graphics object consisting of 13 graphics primitives

The above plots the bipartite graph associated with the matching.

This plot can be accessed directly::

sage: graph = m.bipartite_graph()

sage: graph

Bipartite graph on 8 vertices

It is possible to initiate a matching game without having to name each

suitor and reviewer::

sage: n = 8

sage: big_game = MatchingGame(n)

sage: big_game.suitors()

(1, 2, 3, 4, 5, 6, 7, 8)

sage: big_game.reviewers()

(-1, -2, -3, -4, -5, -6, -7, -8)

If we attempt to obtain the stable matching for the above game,

without defining the preference function we obtain an error::

sage: big_game.solve()

Traceback (most recent call last):

...

ValueError: suitor preferences are not complete

To continue we have to populate the preference dictionary. Here

is one example where the preferences are simply the corresponding

element of the permutation group::

sage: from itertools import permutations

sage: suitr_preferences = list(permutations([-i-1 for i in range(n)]))

sage: revr_preferences = list(permutations([i+1 for i in range(n)]))

sage: for player in range(n):

....: big_game.suitors()[player].pref = suitr_preferences[player]

....: big_game.reviewers()[player].pref = revr_preferences[-player]

sage: big_game.solve()

{1: -1, 2: -8, 3: -6, 4: -7, 5: -5, 6: -4, 7: -3, 8: -2}

Note that we can also combine the two ways of creating a game. For example

here is an initial matching game::

sage: suitrs = {'Romeo': ('Juliet', 'Rosaline'),

....: 'Mercutio': ('Juliet', 'Rosaline')}

sage: revwrs = {'Juliet': ('Romeo', 'Mercutio'),

....: 'Rosaline': ('Mercutio', 'Romeo')}

sage: g = MatchingGame(suitrs, revwrs)

Let us assume that all of a sudden a new pair of suitors and reviewers is

added but their names are not known::

sage: g.add_reviewer()

sage: g.add_suitor()

sage: g.reviewers()

('Rosaline', 'Juliet', -3)

sage: g.suitors()

('Mercutio', 'Romeo', 3)

Note that when adding a reviewer or a suitor all preferences are wiped::

sage: [s.pref for s in g.suitors()]

[[], [], []]

sage: [r.pref for r in g.reviewers()]

[[], [], []]

If we now try to solve the game we will get an error as we have not

specified the preferences which will need to be updated::

sage: g.solve()

Traceback (most recent call last):

...

ValueError: suitor preferences are not complete

Here we update the preferences so that the new reviewers and suitors

don't affect things too much (they prefer each other and are the least

preferred of the others)::

sage: g.suitors()[0].pref = suitrs['Mercutio'] + (-3,)

sage: g.suitors()[1].pref = suitrs['Romeo'] + (-3,)

sage: g.suitors()[2].pref = (-3, 'Juliet', 'Rosaline')

sage: g.reviewers()[0].pref = revwrs['Rosaline'] + (3,)

sage: g.reviewers()[1].pref = revwrs['Juliet'] + (3,)

sage: g.reviewers()[2].pref = (3, 'Romeo', 'Mercutio')

Now the game can be solved::

sage: D = g.solve()

sage: D['Mercutio']

'Rosaline'

sage: D['Romeo']

'Juliet'

sage: D[3]

-3

Note that the above could be equivalently (and more simply) carried out

by simply updated the original preference dictionaries::

sage: for key in suitrs:

....: suitrs[key] = suitrs[key] + (-3,)

sage: for key in revwrs:

....: revwrs[key] = revwrs[key] + (3,)

sage: suitrs[3] = (-3, 'Juliet', 'Rosaline')

sage: revwrs[-3] = (3, 'Romeo', 'Mercutio')

sage: g = MatchingGame(suitrs, revwrs)

sage: D = g.solve()

sage: D['Mercutio']

'Rosaline'

sage: D['Romeo']

'Juliet'

sage: D[3]

-3

It can be shown that the Gale-Shapley algorithm will return the stable

matching that is optimal from the point of view of the suitors and is in

fact the worst possible matching from the point of view of the reviewers.

To quickly obtain the matching that is optimal for the reviewers we

use the ``solve`` method with the ``invert=True`` option::

sage: left_dict = {'a': ('A', 'B', 'C'),

....: 'b': ('B', 'C', 'A'),

....: 'c': ('B', 'A', 'C')}

sage: right_dict = {'A': ('b', 'c', 'a'),

....: 'B': ('a', 'c', 'b'),

....: 'C': ('a', 'b', 'c')}

sage: quick_game = MatchingGame([left_dict, right_dict])

sage: quick_game.solve()

{'a': 'A', 'b': 'C', 'c': 'B'}

sage: quick_game.solve(invert=True)

{'A': 'c', 'B': 'a', 'C': 'b'}

EXAMPLES:

8 player letter game::

sage: suitr_pref = {'J': ('A', 'D', 'C', 'B'),

....: 'K': ('A', 'B', 'C', 'D'),

....: 'L': ('B', 'D', 'C', 'A'),

....: 'M': ('C', 'A', 'B', 'D')}

sage: reviewr_pref = {'A': ('L', 'J', 'K', 'M'),

....: 'B': ('J', 'M', 'L', 'K'),

....: 'C': ('K', 'M', 'L', 'J'),

....: 'D': ('M', 'K', 'J', 'L')}

sage: m = MatchingGame([suitr_pref, reviewr_pref])

sage: m._suitors

['K', 'J', 'M', 'L']

sage: m._reviewers

['A', 'C', 'B', 'D']

Also works for numbers::

sage: suit = {0: (3, 4),

....: 1: (3, 4)}

sage: revr = {3: (0, 1),

....: 4: (1, 0)}

sage: g = MatchingGame([suit, revr])

Can create a game from an integer. This gives default set of preference

functions::

sage: g = MatchingGame(3)

sage: g

A matching game with 3 suitors and 3 reviewers

We have an empty set of preferences for a default named set of

preferences::

sage: for s in g.suitors():

....: s, s.pref

(1, [])

(2, [])

(3, [])

sage: for r in g.reviewers():

....: r, r.pref

(-1, [])

(-2, [])

(-3, [])

Before trying to solve such a game the algorithm will check if it is

complete or not::

sage: g.solve()

Traceback (most recent call last):

...

ValueError: suitor preferences are not complete

To be able to obtain the stable matching we must input the preferences::

sage: for s in g.suitors():

....: s.pref = (-1, -2, -3)

sage: for r in g.reviewers():

....: r.pref = (1, 2, 3)

sage: g.solve()

{1: -1, 2: -2, 3: -3}

"""

def __init__(self, generator, revr=None):

r"""

Initialize a matching game and check the inputs.

TESTS::

sage: suit = {0: (3, 4), 1: (3, 4)}

sage: revr = {3: (0, 1), 4: (1, 0)}

sage: g = MatchingGame([suit, revr])

sage: TestSuite(g).run()

sage: g = MatchingGame(3)

sage: TestSuite(g).run()

sage: g2 = MatchingGame(QQ(3))

sage: g == g2

True

The above shows that the input can be either two dictionaries

or an integer::

sage: g = MatchingGame(suit, 3)

Traceback (most recent call last):

...

TypeError: generator must be an integer or a pair of 2 dictionaries

sage: g = MatchingGame(matrix(2, [1, 2, 3, 4]))

Traceback (most recent call last):

...

TypeError: generator must be an integer or a pair of 2 dictionaries

sage: g = MatchingGame('1,2,3', 'A,B,C')

Traceback (most recent call last):

...

TypeError: generator must be an integer or a pair of 2 dictionaries

"""

self._suitors = []

self._reviewers = []

if revr is not None:

generator = [generator, revr]

if generator in ZZ:

for i in range(generator):

self.add_suitor()

self.add_reviewer()

elif isinstance(generator[0], dict) and isinstance(generator[1], dict):

for i in generator[0]:

self.add_suitor(i)

for k in generator[1]:

self.add_reviewer(k)

for i in self._suitors:

i.pref = generator[0][i._name]

for k in self._reviewers:

k.pref = generator[1][k._name]

else:

raise TypeError("generator must be an integer or a pair of 2 dictionaries")

def _repr_(self):

r"""

Return a basic representation of the game stating how many

players are in the game.

EXAMPLES:

Matching game with 2 reviewers and 2 suitors::

sage: M = MatchingGame(2)

sage: M

A matching game with 2 suitors and 2 reviewers

"""

txt = 'A matching game with {} suitors and {} reviewers'

return txt.format(len(self._suitors), len(self._reviewers))

def _latex_(self):

r"""

Create the LaTeX representation of the dictionaries for suitors

and reviewers.

EXAMPLES::

sage: suit = {0: (3, 4), 1: (3, 4)}

sage: revr = {3: (0, 1), 4: (1, 0)}

sage: g = MatchingGame([suit, revr])

sage: latex(g)

\text{Suitors:}

\begin{aligned}

\\ 0 & \to (3, 4)

\\ 1 & \to (3, 4)

\end{aligned}

\text{Reviewers:}

\begin{aligned}

\\ 3 & \to (0, 1)

\\ 4 & \to (1, 0)

\end{aligned}

"""

output = "\\text{Suitors:}\n\\begin{aligned}"

for suitor in self._suitors:

output += "\n\\\\ %s & \\to %s" % (suitor, suitor.pref)

output += "\n\\end{aligned}\n\\text{Reviewers:}\n\\begin{aligned}"

for reviewer in self._reviewers:

output += "\n\\\\ %s & \\to %s" % (reviewer, reviewer.pref)

return output + "\n\\end{aligned}"

def __eq__(self, other):

"""

Check equality.

sage: suit = {0: (3, 4), 1: (3, 4)}

sage: revr = {3: (0, 1), 4: (1, 0)}

sage: g = MatchingGame([suit, revr])

sage: g2 = MatchingGame([suit, revr])

sage: g == g2

True

Here the two sets of suitors have different preferences::

sage: suit1 = {0: (3, 4), 1: (3, 4)}

sage: revr1 = {3: (1, 0), 4: (1, 0)}

sage: g1 = MatchingGame([suit1, revr1])

sage: suit2 = {0: (4, 3), 1: (3, 4)}

sage: revr2 = {3: (1, 0), 4: (1, 0)}

sage: g2 = MatchingGame([suit2, revr2])

sage: g == g2

False

Here the two sets of reviewers have different preferences::

sage: suit1 = {0: (3, 4), 1: (3, 4)}

sage: revr1 = {3: (0, 1), 4: (1, 0)}

sage: g1 = MatchingGame([suit1, revr1])

sage: suit2 = {0: (3, 4), 1: (3, 4)}

sage: revr2 = {3: (1, 0), 4: (0, 1)}

sage: g2 = MatchingGame([suit2, revr2])

sage: g == g2

False

Note that if two games are created with players ordered differently

they can still be equal::

sage: g1 = MatchingGame(1)

sage: g1.add_reviewer(-2)

sage: g1.add_reviewer(-3)

sage: g1.add_suitor(3)

sage: g1.add_suitor(2)

sage: g1.reviewers()

(-1, -2, -3)

sage: g1.suitors()

(1, 3, 2)

sage: g2 = MatchingGame(1)

sage: g2.add_reviewer(-2)

sage: g2.add_reviewer(-3)

sage: g2.add_suitor(2)

sage: g2.add_suitor(3)

sage: g2.reviewers()

(-1, -2, -3)

sage: g2.suitors()

(1, 2, 3)

sage: g1 == g2

True

"""

return (isinstance(other, MatchingGame)

and set(self._suitors) == set(other._suitors)

and set(self._reviewers) == set(other._reviewers)

and all(r1.pref == r2.pref for r1, r2 in

zip(set(self._reviewers), set(other._reviewers)))

and all(s1.pref == s2.pref for s1, s2 in

zip(set(self._suitors), set(other._suitors))))

def __hash__(self):

"""

Raise an error because this is mutable.

EXAMPLES::

sage: hash(MatchingGame(3))

Traceback (most recent call last):

...

TypeError: unhashable because matching games are mutable

"""

raise TypeError("unhashable because matching games are mutable")

def plot(self):

r"""

Create the plot representing the stable matching for the game.

Note that the game must be solved for this to work.

EXAMPLES:

An error is returned if the game is not solved::

sage: suit = {0: (3, 4),

....: 1: (3, 4)}

sage: revr = {3: (0, 1),

....: 4: (1, 0)}

sage: g = MatchingGame([suit, revr])

sage: plot(g)

Traceback (most recent call last):

...

ValueError: game has not been solved yet

sage: g.solve()

{0: 3, 1: 4}

sage: plot(g)

Graphics object consisting of 7 graphics primitives

"""

pl = self.bipartite_graph()

return pl.plot()

def bipartite_graph(self):

r"""

Construct a ``BipartiteGraph`` Object of the game.

This method is similar to the plot method.

Note that the game must be solved for this to work.

EXAMPLES:

An error is returned if the game is not solved::

sage: suit = {0: (3, 4),

....: 1: (3, 4)}

sage: revr = {3: (0, 1),

....: 4: (1, 0)}

sage: g = MatchingGame([suit, revr])

sage: g.bipartite_graph()

Traceback (most recent call last):

...

ValueError: game has not been solved yet

sage: g.solve()

{0: 3, 1: 4}

sage: g.bipartite_graph()

Bipartite graph on 4 vertices

"""

self._is_solved()

graph = BipartiteGraph(self._sol_dict)

return graph

def _is_solved(self):

r"""

Raise an error if the game has not been solved yet.

EXAMPLES::

sage: suit = {0: (3, 4),

....: 1: (3, 4)}

sage: revr = {3: (0, 1),

....: 4: (1, 0)}

sage: g = MatchingGame([suit, revr])

sage: g._is_solved()

Traceback (most recent call last):

...

ValueError: game has not been solved yet

sage: g.solve()

{0: 3, 1: 4}

sage: g._is_solved()

"""

suitor_check = all(s.partner for s in self._suitors)

reviewer_check = all(r.partner for r in self._reviewers)

if not suitor_check or not reviewer_check:

raise ValueError("game has not been solved yet")

def _is_complete(self):

r"""

Raise an error if all players do not have acceptable preferences.

EXAMPLES:

Not enough reviewers::

sage: suit = {0: (3, 4),

....: 1: (3, 4)}

sage: revr = {3: (0, 1)}

sage: g = MatchingGame([suit, revr])

sage: g._is_complete()

Traceback (most recent call last):

...

ValueError: must have the same number of reviewers as suitors

Not enough suitors::

sage: suit = {0: (3, 4)}

sage: revr = {1: (0, 2),

....: 3: (0, 1)}

sage: g = MatchingGame([suit, revr])

sage: g._is_complete()

Traceback (most recent call last):

...

ValueError: must have the same number of reviewers as suitors

Suitors preferences are incomplete::

sage: suit = {0: (3, 8),

....: 1: (0, 0)}

sage: revr = {3: (0, 1),

....: 4: (1, 0)}

sage: g = MatchingGame([suit, revr])

sage: g._is_complete()

Traceback (most recent call last):

...

ValueError: suitor preferences are not complete

Reviewer preferences are incomplete::

sage: suit = {0: (3, 4),

....: 1: (3, 4)}

sage: revr = {3: (0, 2, 1),

....: 4: (1, 0)}

sage: g = MatchingGame([suit, revr])

sage: g._is_complete()

Traceback (most recent call last):

...

ValueError: reviewer preferences are not complete

Suitor preferences have repetitions::

sage: suit = {0: (3, 4),

....: 1: (3, 4)}

sage: revr = {3: (0, 0, 1),

....: 4: (1, 0)}

sage: g = MatchingGame([suit, revr])

sage: g._is_complete()

Traceback (most recent call last):

...

ValueError: reviewer preferences contain repetitions

Reviewer preferences have repetitions::

sage: suit = {0: (3, 4, 3),

....: 1: (3, 4)}

sage: revr = {3: (0, 1),

....: 4: (1, 0)}

sage: g = MatchingGame([suit, revr])

sage: g._is_complete()

Traceback (most recent call last):

...

ValueError: suitor preferences contain repetitions

"""

if len(self._suitors) != len(self._reviewers):

raise ValueError("must have the same number of reviewers as suitors")

for suitor in self._suitors:

if set(suitor.pref) != set(self._reviewers):

raise ValueError("suitor preferences are not complete")

for reviewer in self._reviewers:

if set(reviewer.pref) != set(self._suitors):

raise ValueError("reviewer preferences are not complete")

for reviewer in self._reviewers:

if len(set(reviewer.pref)) < len(reviewer.pref):

raise ValueError("reviewer preferences contain repetitions")

for suitor in self._suitors:

if len(set(suitor.pref)) < len(suitor.pref):

raise ValueError("suitor preferences contain repetitions")

def add_suitor(self, name=None):

r"""

Add a suitor to the game.

INPUT:

- ``name`` -- can be a string or a number; if left blank will

automatically generate an integer

EXAMPLES:

Creating a two player game::

sage: g = MatchingGame(2)

sage: g.suitors()

(1, 2)

Adding a suitor without specifying a name::

sage: g.add_suitor()

sage: g.suitors()

(1, 2, 3)

Adding a suitor while specifying a name::

sage: g.add_suitor('D')

sage: g.suitors()

(1, 2, 3, 'D')

Note that now our game is no longer complete::

sage: g._is_complete()

Traceback (most recent call last):

...

ValueError: must have the same number of reviewers as suitors

Note that an error is raised if one tries to add a suitor

with a name that already exists::

sage: g.add_suitor('D')

Traceback (most recent call last):

...

ValueError: a suitor with name "D" already exists

If we add a suitor without passing a name then the name

of the suitor will not use one that is already chosen::

sage: suit = {0: (-1, -2),

....: 2: (-2, -1)}

sage: revr = {-1: (0, 1),

....: -2: (1, 0)}

sage: g = MatchingGame([suit, revr])

sage: g.suitors()

(0, 2)

sage: g.add_suitor()

sage: g.suitors()

(0, 2, 3)

"""

if name is None:

name = len(self._suitors) + 1

while name in self._suitors:

name += 1

if any(s._name == name for s in self._suitors):

raise ValueError('a suitor with name "{}" already exists'.format(name))

new_suitor = Player(name)

self._suitors.append(new_suitor)

for r in self._reviewers:

r.pref = []

def add_reviewer(self, name=None):

r"""

Add a reviewer to the game.

INPUT:

- ``name`` -- can be a string or number; if left blank will

automatically generate an integer

EXAMPLES:

Creating a two player game::

sage: g = MatchingGame(2)

sage: g.reviewers()

(-1, -2)

Adding a suitor without specifying a name::

sage: g.add_reviewer()

sage: g.reviewers()

(-1, -2, -3)

Adding a suitor while specifying a name::

sage: g.add_reviewer(10)

sage: g.reviewers()

(-1, -2, -3, 10)

Note that now our game is no longer complete::

sage: g._is_complete()

Traceback (most recent call last):

...

ValueError: must have the same number of reviewers as suitors

Note that an error is raised if one tries to add a reviewer

with a name that already exists::

sage: g.add_reviewer(10)

Traceback (most recent call last):

...

ValueError: a reviewer with name "10" already exists

If we add a reviewer without passing a name then the name

of the reviewer will not use one that is already chosen::

sage: suit = {0: (-1, -3),

....: 1: (-3, -1)}

sage: revr = {-1: (0, 1),

....: -3: (1, 0)}

sage: g = MatchingGame([suit, revr])

sage: g.reviewers()

(-3, -1)

sage: g.add_reviewer()

sage: g.reviewers()

(-3, -1, -4)

"""

if name is None:

name = -len(self._reviewers) - 1

while name in self._reviewers:

name -= 1

if any(r._name == name for r in self._reviewers):

raise ValueError('a reviewer with name "{}" already exists'.format(name))

new_reviewer = Player(name)

self._reviewers.append(new_reviewer)

for s in self._suitors:

s.pref = []

def suitors(self):

"""

Return the suitors of ``self``.

EXAMPLES::

sage: g = MatchingGame(2)

sage: g.suitors()

(1, 2)

"""

return tuple(self._suitors)

def reviewers(self):

"""

Return the reviewers of ``self``.

EXAMPLES::

sage: g = MatchingGame(2)

sage: g.reviewers()

(-1, -2)

"""

return tuple(self._reviewers)

def solve(self, invert=False):

r"""

Compute a stable matching for the game using the Gale-Shapley

algorithm.

EXAMPLES::

sage: suitr_pref = {'J': ('A', 'D', 'C', 'B'),

....: 'K': ('A', 'B', 'C', 'D'),

....: 'L': ('B', 'C', 'D', 'A'),

....: 'M': ('C', 'A', 'B', 'D')}

sage: reviewr_pref = {'A': ('L', 'J', 'K', 'M'),

....: 'B': ('J', 'M', 'L', 'K'),

....: 'C': ('M', 'K', 'L', 'J'),

....: 'D': ('M', 'K', 'J', 'L')}

sage: m = MatchingGame([suitr_pref, reviewr_pref])

sage: m.solve()

{'J': 'A', 'K': 'D', 'L': 'B', 'M': 'C'}

sage: suitr_pref = {'J': ('A', 'D', 'C', 'B'),

....: 'K': ('A', 'B', 'C', 'D'),

....: 'L': ('B', 'C', 'D', 'A'),

....: 'M': ('C', 'A', 'B', 'D')}

sage: reviewr_pref = {'A': ('L', 'J', 'K', 'M'),

....: 'B': ('J', 'M', 'L', 'K'),

....: 'C': ('M', 'K', 'L', 'J'),

....: 'D': ('M', 'K', 'J', 'L')}

sage: m = MatchingGame([suitr_pref, reviewr_pref])

sage: m.solve(invert=True)

{'A': 'L', 'B': 'J', 'C': 'M', 'D': 'K'}

sage: suitr_pref = {1: (-1,)}

sage: reviewr_pref = {-1: (1,)}

sage: m = MatchingGame([suitr_pref, reviewr_pref])

sage: m.solve()

{1: -1}

sage: suitr_pref = {}

sage: reviewr_pref = {}

sage: m = MatchingGame([suitr_pref, reviewr_pref])

sage: m.solve()

{}

TESTS:

This also works for players who are both a suitor and reviewer::

sage: suit = {0: (3,4,2), 1: (3,4,2), 2: (2,3,4)}

sage: revr = {2: (2,0,1), 3: (0,1,2), 4: (1,0,2)}

sage: g = MatchingGame(suit, revr)

sage: g.solve()

{0: 3, 1: 4, 2: 2}

"""

self._is_complete()

for s in self._suitors:

s.partner = None

for r in self._reviewers:

r.partner = None

if invert:

reviewers = deepcopy(self._suitors)

suitors = deepcopy(self._reviewers)

else:

suitors = deepcopy(self._suitors)

reviewers = deepcopy(self._reviewers)

while any(s.partner is None for s in suitors):

s = None

for x in suitors:

if x.partner is None:

s = x

break

r = next((x for x in reviewers if x == s.pref[0]), None)

if r.partner is None:

r.partner = s

s.partner = r

elif r.pref.index(s._name) < r.pref.index(r.partner._name):

r.partner.partner = None

r.partner = s

s.partner = r

else:

s.pref = s.pref[1:]

if invert:

suitors, reviewers = reviewers, suitors

for i, j in zip(self._suitors, suitors):

i.partner = j.partner

for i, j in zip(self._reviewers, reviewers):

i.partner = j.partner

self._sol_dict = {}

for s in self._suitors:

self._sol_dict[s] = [s.partner]

for r in self._reviewers:

self._sol_dict[r] = [r.partner]

if invert:

return {key: self._sol_dict[key][0] for key in self._reviewers}

return {key: self._sol_dict[key][0] for key in self._suitors}

class Player(object):

r"""

A class to act as a data holder for the players used of the

matching games.

These instances are used when initiating players and to keep track of

whether or not partners have a preference.

"""

def __init__(self, name):

r"""

TESTS::

sage: from sage.game_theory.matching_game import Player

sage: p = Player(10)

sage: p

sage: p.pref

[]

sage: p.partner is None

True

"""

self._name = name

self.pref = []

self.partner = None

def __hash__(self):

r"""

TESTS::

sage: from sage.game_theory.matching_game import Player

sage: p = Player(10)

sage: d = {p : (1, 2, 3)}

sage: d

{10: (1, 2, 3)}

"""

return hash(self._name)

def __repr__(self):

r"""

TESTS::

sage: from sage.game_theory.matching_game import Player

sage: p = Player(10)

sage: p

sage: p = Player('Karl')

sage: p

'Karl'

"""

return repr(self._name)

def __eq__(self, other):

r"""

Tests equality of two players. This only checks the name of the player

and not their preferences.

TESTS::

sage: from sage.game_theory.matching_game import Player

sage: p = Player(10)

sage: q = Player('Karl')

sage: p == q

False

sage: from sage.game_theory.matching_game import Player

sage: p = Player(10)

sage: q = Player(10)

sage: p == q

True

sage: from sage.game_theory.matching_game import Player

sage: p = Player(10)

sage: q = Player(10)

sage: p.pref = (1, 2)

sage: p.pref = (2, 1)

sage: p == q

True

"""

if isinstance(other, Player):

return self._name == other._name

return self._name == other

def __lt__(self, other):

"""

Tests less than inequality of two players. Allows for players to be

sorted on their names.

TESTS::

sage: from sage.game_theory.matching_game import Player

sage: p = Player('A')

sage: q = Player('B')

sage: p < q

True

sage: q < p

False

sage: p = Player(0)

sage: q = Player(1)

sage: p < q

True

sage: q < p

False

"""

if isinstance(other, Player):

return self._name < other._name

return self._name < other

def __gt__(self, other):

"""

Tests greater than inequality of two players. Allows for players to be

sorted on their names.

TESTS::

sage: from sage.game_theory.matching_game import Player

sage: p = Player('A')

sage: q = Player('B')

sage: p > q

False

sage: q > p

True

sage: p = Player(0)

sage: q = Player(1)

sage: p > q

False

sage: q > p

True

"""

if isinstance(other, Player):

return self._name > other._name

return self._name > other

def __ge__(self, other):

"""

Tests greater than or equal inequality of two players. Allows for

players to be sorted on their names.

TESTS::

sage: from sage.game_theory.matching_game import Player

sage: p = Player('A')

sage: q = Player('B')

sage: p >= q

False

sage: q >= p

True

sage: p = Player(0)

sage: q = Player(1)

sage: p >= q

False

sage: q >= p

True

sage: p = Player(0)

sage: q = Player(0)

sage: p >= q

True

sage: p = Player('C')

sage: q = Player('C')

sage: p >= q

True

"""

if isinstance(other, Player):

return self._name >= other._name

return self._name >= other

def __le__(self, other):

"""

Tests less than or equal inequality of two players. Allows for

players to be sorted on their names.

TESTS::

sage: from sage.game_theory.matching_game import Player

sage: p = Player('A')

sage: q = Player('B')

sage: p <= q

True

sage: q <= p

False

sage: p = Player(0)

sage: q = Player(1)

sage: p <= q

True

sage: q <= p

False

sage: p = Player(0)

sage: q = Player(0)

sage: p <= q

True

sage: p = Player('C')

sage: q = Player('C')

sage: p <= q

True

"""

if isinstance(other, Player):

return self._name <= other._name

return self._name <= other

def __ne__(self, other):

"""

Tests inequality of two players. Allows for

players to be sorted on their names.

TESTS::

sage: from sage.game_theory.matching_game import Player

sage: p = Player('A')

sage: q = Player('B')

sage: p != q

True

sage: p = Player(0)

sage: q = Player(1)

sage: p != q

True

sage: p = Player(0)

sage: q = Player(0)

sage: p != q

False

sage: p = Player('C')

sage: q = Player('C')

sage: p != q

False

"""

if isinstance(other, Player):

return self._name != other._name

return self._name != other

Coverage for local/lib/python2.7/site-packages/sage/game_theory/matching_game.py : 96%

165 statements 159 run 6 missing 0 excluded