File: /projects/2a31f88b-4244-4bd1-8e3a-3169ff24daac/sage/src/sage/misc/lazy_import.pyx
Source:
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 = 10
sage: big_game = MatchingGame(n)
sage: big_game.suitors()
(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
sage: big_game.reviewers()
(-1, -2, -3, -4, -5, -6, -7, -8, -9, -10)
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: -9, 4: -10, 5: -7, 6: -6, 7: -5, 8: -4, 9: -3, 10: -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}
REFERENCES:
.. [DI1989] Dan Gusfield and Robert W. Irving.
*The stable marriage problem: structure and algorithms*.
Vol. 54. Cambridge: MIT press, 1989.
"""
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
"""
return 'A matching game with {} suitors and {} reviewers'.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.
INPUTS:
- ``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.
INPUTS:
- ``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}
