求婚拒绝算法(GS算法)的Python实现

问题

给定一组男人和一组女人，每个人在心目中都对所有的异性有一个倾慕度排序，从最喜欢到最不喜欢依次排序1、2、3。现在给出问题，如何对这些男女进行配对使得在分配好后不出现偷情的现象。

算法

可以有男人优先和女人优先两种算法。以男人优先为例，为代码如下：

while  存在男人m是自由的且还没对每个女人都求过婚
选择这个男人m
令w是m的优先表中还没求过婚的最高排名的女人
if  w是自由的
（m，w）变成约会状态
else  w当前与m1约会
if  w更偏爱m1而不爱m
m保持自由
else    w更偏爱m而不爱m1
（m，w）变成约会状态
m1变成自由
endif
endif
endwhile

需要特别注意的是！虽然从第9、10行来看，女人能够选择更好的伴侣。但从第3行来看，男人能够优先选择排名最高的女人。实际上，第9、10行只是为了保证婚姻的稳定性。

Python实现

# Homework 1, Problem 4: Implementing the Gale-Shapley algorithm

# You are to code the function "find_stable_matching". DO NOT rename
# the function. Details of the format of the input/output are given in
# the function's comments. Edit this file and use blackboard to submit
# the file along with your homework solutions.

# Some basic testing for your code is provided below. DO NOT modify
# these tests. Your code MUST pass these tests. Note, however, that
# passing these tests does not guarantee that your algorithm is
# correct. You should carry out more testing!

# Use Python 2.x for your implementation

def find_stable_matching(MP,WP):
""" The input of this function is defined by two lists MP and WP

Men and women are numbered 0 through n-1

MP[i] encodes the ith man's preferences. It is simply a list
containing the numbers 0, 1, ... , n-1 in some order

WP[i] encodes the ith woman's preferences. It is simply a list
containing the numbers 0, 1,... , n-1 in some order

The output is defined by a list of pairs of the form (i,j)
indicating that man i is married to woman j

Your output should be the man-optimal stable matching found by the
GS-algorithm. """

# your code goes here!
n=len(MP)
isManFree=[True]*n
isWomanFree=[True]*n
#isManProposed=[[False]*n]*n
isManProposed=[[False for i in range(n)] for j in range(n)]
match=[(-1,-1)]*n

while(True in isManFree):
indexM=isManFree.index(True)
if(False in isManProposed[indexM]):
indexW=-1
for i in range(n):
w=MP[indexM][i]
if(not isManProposed[indexM][w]):
indexW=w
break
isManProposed[indexM][indexW]=True
if(isWomanFree[indexW]):
#isManProposed[indexM][indexW]=True
isWomanFree[indexW]=False
isManFree[indexM]=False
match[indexM]=(indexM,indexW)
else:
indexM1=-1
for j in range(n):
if(match[j][1]==indexW):
indexM1=j
break
if(WP[indexW].index(indexM)<WP[indexW].index(indexM1)):
isManFree[indexM1]=True
isManFree[indexM]=False
match[indexM]=(indexM,indexW)
print match
return match

def test1():
""" basic test for your code """

MP = [ [0,1], [1,0] ]
WP = [ [0,1], [0,1] ]

SM = find_stable_matching(MP,WP)

assert ( (0,0) in SM and (1,1) in SM )

def test2():
""" basic test for your code """

MP = [ [0,1], [0,1] ]
WP = [ [0,1], [0,1] ]

SM = find_stable_matching(MP,WP)

assert ( (0,0) in SM and (1,1) in SM )

def test3():
""" basic test for your code """

MP = [ [0,1], [0,1] ]
WP = [ [1,0], [1,0] ]

SM = find_stable_matching(MP,WP)

assert ( (0,1) in SM and (1,0) in SM )

if __name__=="__main__":
print "**********test1************"
test1()
print "**********test2************"
test2()
print "**********test3************"
test3()

面向对象的Python实现请参见这里