关于算法:匹配和完美匹配之间的区别

Difference between matching and perfect matching

(P)考虑到一个男人,和一个男人,一个男人,一个女人,一个女人,一个女人of n women.让我X W给所有可能的秩序派一组(m,w),where m belongs to m and w belongs to w.(p)(P)a matching s is a set of ordered pairs,each from m x w,with the propertyThat each member of M and each member of W Appeals in at most one pairin,in(p)(P)A perfect matching s1 is a matching with the property that each member of Mand each member of W Appeals in exactly one pair in 1.(p)(P)I am having tough time to understand above statment on definitions ofMatching and perfect matching.(p)(P)Can any one give me an example on matching and perfect matching onFollowing example.M={M1,m2,m3}and W={W1,W2,W3}.(p)(P)Thanks for Help(p)


更好的例子是使用M={m1,m2,m3,m4}W={w1,w2,w3}。有一个完美的比赛,因为在至少一个成员可能无法匹配的M W到成员,但有一个可能的匹配。一个例子是[{m1,w1},{m2,w2},{m3,w3}] (m4 is unmatched)匹配

你给的例子可能的匹配可以完美匹配M,因为每一个成员可以匹配到独特的成员。


匹配:

1
 {(m1,w1), (m2,w2)}

完美匹配:

1
 {(m1,w1), (m2,w2), (m3,w3)}


这是匹配的?的成员。在M或W的任何成员,出现在一个以上的对?操作系统的定义,trivially,是满意的。

???????不是一个完美的匹配,但是,由于在W或M的成员在其对appear(因为有在对在它)。