#!/usr/bin/env?python
#?-*-?coding:?iso-8859-1?-*-

#?Documentation?is?intended?to?be?processed?by?Epydoc.

“““
Introduction
============

The?Munkres?module?provides?an?implementation?of?the?Munkres?algorithm
（also?called?the?Hungarian?algorithm?or?the?Kuhn-Munkres?algorithm）
useful?for?solving?the?Assignment?Problem.

Assignment?Problem
==================

Let?*C*?be?an?*n*\?x\?*n*?matrix?representing?the?costs?of?each?of?*n*?workers
to?perform?any?of?*n*?jobs.?The?assignment?problem?is?to?assign?jobs?to
workers?in?a?way?that?minimizes?the?total?cost.?Since?each?worker?can?perform
only?one?job?and?each?job?can?be?assigned?to?only?one?worker?the?assignments
represent?an?independent?set?of?the?matrix?*C*.

One?way?to?generate?the?optimal?set?is?to?create?all?permutations?of
the?indexes?necessary?to?traverse?the?matrix?so?that?no?row?and?column
are?used?more?than?once.?For?instance?given?this?matrix?（expressed?in
Python）::

????matrix?=?[[5?9?1]
??????????????[10?3?2]
??????????????[8?7?4]]

You?could?use?this?code?to?generate?the?traversal?indexes::

????def?permute（a?results）:
????????if?len（a）?==?1:
????????????results.insert（len（results）?a）

????????else:
????????????for?i?in?xrange（0?len（a））:
????????????????element?=?a[i]
????????????????a_copy?=?[a[j]?for?j?in?xrange（0?len（a））?if?j?!=?i]
????????????????subresults?=?[]
????????????????permute（a_copy?subresults）
????????????????for?subresult?in?subresults:
????????????????????result?=?[element]?+?subresult
????????????????????results.insert（len（results）?result）

????results?=?[]
????permute（range（len（matrix））?results）?#?[0?1?2]?for?a?3x3?matrix

After?the?call?to?permute（）?the?results?matrix?would?look?like?this::

????[[0?1?2]
?????[0?2?1]
?????[1?0?2]
?????[1?2?0]
?????[2?0?1]
?????[2?1?0]]

You?could?then?use?that?index?matrix?to?loop?over?the?original?cost?matrix
and?calculate?the?smallest?cost?of?the?combinations::

????n?=?len（matrix）
????minval?=?sys.maxint
????for?row?in?xrange（n）:
????????cost?=?0
????????for?col?in?xrange（n）:
????????????cost?+=?matrix[row][col]
????????minval?=?min（cost?minval）

????print?minval

While?this?approach?works?fine?for?small?matrices?it?does?not?scale.?It
executes?in?O（*n*!）?time:?Calculating?the?permutations?for?an?*n*\?x\?*n*
matrix?requires?*n*!?operations.?For?a?12x12?matrix?that‘s?479001600
traversals.?Even?if?you?could?manage?to?perform?each?traversal?in?just?one
millisecond?it?would?still?take?more?than?133?hours?to?perform?the?entire
traversal.?A?20x20?matrix?would?take?2432902008176640000?operations.?At
an?optimistic?millisecond?per?operation?that‘s?more?than?77?million?years.

The?Munkres?algorithm?runs?in?O（*n*\?^3）?time?rather?than?O（*n*!）.?This
package?provides?an?implementation?of?that?algorithm.

This?version?is?based?on
http://www.public.iastate.edu/~ddoty/HungarianAlgorithm.html.

This?version?was?written?for?Python?by?Brian?Clapper?from?the?（Ada）?algorithm
at?the?above?web?site.?（The?

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2011-05-28?08:27??Python-Shape-Context-master\
?????文件???????13295??2011-05-28?08:27??Python-Shape-Context-master\9.png
?????文件????????1433??2011-05-28?08:27??Python-Shape-Context-master\9M.png
?????文件?????????564??2011-05-28?08:27??Python-Shape-Context-master\9M2.png
?????文件????????9437??2011-05-28?08:27??Python-Shape-Context-master\A.png
?????文件???????10433??2011-05-28?08:27??Python-Shape-Context-master\A2.png
?????文件???????14930??2011-05-28?08:27??Python-Shape-Context-master\AM.png
?????文件????????5634??2011-05-28?08:27??Python-Shape-Context-master\AM2.png
?????文件???????14996??2011-05-28?08:27??Python-Shape-Context-master\AM3.png
?????文件???????14784??2011-05-28?08:27??Python-Shape-Context-master\B.png
?????文件???????19847??2011-05-28?08:27??Python-Shape-Context-master\BM.png
?????文件???????19439??2011-05-28?08:27??Python-Shape-Context-master\BM2.png
?????文件????????9142??2011-05-28?08:27??Python-Shape-Context-master\D.png
?????目錄???????????0??2011-05-28?08:27??Python-Shape-Context-master\LAPJV\
?????文件?????????515??2011-05-28?08:27??Python-Shape-Context-master\LAPJV\GNRL.H
?????文件???????10509??2011-05-28?08:27??Python-Shape-Context-master\LAPJV\LAP.CPP
?????文件?????????746??2011-05-28?08:27??Python-Shape-Context-master\LAPJV\LAP.H
?????文件????????4236??2011-05-28?08:27??Python-Shape-Context-master\LAPJV\LAPJV.p
?????文件????????2023??2011-05-28?08:27??Python-Shape-Context-master\LAPJV\LAPMAIN.CPP
?????文件?????????516??2011-05-28?08:27??Python-Shape-Context-master\LAPJV\SYSTEM.CPP
?????文件?????????351??2011-05-28?08:27??Python-Shape-Context-master\LAPJV\SYSTEM.H
?????文件??????????83??2011-05-28?08:27??Python-Shape-Context-master\README
?????文件????????6732??2011-05-28?08:27??Python-Shape-Context-master\SC.py
?????文件????????8067??2011-05-28?08:27??Python-Shape-Context-master\SC.pyc
?????文件????????7454??2011-05-28?08:27??Python-Shape-Context-master\SC2.py
?????目錄???????????0??2011-05-28?08:27??Python-Shape-Context-master\info\
?????文件??????890980??2011-05-28?08:27??Python-Shape-Context-master\info\10.1.1.112.2716.pdf
?????文件??????965316??2011-05-28?08:27??Python-Shape-Context-master\info\10.1.1.18.8852.pdf
?????文件??????606363??2011-05-28?08:27??Python-Shape-Context-master\info\13_diplaros.pdf
?????文件?????1956862??2011-05-28?08:27??Python-Shape-Context-master\info\2009_ijra_bk.pdf
?????文件??????991291??2011-05-28?08:27??Python-Shape-Context-master\info\54.pdf
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