Zoj 2344 Toral Tickets (数学_Polya)

题目大意：给定一张有n*m个格子的纸，每个格子有黑白两种颜色可以染。现在先将纸按长边粘起来得到一个圆柱，再将纸按短边拈起来得到一个游泳圈。如果两种染色方案卷起来后是一样的，那么它们同构。问不同构的的染色方案。n,m <= 20.www.zzzyk.com

解题思路：Polya的核心是找置换，本题有两类置换，一类是滚动，一类是旋转。
    我们将n*m的纸想成一个矩阵，那么第一行是1,2,3...m,第二行是m+1...m*2，以此类推。
    第一类滚动置换有n*m个。行和列是分开的，行的滚动有n个，列的滚动有m个，它们相乘就是总置换数。每个置换的循环节个数我们就模拟下，O（n*m）找到循环节。
    第二类旋转置换要分类讨论，当n！= m时，我们可以将整个矩阵旋转180度，这里是旋转而不是翻转，我写了Rorate函数将矩阵旋转九十度，Rorate两次.当n==m时，不仅可以旋转180度，旋转90度和270度都要考虑在内。
     也就是说当n！=m时，置换有2*n*m个，当n==m时，置换有4*n*m个，再套个高精度模板就AC了。n和m很小，随便模拟。
     ac后我很ws地把结果打成表拿去提交，时间就是0s...
     高精度模板太长，我就不发上来了，百度下一坨。

测试数据：
[cpp]
"2","3","4","6","8","13","18","30","46","78","126","224",
"380","687","1224","2250","4112","7685","14310","27012",
"3","6","13","34","78","237","687","2299","7685","27190","96909","353384","1296858",
"4808707","17920860","67169299","252745368","954677597","3617214681","13744852240",
"4","13","28","224","1224","7696","50964","352698","2493784","17920860","130216124",
"954637904","7048675960","52359294790","390941664896","2932043766538","22076502318624",
"166800088124428","1264168584899532","9607680019329456",
"6","34","224","1171","27012","353384","4806078","67169332","954637558","13744852240",
"199914398490","2932046213652","43303893547956","643371617410504","9607680019329456",
"144115191934621732","2170205198153526576","32794211748156196824","497091208931087393202","7555786373574120939544",
"8","78","1224","27012","337664","17920860","490984488","13744694928","390941662712",
"11259024570048","327534652572024","9607680019329456","283796066967422192","8432797316853883164",
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"30","2299","352698","67169332","13744694928","2932046213314","643371579062292","72057595967392816","32794211738611821312",
"7555786373574120887164","1758437555816391076574364","412646679762044113663297912","97511584632944122543696551480",
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"3201137879364778610385398532","1502400711381618810790106910044","710057690056045092131987186099464","337581713215216736580493443081144242",
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"78","27190","17920860","13744852240","11259024570048","9607680171442372","8432797316853883164","7555786373574120887164","6877444662723140842510068","3169126500571074529242309120",
"5900337339244149490513314759636","5538449982437150493650373937210144","5235113337245207158017777333159559848","4977844910386299809424175407065863134364","4757492309019866270222746693509250935268480",
"4567192616659071619387584246010106137898781148","4401699048902484083060538741828788515205714226528","4256932057960802384328742835597893551876416196246244","4129672194333342607786703597714589062014181942348177028","4017345110647475688854905231971608161006919942602792622080",
"126","96909","130216124","199914398490","327534652572024","558992251165454994","981270957754284704684","1758437555816391076574364","3201137879364778610385398532","5900337339244149490513314759636","5492677668532710795071526353530880","20623173752784149356430310745388844192",
"38987316780647942557493557843966923142152","74142737283426487327816994675197228663038210","141721370892693616310665183118190969688269247088","27210503211397174331646810002960774611548179429828

补充：软件开发 , C++ ,