PNG  IHDRX cHRMz&u0`:pQ<bKGD pHYsodtIME MeqIDATxw]Wug^Qd˶ 6`!N:!@xI~)%7%@Bh&`lnjVF29gΨ4E$|>cɚ{gk= %,a KX%,a KX%,a KX%,a KX%,a KX%,a KX%, b` ǟzeאfp]<!SJmɤY޲ڿ,%c ~ع9VH.!Ͳz&QynֺTkRR.BLHi٪:l;@(!MԴ=žI,:o&N'Kù\vRmJ雵֫AWic H@" !: Cé||]k-Ha oݜ:y F())u]aG7*JV@J415p=sZH!=!DRʯvɱh~V\}v/GKY$n]"X"}t@ xS76^[bw4dsce)2dU0 CkMa-U5tvLƀ~mlMwfGE/-]7XAƟ`׮g ewxwC4\[~7@O-Q( a*XGƒ{ ՟}$_y3tĐƤatgvێi|K=uVyrŲlLӪuܿzwk$m87k( `múcE)"@rK( z4$D; 2kW=Xb$V[Ru819קR~qloѱDyįݎ*mxw]y5e4K@ЃI0A D@"BDk_)N\8͜9dz"fK0zɿvM /.:2O{ Nb=M=7>??Zuo32 DLD@D| &+֎C #B8ַ`bOb $D#ͮҪtx]%`ES`Ru[=¾!@Od37LJ0!OIR4m]GZRJu$‡c=%~s@6SKy?CeIh:[vR@Lh | (BhAMy=݃  G"'wzn޺~8ԽSh ~T*A:xR[ܹ?X[uKL_=fDȊ؂p0}7=D$Ekq!/t.*2ʼnDbŞ}DijYaȲ(""6HA;:LzxQ‘(SQQ}*PL*fc\s `/d'QXW, e`#kPGZuŞuO{{wm[&NBTiiI0bukcA9<4@SӊH*؎4U/'2U5.(9JuDfrޱtycU%j(:RUbArLֺN)udA':uGQN"-"Is.*+k@ `Ojs@yU/ H:l;@yyTn}_yw!VkRJ4P)~y#)r,D =ě"Q]ci'%HI4ZL0"MJy 8A{ aN<8D"1#IJi >XjX֔#@>-{vN!8tRݻ^)N_╗FJEk]CT՟ YP:_|H1@ CBk]yKYp|og?*dGvzنzӴzjֺNkC~AbZƷ`.H)=!QͷVTT(| u78y֮}|[8-Vjp%2JPk[}ԉaH8Wpqhwr:vWª<}l77_~{s۴V+RCģ%WRZ\AqHifɤL36: #F:p]Bq/z{0CU6ݳEv_^k7'>sq*+kH%a`0ԣisqにtү04gVgW΂iJiS'3w.w}l6MC2uԯ|>JF5`fV5m`Y**Db1FKNttu]4ccsQNnex/87+}xaUW9y>ͯ骵G{䩓Գ3+vU}~jJ.NFRD7<aJDB1#ҳgSb,+CS?/ VG J?|?,2#M9}B)MiE+G`-wo߫V`fio(}S^4e~V4bHOYb"b#E)dda:'?}׮4繏`{7Z"uny-?ǹ;0MKx{:_pÚmFמ:F " .LFQLG)Q8qN q¯¯3wOvxDb\. BKD9_NN &L:4D{mm o^tֽ:q!ƥ}K+<"m78N< ywsard5+Š²z~mnG)=}lYݧNj'QJS{S :UYS-952?&O-:W}(!6Mk4+>A>j+i|<<|;ر^߉=HE|V#F)Emm#}/"y GII웻Jі94+v뾧xu~5C95~ūH>c@덉pʃ1/4-A2G%7>m;–Y,cyyaln" ?ƻ!ʪ<{~h~i y.zZB̃/,雋SiC/JFMmBH&&FAbϓO^tubbb_hZ{_QZ-sύodFgO(6]TJA˯#`۶ɟ( %$&+V'~hiYy>922 Wp74Zkq+Ovn錄c>8~GqܲcWꂎz@"1A.}T)uiW4="jJ2W7mU/N0gcqܗOO}?9/wìXžΏ0 >֩(V^Rh32!Hj5`;O28؇2#ݕf3 ?sJd8NJ@7O0 b־?lldщ̡&|9C.8RTWwxWy46ah嘦mh٤&l zCy!PY?: CJyв]dm4ǜҐR޻RլhX{FƯanшQI@x' ao(kUUuxW_Ñ줮[w8 FRJ(8˼)_mQ _!RJhm=!cVmm ?sFOnll6Qk}alY}; "baӌ~M0w,Ggw2W:G/k2%R,_=u`WU R.9T"v,<\Ik޽/2110Ӿxc0gyC&Ny޽JҢrV6N ``یeA16"J³+Rj*;BϜkZPJaÍ<Jyw:NP8/D$ 011z֊Ⱳ3ι֘k1V_"h!JPIΣ'ɜ* aEAd:ݺ>y<}Lp&PlRfTb1]o .2EW\ͮ]38؋rTJsǏP@芎sF\> P^+dYJLbJ C-xϐn> ι$nj,;Ǖa FU *择|h ~izť3ᤓ`K'-f tL7JK+vf2)V'-sFuB4i+m+@My=O҈0"|Yxoj,3]:cо3 $#uŘ%Y"y죯LebqtҢVzq¼X)~>4L׶m~[1_k?kxֺQ`\ |ٛY4Ѯr!)N9{56(iNq}O()Em]=F&u?$HypWUeB\k]JɩSع9 Zqg4ZĊo oMcjZBU]B\TUd34ݝ~:7ڶSUsB0Z3srx 7`:5xcx !qZA!;%͚7&P H<WL!džOb5kF)xor^aujƍ7 Ǡ8/p^(L>ὴ-B,{ۇWzֺ^k]3\EE@7>lYBȝR.oHnXO/}sB|.i@ɥDB4tcm,@ӣgdtJ!lH$_vN166L__'Z)y&kH;:,Y7=J 9cG) V\hjiE;gya~%ks_nC~Er er)muuMg2;֫R)Md) ,¶ 2-wr#F7<-BBn~_(o=KO㭇[Xv eN_SMgSҐ BS헃D%g_N:/pe -wkG*9yYSZS.9cREL !k}<4_Xs#FmҶ:7R$i,fi!~' # !6/S6y@kZkZcX)%5V4P]VGYq%H1!;e1MV<!ϐHO021Dp= HMs~~a)ަu7G^];git!Frl]H/L$=AeUvZE4P\.,xi {-~p?2b#amXAHq)MWǾI_r`S Hz&|{ +ʖ_= (YS(_g0a03M`I&'9vl?MM+m~}*xT۲(fY*V4x@29s{DaY"toGNTO+xCAO~4Ϳ;p`Ѫ:>Ҵ7K 3}+0 387x\)a"/E>qpWB=1 ¨"MP(\xp߫́A3+J] n[ʼnӼaTbZUWb={~2ooKױӰp(CS\S筐R*JغV&&"FA}J>G֐p1ٸbk7 ŘH$JoN <8s^yk_[;gy-;߉DV{c B yce% aJhDȶ 2IdйIB/^n0tNtџdcKj4϶v~- CBcgqx9= PJ) dMsjpYB] GD4RDWX +h{y`,3ꊕ$`zj*N^TP4L:Iz9~6s) Ga:?y*J~?OrMwP\](21sZUD ?ܟQ5Q%ggW6QdO+\@ ̪X'GxN @'4=ˋ+*VwN ne_|(/BDfj5(Dq<*tNt1х!MV.C0 32b#?n0pzj#!38}޴o1KovCJ`8ŗ_"]] rDUy޲@ Ȗ-;xџ'^Y`zEd?0„ DAL18IS]VGq\4o !swV7ˣι%4FѮ~}6)OgS[~Q vcYbL!wG3 7띸*E Pql8=jT\꘿I(z<[6OrR8ºC~ډ]=rNl[g|v TMTղb-o}OrP^Q]<98S¤!k)G(Vkwyqyr޽Nv`N/e p/~NAOk \I:G6]4+K;j$R:Mi #*[AȚT,ʰ,;N{HZTGMoּy) ]%dHء9Պ䠬|<45,\=[bƟ8QXeB3- &dҩ^{>/86bXmZ]]yޚN[(WAHL$YAgDKp=5GHjU&99v簪C0vygln*P)9^͞}lMuiH!̍#DoRBn9l@ xA/_v=ȺT{7Yt2N"4!YN`ae >Q<XMydEB`VU}u]嫇.%e^ánE87Mu\t`cP=AD/G)sI"@MP;)]%fH9'FNsj1pVhY&9=0pfuJ&gޤx+k:!r˭wkl03׼Ku C &ѓYt{.O.zҏ z}/tf_wEp2gvX)GN#I ݭ߽v/ .& и(ZF{e"=V!{zW`, ]+LGz"(UJp|j( #V4, 8B 0 9OkRrlɱl94)'VH9=9W|>PS['G(*I1==C<5"Pg+x'K5EMd؞Af8lG ?D FtoB[je?{k3zQ vZ;%Ɠ,]E>KZ+T/ EJxOZ1i #T<@ I}q9/t'zi(EMqw`mYkU6;[t4DPeckeM;H}_g pMww}k6#H㶏+b8雡Sxp)&C $@'b,fPߑt$RbJ'vznuS ~8='72_`{q纶|Q)Xk}cPz9p7O:'|G~8wx(a 0QCko|0ASD>Ip=4Q, d|F8RcU"/KM opKle M3#i0c%<7׿p&pZq[TR"BpqauIp$ 8~Ĩ!8Սx\ւdT>>Z40ks7 z2IQ}ItԀ<-%S⍤};zIb$I 5K}Q͙D8UguWE$Jh )cu4N tZl+[]M4k8֦Zeq֮M7uIqG 1==tLtR,ƜSrHYt&QP윯Lg' I,3@P'}'R˪e/%-Auv·ñ\> vDJzlӾNv5:|K/Jb6KI9)Zh*ZAi`?S {aiVDԲuy5W7pWeQJk֤#5&V<̺@/GH?^τZL|IJNvI:'P=Ϛt"¨=cud S Q.Ki0 !cJy;LJR;G{BJy޺[^8fK6)=yʊ+(k|&xQ2`L?Ȓ2@Mf 0C`6-%pKpm')c$׻K5[J*U[/#hH!6acB JA _|uMvDyk y)6OPYjœ50VT K}cǻP[ $:]4MEA.y)|B)cf-A?(e|lɉ#P9V)[9t.EiQPDѠ3ϴ;E:+Օ t ȥ~|_N2,ZJLt4! %ա]u {+=p.GhNcŞQI?Nd'yeh n7zi1DB)1S | S#ًZs2|Ɛy$F SxeX{7Vl.Src3E℃Q>b6G ўYCmtկ~=K0f(=LrAS GN'ɹ9<\!a`)֕y[uՍ[09` 9 +57ts6}b4{oqd+J5fa/,97J#6yν99mRWxJyѡyu_TJc`~W>l^q#Ts#2"nD1%fS)FU w{ܯ R{ ˎ󅃏џDsZSQS;LV;7 Od1&1n$ N /.q3~eNɪ]E#oM~}v֯FڦwyZ=<<>Xo稯lfMFV6p02|*=tV!c~]fa5Y^Q_WN|Vs 0ҘދU97OI'N2'8N֭fgg-}V%y]U4 峧p*91#9U kCac_AFңĪy뚇Y_AiuYyTTYЗ-(!JFLt›17uTozc. S;7A&&<ԋ5y;Ro+:' *eYJkWR[@F %SHWP 72k4 qLd'J "zB6{AC0ƁA6U.'F3:Ȅ(9ΜL;D]m8ڥ9}dU "v!;*13Rg^fJyShyy5auA?ɩGHRjo^]׽S)Fm\toy 4WQS@mE#%5ʈfFYDX ~D5Ϡ9tE9So_aU4?Ѽm%&c{n>.KW1Tlb}:j uGi(JgcYj0qn+>) %\!4{LaJso d||u//P_y7iRJ߬nHOy) l+@$($VFIQ9%EeKʈU. ia&FY̒mZ=)+qqoQn >L!qCiDB;Y<%} OgBxB!ØuG)WG9y(Ą{_yesuZmZZey'Wg#C~1Cev@0D $a@˲(.._GimA:uyw֬%;@!JkQVM_Ow:P.s\)ot- ˹"`B,e CRtaEUP<0'}r3[>?G8xU~Nqu;Wm8\RIkբ^5@k+5(By'L&'gBJ3ݶ!/㮻w҅ yqPWUg<e"Qy*167΃sJ\oz]T*UQ<\FԎ`HaNmڜ6DysCask8wP8y9``GJ9lF\G g's Nn͵MLN֪u$| /|7=]O)6s !ĴAKh]q_ap $HH'\1jB^s\|- W1:=6lJBqjY^LsPk""`]w)󭃈,(HC ?䔨Y$Sʣ{4Z+0NvQkhol6C.婧/u]FwiVjZka&%6\F*Ny#8O,22+|Db~d ~Çwc N:FuuCe&oZ(l;@ee-+Wn`44AMK➝2BRՈt7g*1gph9N) *"TF*R(#'88pm=}X]u[i7bEc|\~EMn}P瘊J)K.0i1M6=7'_\kaZ(Th{K*GJyytw"IO-PWJk)..axӝ47"89Cc7ĐBiZx 7m!fy|ϿF9CbȩV 9V-՛^pV̌ɄS#Bv4-@]Vxt-Z, &ֺ*diؠ2^VXbs֔Ìl.jQ]Y[47gj=幽ex)A0ip׳ W2[ᎇhuE^~q흙L} #-b۸oFJ_QP3r6jr+"nfzRJTUqoaۍ /$d8Mx'ݓ= OՃ| )$2mcM*cЙj}f };n YG w0Ia!1Q.oYfr]DyISaP}"dIӗթO67jqR ҊƐƈaɤGG|h;t]䗖oSv|iZqX)oalv;۩meEJ\!8=$4QU4Xo&VEĊ YS^E#d,yX_> ۘ-e\ "Wa6uLĜZi`aD9.% w~mB(02G[6y.773a7 /=o7D)$Z 66 $bY^\CuP. (x'"J60׿Y:Oi;F{w佩b+\Yi`TDWa~|VH)8q/=9!g߆2Y)?ND)%?Ǐ`k/sn:;O299yB=a[Ng 3˲N}vLNy;*?x?~L&=xyӴ~}q{qE*IQ^^ͧvü{Huu=R|>JyUlZV, B~/YF!Y\u_ݼF{_C)LD]m {H 0ihhadd nUkf3oٺCvE\)QJi+֥@tDJkB$1!Đr0XQ|q?d2) Ӣ_}qv-< FŊ߫%roppVBwü~JidY4:}L6M7f٬F "?71<2#?Jyy4뷢<_a7_=Q E=S1И/9{+93֮E{ǂw{))?maÆm(uLE#lïZ  ~d];+]h j?!|$F}*"4(v'8s<ŏUkm7^7no1w2ؗ}TrͿEk>p'8OB7d7R(A 9.*Mi^ͳ; eeUwS+C)uO@ =Sy]` }l8^ZzRXj[^iUɺ$tj))<sbDJfg=Pk_{xaKo1:-uyG0M ԃ\0Lvuy'ȱc2Ji AdyVgVh!{]/&}}ċJ#%d !+87<;qN޼Nفl|1N:8ya  8}k¾+-$4FiZYÔXk*I&'@iI99)HSh4+2G:tGhS^繿 Kتm0 вDk}֚+QT4;sC}rՅE,8CX-e~>G&'9xpW,%Fh,Ry56Y–hW-(v_,? ; qrBk4-V7HQ;ˇ^Gv1JVV%,ik;D_W!))+BoS4QsTM;gt+ndS-~:11Sgv!0qRVh!"Ȋ(̦Yl.]PQWgٳE'`%W1{ndΗBk|Ž7ʒR~,lnoa&:ü$ 3<a[CBݮwt"o\ePJ=Hz"_c^Z.#ˆ*x z̝grY]tdkP*:97YľXyBkD4N.C_[;F9`8& !AMO c `@BA& Ost\-\NX+Xp < !bj3C&QL+*&kAQ=04}cC!9~820G'PC9xa!w&bo_1 Sw"ܱ V )Yl3+ס2KoXOx]"`^WOy :3GO0g;%Yv㐫(R/r (s } u B &FeYZh0y> =2<Ϟc/ -u= c&׭,.0"g"7 6T!vl#sc>{u/Oh Bᾈ)۴74]x7 gMӒ"d]U)}" v4co[ ɡs 5Gg=XR14?5A}D "b{0$L .\4y{_fe:kVS\\O]c^W52LSBDM! C3Dhr̦RtArx4&agaN3Cf<Ԉp4~ B'"1@.b_/xQ} _߃҉/gٓ2Qkqp0շpZ2fԫYz< 4L.Cyυι1t@鎫Fe sYfsF}^ V}N<_`p)alٶ "(XEAVZ<)2},:Ir*#m_YӼ R%a||EƼIJ,,+f"96r/}0jE/)s)cjW#w'Sʯ5<66lj$a~3Kʛy 2:cZ:Yh))+a߭K::N,Q F'qB]={.]h85C9cr=}*rk?vwV렵ٸW Rs%}rNAkDv|uFLBkWY YkX מ|)1!$#3%y?pF<@<Rr0}: }\J [5FRxY<9"SQdE(Q*Qʻ)q1E0B_O24[U'],lOb ]~WjHޏTQ5Syu wq)xnw8~)c 쫬gٲߠ H% k5dƝk> kEj,0% b"vi2Wس_CuK)K{n|>t{P1򨾜j>'kEkƗBg*H%'_aY6Bn!TL&ɌOb{c`'d^{t\i^[uɐ[}q0lM˕G:‚4kb祔c^:?bpg… +37stH:0}en6x˟%/<]BL&* 5&fK9Mq)/iyqtA%kUe[ڛKN]Ě^,"`/ s[EQQm?|XJ߅92m]G.E΃ח U*Cn.j_)Tѧj̿30ڇ!A0=͜ar I3$C^-9#|pk!)?7.x9 @OO;WƝZBFU keZ75F6Tc6"ZȚs2y/1 ʵ:u4xa`C>6Rb/Yм)^=+~uRd`/|_8xbB0?Ft||Z\##|K 0>>zxv8۴吅q 8ĥ)"6>~\8:qM}#͚'ĉ#p\׶ l#bA?)|g g9|8jP(cr,BwV (WliVxxᡁ@0Okn;ɥh$_ckCgriv}>=wGzβ KkBɛ[˪ !J)h&k2%07δt}!d<9;I&0wV/ v 0<H}L&8ob%Hi|޶o&h1L|u֦y~󛱢8fٲUsւ)0oiFx2}X[zVYr_;N(w]_4B@OanC?gĦx>мgx>ΛToZoOMp>40>V Oy V9iq!4 LN,ˢu{jsz]|"R޻&'ƚ{53ўFu(<٪9:΋]B;)B>1::8;~)Yt|0(pw2N%&X,URBK)3\zz&}ax4;ǟ(tLNg{N|Ǽ\G#C9g$^\}p?556]/RP.90 k,U8/u776s ʪ_01چ|\N 0VV*3H鴃J7iI!wG_^ypl}r*jɤSR 5QN@ iZ#1ٰy;_\3\BQQ x:WJv츟ٯ$"@6 S#qe딇(/P( Dy~TOϻ<4:-+F`0||;Xl-"uw$Цi󼕝mKʩorz"mϺ$F:~E'ҐvD\y?Rr8_He@ e~O,T.(ފR*cY^m|cVR[8 JҡSm!ΆԨb)RHG{?MpqrmN>߶Y)\p,d#xۆWY*,l6]v0h15M˙MS8+EdI='LBJIH7_9{Caз*Lq,dt >+~ّeʏ?xԕ4bBAŚjﵫ!'\Ը$WNvKO}ӽmSşذqsOy?\[,d@'73'j%kOe`1.g2"e =YIzS2|zŐƄa\U,dP;jhhhaxǶ?КZ՚.q SE+XrbOu%\GتX(H,N^~]JyEZQKceTQ]VGYqnah;y$cQahT&QPZ*iZ8UQQM.qo/T\7X"u?Mttl2Xq(IoW{R^ ux*SYJ! 4S.Jy~ BROS[V|žKNɛP(L6V^|cR7i7nZW1Fd@ Ara{詑|(T*dN]Ko?s=@ |_EvF]׍kR)eBJc" MUUbY6`~V޴dJKß&~'d3i WWWWWW

F1l3 Manager

Current Directory: /usr/share/doc/python2-docs/html/library
/usr/share/doc/python2-docs/html/library/
Viewing File: /usr/share/doc/python2-docs/html/library/sets.html
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="X-UA-Compatible" content="IE=Edge" /> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <title>8.7. sets — Unordered collections of unique elements &#8212; Python 2.7.16 documentation</title> <link rel="stylesheet" href="../_static/classic.css" type="text/css" /> <link rel="stylesheet" href="../_static/pygments.css" type="text/css" /> <script type="text/javascript" id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script> <script type="text/javascript" src="../_static/jquery.js"></script> <script type="text/javascript" src="../_static/underscore.js"></script> <script type="text/javascript" src="../_static/doctools.js"></script> <script type="text/javascript" src="../_static/sidebar.js"></script> <link rel="search" type="application/opensearchdescription+xml" title="Search within Python 2.7.16 documentation" href="../_static/opensearch.xml"/> <link rel="author" title="About these documents" href="../about.html" /> <link rel="index" title="Index" href="../genindex.html" /> <link rel="search" title="Search" href="../search.html" /> <link rel="copyright" title="Copyright" href="../copyright.html" /> <link rel="next" title="8.8. sched — Event scheduler" href="sched.html" /> <link rel="prev" title="8.6. array — Efficient arrays of numeric values" href="array.html" /> <link rel="shortcut icon" type="image/png" href="../_static/py.png" /> <link rel="canonical" href="https://docs.python.org/2/library/sets.html" /> <script type="text/javascript" src="../_static/copybutton.js"></script> </head><body> <div class="related" role="navigation" aria-label="related navigation"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" accesskey="I">index</a></li> <li class="right" > <a href="../py-modindex.html" title="Python Module Index" >modules</a> |</li> <li class="right" > <a href="sched.html" title="8.8. sched — Event scheduler" accesskey="N">next</a> |</li> <li class="right" > <a href="array.html" title="8.6. array — Efficient arrays of numeric values" accesskey="P">previous</a> |</li> <li><img src="../_static/py.png" alt="" style="vertical-align: middle; margin-top: -1px"/></li> <li><a href="https://www.python.org/">Python</a> &#187;</li> <li> <a href="../index.html">Python 2.7.16 documentation</a> &#187; </li> <li class="nav-item nav-item-1"><a href="index.html" >The Python Standard Library</a> &#187;</li> <li class="nav-item nav-item-2"><a href="datatypes.html" accesskey="U">8. Data Types</a> &#187;</li> </ul> </div> <div class="document"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body" role="main"> <div class="section" id="module-sets"> <span id="sets-unordered-collections-of-unique-elements"></span><h1>8.7. <a class="reference internal" href="#module-sets" title="sets: Implementation of sets of unique elements. (deprecated)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sets</span></code></a> — Unordered collections of unique elements<a class="headerlink" href="#module-sets" title="Permalink to this headline">¶</a></h1> <div class="versionadded"> <p><span class="versionmodified">New in version 2.3.</span></p> </div> <div class="deprecated"> <p><span class="versionmodified">Deprecated since version 2.6: </span>The built-in <a class="reference internal" href="stdtypes.html#set" title="set"><code class="xref py py-class docutils literal notranslate"><span class="pre">set</span></code></a>/<a class="reference internal" href="stdtypes.html#frozenset" title="frozenset"><code class="xref py py-class docutils literal notranslate"><span class="pre">frozenset</span></code></a> types replace this module.</p> </div> <p>The <a class="reference internal" href="#module-sets" title="sets: Implementation of sets of unique elements. (deprecated)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sets</span></code></a> module provides classes for constructing and manipulating unordered collections of unique elements. Common uses include membership testing, removing duplicates from a sequence, and computing standard math operations on sets such as intersection, union, difference, and symmetric difference.</p> <p>Like other collections, sets support <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">in</span> <span class="pre">set</span></code>, <code class="docutils literal notranslate"><span class="pre">len(set)</span></code>, and <code class="docutils literal notranslate"><span class="pre">for</span> <span class="pre">x</span> <span class="pre">in</span> <span class="pre">set</span></code>. Being an unordered collection, sets do not record element position or order of insertion. Accordingly, sets do not support indexing, slicing, or other sequence-like behavior.</p> <p>Most set applications use the <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> class which provides every set method except for <a class="reference internal" href="../reference/datamodel.html#object.__hash__" title="object.__hash__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__hash__()</span></code></a>. For advanced applications requiring a hash method, the <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> class adds a <a class="reference internal" href="../reference/datamodel.html#object.__hash__" title="object.__hash__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__hash__()</span></code></a> method but omits methods which alter the contents of the set. Both <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> and <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> derive from <code class="xref py py-class docutils literal notranslate"><span class="pre">BaseSet</span></code>, an abstract class useful for determining whether something is a set: <code class="docutils literal notranslate"><span class="pre">isinstance(obj,</span> <span class="pre">BaseSet)</span></code>.</p> <p>The set classes are implemented using dictionaries. Accordingly, the requirements for set elements are the same as those for dictionary keys; namely, that the element defines both <a class="reference internal" href="../reference/datamodel.html#object.__eq__" title="object.__eq__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__eq__()</span></code></a> and <a class="reference internal" href="../reference/datamodel.html#object.__hash__" title="object.__hash__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__hash__()</span></code></a>. As a result, sets cannot contain mutable elements such as lists or dictionaries. However, they can contain immutable collections such as tuples or instances of <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a>. For convenience in implementing sets of sets, inner sets are automatically converted to immutable form, for example, <code class="docutils literal notranslate"><span class="pre">Set([Set(['dog'])])</span></code> is transformed to <code class="docutils literal notranslate"><span class="pre">Set([ImmutableSet(['dog'])])</span></code>.</p> <dl class="class"> <dt id="sets.Set"> <em class="property">class </em><code class="descclassname">sets.</code><code class="descname">Set</code><span class="sig-paren">(</span><span class="optional">[</span><em>iterable</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#sets.Set" title="Permalink to this definition">¶</a></dt> <dd><p>Constructs a new empty <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> object. If the optional <em>iterable</em> parameter is supplied, updates the set with elements obtained from iteration. All of the elements in <em>iterable</em> should be immutable or be transformable to an immutable using the protocol described in section <a class="reference internal" href="#immutable-transforms"><span class="std std-ref">Protocol for automatic conversion to immutable</span></a>.</p> </dd></dl> <dl class="class"> <dt id="sets.ImmutableSet"> <em class="property">class </em><code class="descclassname">sets.</code><code class="descname">ImmutableSet</code><span class="sig-paren">(</span><span class="optional">[</span><em>iterable</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#sets.ImmutableSet" title="Permalink to this definition">¶</a></dt> <dd><p>Constructs a new empty <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> object. If the optional <em>iterable</em> parameter is supplied, updates the set with elements obtained from iteration. All of the elements in <em>iterable</em> should be immutable or be transformable to an immutable using the protocol described in section <a class="reference internal" href="#immutable-transforms"><span class="std std-ref">Protocol for automatic conversion to immutable</span></a>.</p> <p>Because <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> objects provide a <a class="reference internal" href="../reference/datamodel.html#object.__hash__" title="object.__hash__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__hash__()</span></code></a> method, they can be used as set elements or as dictionary keys. <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> objects do not have methods for adding or removing elements, so all of the elements must be known when the constructor is called.</p> </dd></dl> <div class="section" id="set-objects"> <span id="id1"></span><h2>8.7.1. Set Objects<a class="headerlink" href="#set-objects" title="Permalink to this headline">¶</a></h2> <p>Instances of <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> and <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> both provide the following operations:</p> <table border="1" class="docutils"> <colgroup> <col width="41%" /> <col width="16%" /> <col width="43%" /> </colgroup> <thead valign="bottom"> <tr class="row-odd"><th class="head">Operation</th> <th class="head">Equivalent</th> <th class="head">Result</th> </tr> </thead> <tbody valign="top"> <tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">len(s)</span></code></td> <td>&#160;</td> <td>number of elements in set <em>s</em> (cardinality)</td> </tr> <tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">in</span> <span class="pre">s</span></code></td> <td>&#160;</td> <td>test <em>x</em> for membership in <em>s</em></td> </tr> <tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">not</span> <span class="pre">in</span> <span class="pre">s</span></code></td> <td>&#160;</td> <td>test <em>x</em> for non-membership in <em>s</em></td> </tr> <tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">s.issubset(t)</span></code></td> <td><code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">&lt;=</span> <span class="pre">t</span></code></td> <td>test whether every element in <em>s</em> is in <em>t</em></td> </tr> <tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">s.issuperset(t)</span></code></td> <td><code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">&gt;=</span> <span class="pre">t</span></code></td> <td>test whether every element in <em>t</em> is in <em>s</em></td> </tr> <tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">s.union(t)</span></code></td> <td><code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">|</span> <span class="pre">t</span></code></td> <td>new set with elements from both <em>s</em> and <em>t</em></td> </tr> <tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">s.intersection(t)</span></code></td> <td><code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">&amp;</span> <span class="pre">t</span></code></td> <td>new set with elements common to <em>s</em> and <em>t</em></td> </tr> <tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">s.difference(t)</span></code></td> <td><code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">-</span> <span class="pre">t</span></code></td> <td>new set with elements in <em>s</em> but not in <em>t</em></td> </tr> <tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">s.symmetric_difference(t)</span></code></td> <td><code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">^</span> <span class="pre">t</span></code></td> <td>new set with elements in either <em>s</em> or <em>t</em> but not both</td> </tr> <tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">s.copy()</span></code></td> <td>&#160;</td> <td>new set with a shallow copy of <em>s</em></td> </tr> </tbody> </table> <p>Note, the non-operator versions of <code class="xref py py-meth docutils literal notranslate"><span class="pre">union()</span></code>, <code class="xref py py-meth docutils literal notranslate"><span class="pre">intersection()</span></code>, <code class="xref py py-meth docutils literal notranslate"><span class="pre">difference()</span></code>, and <code class="xref py py-meth docutils literal notranslate"><span class="pre">symmetric_difference()</span></code> will accept any iterable as an argument. In contrast, their operator based counterparts require their arguments to be sets. This precludes error-prone constructions like <code class="docutils literal notranslate"><span class="pre">Set('abc')</span> <span class="pre">&amp;</span> <span class="pre">'cbs'</span></code> in favor of the more readable <code class="docutils literal notranslate"><span class="pre">Set('abc').intersection('cbs')</span></code>.</p> <div class="versionchanged"> <p><span class="versionmodified">Changed in version 2.3.1: </span>Formerly all arguments were required to be sets.</p> </div> <p>In addition, both <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> and <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> support set to set comparisons. Two sets are equal if and only if every element of each set is contained in the other (each is a subset of the other). A set is less than another set if and only if the first set is a proper subset of the second set (is a subset, but is not equal). A set is greater than another set if and only if the first set is a proper superset of the second set (is a superset, but is not equal).</p> <p>The subset and equality comparisons do not generalize to a complete ordering function. For example, any two disjoint sets are not equal and are not subsets of each other, so <em>all</em> of the following return <code class="docutils literal notranslate"><span class="pre">False</span></code>: <code class="docutils literal notranslate"><span class="pre">a&lt;b</span></code>, <code class="docutils literal notranslate"><span class="pre">a==b</span></code>, or <code class="docutils literal notranslate"><span class="pre">a&gt;b</span></code>. Accordingly, sets do not implement the <a class="reference internal" href="../reference/datamodel.html#object.__cmp__" title="object.__cmp__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__cmp__()</span></code></a> method.</p> <p>Since sets only define partial ordering (subset relationships), the output of the <code class="xref py py-meth docutils literal notranslate"><span class="pre">list.sort()</span></code> method is undefined for lists of sets.</p> <p>The following table lists operations available in <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> but not found in <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a>:</p> <table border="1" class="docutils"> <colgroup> <col width="30%" /> <col width="70%" /> </colgroup> <thead valign="bottom"> <tr class="row-odd"><th class="head">Operation</th> <th class="head">Result</th> </tr> </thead> <tbody valign="top"> <tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">hash(s)</span></code></td> <td>returns a hash value for <em>s</em></td> </tr> </tbody> </table> <p>The following table lists operations available in <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> but not found in <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a>:</p> <table border="1" class="docutils"> <colgroup> <col width="45%" /> <col width="15%" /> <col width="39%" /> </colgroup> <thead valign="bottom"> <tr class="row-odd"><th class="head">Operation</th> <th class="head">Equivalent</th> <th class="head">Result</th> </tr> </thead> <tbody valign="top"> <tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">s.update(t)</span></code></td> <td><em>s</em> |= <em>t</em></td> <td>return set <em>s</em> with elements added from <em>t</em></td> </tr> <tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">s.intersection_update(t)</span></code></td> <td><em>s</em> &amp;= <em>t</em></td> <td>return set <em>s</em> keeping only elements also found in <em>t</em></td> </tr> <tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">s.difference_update(t)</span></code></td> <td><em>s</em> -= <em>t</em></td> <td>return set <em>s</em> after removing elements found in <em>t</em></td> </tr> <tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">s.symmetric_difference_update(t)</span></code></td> <td><em>s</em> ^= <em>t</em></td> <td>return set <em>s</em> with elements from <em>s</em> or <em>t</em> but not both</td> </tr> <tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">s.add(x)</span></code></td> <td>&#160;</td> <td>add element <em>x</em> to set <em>s</em></td> </tr> <tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">s.remove(x)</span></code></td> <td>&#160;</td> <td>remove <em>x</em> from set <em>s</em>; raises <a class="reference internal" href="exceptions.html#exceptions.KeyError" title="exceptions.KeyError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">KeyError</span></code></a> if not present</td> </tr> <tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">s.discard(x)</span></code></td> <td>&#160;</td> <td>removes <em>x</em> from set <em>s</em> if present</td> </tr> <tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">s.pop()</span></code></td> <td>&#160;</td> <td>remove and return an arbitrary element from <em>s</em>; raises <a class="reference internal" href="exceptions.html#exceptions.KeyError" title="exceptions.KeyError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">KeyError</span></code></a> if empty</td> </tr> <tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">s.clear()</span></code></td> <td>&#160;</td> <td>remove all elements from set <em>s</em></td> </tr> </tbody> </table> <p>Note, the non-operator versions of <code class="xref py py-meth docutils literal notranslate"><span class="pre">update()</span></code>, <code class="xref py py-meth docutils literal notranslate"><span class="pre">intersection_update()</span></code>, <code class="xref py py-meth docutils literal notranslate"><span class="pre">difference_update()</span></code>, and <code class="xref py py-meth docutils literal notranslate"><span class="pre">symmetric_difference_update()</span></code> will accept any iterable as an argument.</p> <div class="versionchanged"> <p><span class="versionmodified">Changed in version 2.3.1: </span>Formerly all arguments were required to be sets.</p> </div> <p>Also note, the module also includes a <code class="xref py py-meth docutils literal notranslate"><span class="pre">union_update()</span></code> method which is an alias for <code class="xref py py-meth docutils literal notranslate"><span class="pre">update()</span></code>. The method is included for backwards compatibility. Programmers should prefer the <code class="xref py py-meth docutils literal notranslate"><span class="pre">update()</span></code> method because it is supported by the built-in <a class="reference internal" href="stdtypes.html#set" title="set"><code class="xref py py-class docutils literal notranslate"><span class="pre">set()</span></code></a> and <a class="reference internal" href="stdtypes.html#frozenset" title="frozenset"><code class="xref py py-class docutils literal notranslate"><span class="pre">frozenset()</span></code></a> types.</p> </div> <div class="section" id="example"> <span id="set-example"></span><h2>8.7.2. Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sets</span> <span class="k">import</span> <span class="n">Set</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">engineers</span> <span class="o">=</span> <span class="n">Set</span><span class="p">([</span><span class="s1">&#39;John&#39;</span><span class="p">,</span> <span class="s1">&#39;Jane&#39;</span><span class="p">,</span> <span class="s1">&#39;Jack&#39;</span><span class="p">,</span> <span class="s1">&#39;Janice&#39;</span><span class="p">])</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">programmers</span> <span class="o">=</span> <span class="n">Set</span><span class="p">([</span><span class="s1">&#39;Jack&#39;</span><span class="p">,</span> <span class="s1">&#39;Sam&#39;</span><span class="p">,</span> <span class="s1">&#39;Susan&#39;</span><span class="p">,</span> <span class="s1">&#39;Janice&#39;</span><span class="p">])</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">managers</span> <span class="o">=</span> <span class="n">Set</span><span class="p">([</span><span class="s1">&#39;Jane&#39;</span><span class="p">,</span> <span class="s1">&#39;Jack&#39;</span><span class="p">,</span> <span class="s1">&#39;Susan&#39;</span><span class="p">,</span> <span class="s1">&#39;Zack&#39;</span><span class="p">])</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">employees</span> <span class="o">=</span> <span class="n">engineers</span> <span class="o">|</span> <span class="n">programmers</span> <span class="o">|</span> <span class="n">managers</span> <span class="c1"># union</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">engineering_management</span> <span class="o">=</span> <span class="n">engineers</span> <span class="o">&amp;</span> <span class="n">managers</span> <span class="c1"># intersection</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">fulltime_management</span> <span class="o">=</span> <span class="n">managers</span> <span class="o">-</span> <span class="n">engineers</span> <span class="o">-</span> <span class="n">programmers</span> <span class="c1"># difference</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">engineers</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="s1">&#39;Marvin&#39;</span><span class="p">)</span> <span class="c1"># add element</span> <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span> <span class="n">engineers</span> <span class="go">Set([&#39;Jane&#39;, &#39;Marvin&#39;, &#39;Janice&#39;, &#39;John&#39;, &#39;Jack&#39;])</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">employees</span><span class="o">.</span><span class="n">issuperset</span><span class="p">(</span><span class="n">engineers</span><span class="p">)</span> <span class="c1"># superset test</span> <span class="go">False</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">employees</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">engineers</span><span class="p">)</span> <span class="c1"># update from another set</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">employees</span><span class="o">.</span><span class="n">issuperset</span><span class="p">(</span><span class="n">engineers</span><span class="p">)</span> <span class="go">True</span> <span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">group</span> <span class="ow">in</span> <span class="p">[</span><span class="n">engineers</span><span class="p">,</span> <span class="n">programmers</span><span class="p">,</span> <span class="n">managers</span><span class="p">,</span> <span class="n">employees</span><span class="p">]:</span> <span class="gp">... </span> <span class="n">group</span><span class="o">.</span><span class="n">discard</span><span class="p">(</span><span class="s1">&#39;Susan&#39;</span><span class="p">)</span> <span class="c1"># unconditionally remove element</span> <span class="gp">... </span> <span class="nb">print</span> <span class="n">group</span> <span class="gp">...</span> <span class="go">Set([&#39;Jane&#39;, &#39;Marvin&#39;, &#39;Janice&#39;, &#39;John&#39;, &#39;Jack&#39;])</span> <span class="go">Set([&#39;Janice&#39;, &#39;Jack&#39;, &#39;Sam&#39;])</span> <span class="go">Set([&#39;Jane&#39;, &#39;Zack&#39;, &#39;Jack&#39;])</span> <span class="go">Set([&#39;Jack&#39;, &#39;Sam&#39;, &#39;Jane&#39;, &#39;Marvin&#39;, &#39;Janice&#39;, &#39;John&#39;, &#39;Zack&#39;])</span> </pre></div> </div> </div> <div class="section" id="protocol-for-automatic-conversion-to-immutable"> <span id="immutable-transforms"></span><h2>8.7.3. Protocol for automatic conversion to immutable<a class="headerlink" href="#protocol-for-automatic-conversion-to-immutable" title="Permalink to this headline">¶</a></h2> <p>Sets can only contain immutable elements. For convenience, mutable <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> objects are automatically copied to an <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> before being added as a set element.</p> <p>The mechanism is to always add a <a class="reference internal" href="../glossary.html#term-hashable"><span class="xref std std-term">hashable</span></a> element, or if it is not hashable, the element is checked to see if it has an <code class="xref py py-meth docutils literal notranslate"><span class="pre">__as_immutable__()</span></code> method which returns an immutable equivalent.</p> <p>Since <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> objects have a <code class="xref py py-meth docutils literal notranslate"><span class="pre">__as_immutable__()</span></code> method returning an instance of <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a>, it is possible to construct sets of sets.</p> <p>A similar mechanism is needed by the <a class="reference internal" href="../reference/datamodel.html#object.__contains__" title="object.__contains__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__contains__()</span></code></a> and <code class="xref py py-meth docutils literal notranslate"><span class="pre">remove()</span></code> methods which need to hash an element to check for membership in a set. Those methods check an element for hashability and, if not, check for a <code class="xref py py-meth docutils literal notranslate"><span class="pre">__as_temporarily_immutable__()</span></code> method which returns the element wrapped by a class that provides temporary methods for <a class="reference internal" href="../reference/datamodel.html#object.__hash__" title="object.__hash__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__hash__()</span></code></a>, <a class="reference internal" href="../reference/datamodel.html#object.__eq__" title="object.__eq__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__eq__()</span></code></a>, and <a class="reference internal" href="../reference/datamodel.html#object.__ne__" title="object.__ne__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__ne__()</span></code></a>.</p> <p>The alternate mechanism spares the need to build a separate copy of the original mutable object.</p> <p><a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> objects implement the <code class="xref py py-meth docutils literal notranslate"><span class="pre">__as_temporarily_immutable__()</span></code> method which returns the <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> object wrapped by a new class <code class="xref py py-class docutils literal notranslate"><span class="pre">_TemporarilyImmutableSet</span></code>.</p> <p>The two mechanisms for adding hashability are normally invisible to the user; however, a conflict can arise in a multi-threaded environment where one thread is updating a set while another has temporarily wrapped it in <code class="xref py py-class docutils literal notranslate"><span class="pre">_TemporarilyImmutableSet</span></code>. In other words, sets of mutable sets are not thread-safe.</p> </div> <div class="section" id="comparison-to-the-built-in-set-types"> <span id="comparison-to-builtin-set"></span><h2>8.7.4. Comparison to the built-in <a class="reference internal" href="stdtypes.html#set" title="set"><code class="xref py py-class docutils literal notranslate"><span class="pre">set</span></code></a> types<a class="headerlink" href="#comparison-to-the-built-in-set-types" title="Permalink to this headline">¶</a></h2> <p>The built-in <a class="reference internal" href="stdtypes.html#set" title="set"><code class="xref py py-class docutils literal notranslate"><span class="pre">set</span></code></a> and <a class="reference internal" href="stdtypes.html#frozenset" title="frozenset"><code class="xref py py-class docutils literal notranslate"><span class="pre">frozenset</span></code></a> types were designed based on lessons learned from the <a class="reference internal" href="#module-sets" title="sets: Implementation of sets of unique elements. (deprecated)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sets</span></code></a> module. The key differences are:</p> <ul class="simple"> <li><a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> and <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> were renamed to <a class="reference internal" href="stdtypes.html#set" title="set"><code class="xref py py-class docutils literal notranslate"><span class="pre">set</span></code></a> and <a class="reference internal" href="stdtypes.html#frozenset" title="frozenset"><code class="xref py py-class docutils literal notranslate"><span class="pre">frozenset</span></code></a>.</li> <li>There is no equivalent to <code class="xref py py-class docutils literal notranslate"><span class="pre">BaseSet</span></code>. Instead, use <code class="docutils literal notranslate"><span class="pre">isinstance(x,</span> <span class="pre">(set,</span> <span class="pre">frozenset))</span></code>.</li> <li>The hash algorithm for the built-ins performs significantly better (fewer collisions) for most datasets.</li> <li>The built-in versions have more space efficient pickles.</li> <li>The built-in versions do not have a <code class="xref py py-meth docutils literal notranslate"><span class="pre">union_update()</span></code> method. Instead, use the <code class="xref py py-meth docutils literal notranslate"><span class="pre">update()</span></code> method which is equivalent.</li> <li>The built-in versions do not have a <code class="docutils literal notranslate"><span class="pre">_repr(sorted=True)</span></code> method. Instead, use the built-in <a class="reference internal" href="functions.html#repr" title="repr"><code class="xref py py-func docutils literal notranslate"><span class="pre">repr()</span></code></a> and <a class="reference internal" href="functions.html#sorted" title="sorted"><code class="xref py py-func docutils literal notranslate"><span class="pre">sorted()</span></code></a> functions: <code class="docutils literal notranslate"><span class="pre">repr(sorted(s))</span></code>.</li> <li>The built-in version does not have a protocol for automatic conversion to immutable. Many found this feature to be confusing and no one in the community reported having found real uses for it.</li> </ul> </div> </div> </div> </div> </div> <div class="sphinxsidebar" role="navigation" aria-label="main navigation"> <div class="sphinxsidebarwrapper"> <h3><a href="../contents.html">Table Of Contents</a></h3> <ul> <li><a class="reference internal" href="#">8.7. <code class="docutils literal notranslate"><span class="pre">sets</span></code> — Unordered collections of unique elements</a><ul> <li><a class="reference internal" href="#set-objects">8.7.1. Set Objects</a></li> <li><a class="reference internal" href="#example">8.7.2. Example</a></li> <li><a class="reference internal" href="#protocol-for-automatic-conversion-to-immutable">8.7.3. Protocol for automatic conversion to immutable</a></li> <li><a class="reference internal" href="#comparison-to-the-built-in-set-types">8.7.4. Comparison to the built-in <code class="docutils literal notranslate"><span class="pre">set</span></code> types</a></li> </ul> </li> </ul> <h4>Previous topic</h4> <p class="topless"><a href="array.html" title="previous chapter">8.6. <code class="docutils literal notranslate"><span class="pre">array</span></code> — Efficient arrays of numeric values</a></p> <h4>Next topic</h4> <p class="topless"><a href="sched.html" title="next chapter">8.8. <code class="docutils literal notranslate"><span class="pre">sched</span></code> — Event scheduler</a></p> <div role="note" aria-label="source link"> <h3>This Page</h3> <ul class="this-page-menu"> <li><a href="../_sources/library/sets.rst.txt" rel="nofollow">Show Source</a></li> </ul> </div> <div id="searchbox" style="display: none" role="search"> <h3>Quick search</h3> <div class="searchformwrapper"> <form class="search" action="../search.html" method="get"> <input type="text" name="q" /> <input type="submit" value="Go" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form> </div> </div> <script type="text/javascript">$('#searchbox').show(0);</script> </div> </div> <div class="clearer"></div> </div> <div class="related" role="navigation" aria-label="related navigation"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" >index</a></li> <li class="right" > <a href="../py-modindex.html" title="Python Module Index" >modules</a> |</li> <li class="right" > <a href="sched.html" title="8.8. sched — Event scheduler" >next</a> |</li> <li class="right" > <a href="array.html" title="8.6. array — Efficient arrays of numeric values" >previous</a> |</li> <li><img src="../_static/py.png" alt="" style="vertical-align: middle; margin-top: -1px"/></li> <li><a href="https://www.python.org/">Python</a> &#187;</li> <li> <a href="../index.html">Python 2.7.16 documentation</a> &#187; </li> <li class="nav-item nav-item-1"><a href="index.html" >The Python Standard Library</a> &#187;</li> <li class="nav-item nav-item-2"><a href="datatypes.html" >8. Data Types</a> &#187;</li> </ul> </div> <div class="footer"> &copy; <a href="../copyright.html">Copyright</a> 1990-2019, Python Software Foundation. <br /> The Python Software Foundation is a non-profit corporation. <a href="https://www.python.org/psf/donations/">Please donate.</a> <br /> Last updated on Mar 27, 2019. <a href="../bugs.html">Found a bug</a>? <br /> Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 1.7.6. </div> </body> </html>
webs 1.0 - Enhanced UI