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/python3-docs/html/library
/usr/share/doc/python3-docs/html/library/
Viewing File: /usr/share/doc/python3-docs/html/library/bisect.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>8.6. bisect — Array bisection algorithm &#8212; Python 3.6.7 documentation</title> <link rel="stylesheet" href="../_static/pydoctheme.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 3.6.7 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="8.7. array — Efficient arrays of numeric values" href="array.html" /> <link rel="prev" title="8.5. heapq — Heap queue algorithm" href="heapq.html" /> <link rel="shortcut icon" type="image/png" href="../_static/py.png" /> <link rel="canonical" href="https://docs.python.org/3/library/bisect.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="array.html" title="8.7. array — Efficient arrays of numeric values" accesskey="N">next</a> |</li> <li class="right" > <a href="heapq.html" title="8.5. heapq — Heap queue algorithm" 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">3.6.7 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> <li class="right"> <div class="inline-search" style="display: none" role="search"> <form class="inline-search" action="../search.html" method="get"> <input placeholder="Quick search" 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> <script type="text/javascript">$('.inline-search').show(0);</script> | </li> </ul> </div> <div class="document"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body" role="main"> <div class="section" id="module-bisect"> <span id="bisect-array-bisection-algorithm"></span><h1>8.6. <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-mod docutils literal notranslate"><span class="pre">bisect</span></code></a> — Array bisection algorithm<a class="headerlink" href="#module-bisect" title="Permalink to this headline">¶</a></h1> <p><strong>Source code:</strong> <a class="reference external" href="https://github.com/python/cpython/tree/3.6/Lib/bisect.py">Lib/bisect.py</a></p> <hr class="docutils" /> <p>This module provides support for maintaining a list in sorted order without having to sort the list after each insertion. For long lists of items with expensive comparison operations, this can be an improvement over the more common approach. The module is called <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-mod docutils literal notranslate"><span class="pre">bisect</span></code></a> because it uses a basic bisection algorithm to do its work. The source code may be most useful as a working example of the algorithm (the boundary conditions are already right!).</p> <p>The following functions are provided:</p> <dl class="function"> <dt id="bisect.bisect_left"> <code class="descclassname">bisect.</code><code class="descname">bisect_left</code><span class="sig-paren">(</span><em>a</em>, <em>x</em>, <em>lo=0</em>, <em>hi=len(a)</em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.bisect_left" title="Permalink to this definition">¶</a></dt> <dd><p>Locate the insertion point for <em>x</em> in <em>a</em> to maintain sorted order. The parameters <em>lo</em> and <em>hi</em> may be used to specify a subset of the list which should be considered; by default the entire list is used. If <em>x</em> is already present in <em>a</em>, the insertion point will be before (to the left of) any existing entries. The return value is suitable for use as the first parameter to <code class="docutils literal notranslate"><span class="pre">list.insert()</span></code> assuming that <em>a</em> is already sorted.</p> <p>The returned insertion point <em>i</em> partitions the array <em>a</em> into two halves so that <code class="docutils literal notranslate"><span class="pre">all(val</span> <span class="pre">&lt;</span> <span class="pre">x</span> <span class="pre">for</span> <span class="pre">val</span> <span class="pre">in</span> <span class="pre">a[lo:i])</span></code> for the left side and <code class="docutils literal notranslate"><span class="pre">all(val</span> <span class="pre">&gt;=</span> <span class="pre">x</span> <span class="pre">for</span> <span class="pre">val</span> <span class="pre">in</span> <span class="pre">a[i:hi])</span></code> for the right side.</p> </dd></dl> <dl class="function"> <dt id="bisect.bisect_right"> <code class="descclassname">bisect.</code><code class="descname">bisect_right</code><span class="sig-paren">(</span><em>a</em>, <em>x</em>, <em>lo=0</em>, <em>hi=len(a)</em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.bisect_right" title="Permalink to this definition">¶</a></dt> <dt id="bisect.bisect"> <code class="descclassname">bisect.</code><code class="descname">bisect</code><span class="sig-paren">(</span><em>a</em>, <em>x</em>, <em>lo=0</em>, <em>hi=len(a)</em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.bisect" title="Permalink to this definition">¶</a></dt> <dd><p>Similar to <a class="reference internal" href="#bisect.bisect_left" title="bisect.bisect_left"><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect_left()</span></code></a>, but returns an insertion point which comes after (to the right of) any existing entries of <em>x</em> in <em>a</em>.</p> <p>The returned insertion point <em>i</em> partitions the array <em>a</em> into two halves so that <code class="docutils literal notranslate"><span class="pre">all(val</span> <span class="pre">&lt;=</span> <span class="pre">x</span> <span class="pre">for</span> <span class="pre">val</span> <span class="pre">in</span> <span class="pre">a[lo:i])</span></code> for the left side and <code class="docutils literal notranslate"><span class="pre">all(val</span> <span class="pre">&gt;</span> <span class="pre">x</span> <span class="pre">for</span> <span class="pre">val</span> <span class="pre">in</span> <span class="pre">a[i:hi])</span></code> for the right side.</p> </dd></dl> <dl class="function"> <dt id="bisect.insort_left"> <code class="descclassname">bisect.</code><code class="descname">insort_left</code><span class="sig-paren">(</span><em>a</em>, <em>x</em>, <em>lo=0</em>, <em>hi=len(a)</em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.insort_left" title="Permalink to this definition">¶</a></dt> <dd><p>Insert <em>x</em> in <em>a</em> in sorted order. This is equivalent to <code class="docutils literal notranslate"><span class="pre">a.insert(bisect.bisect_left(a,</span> <span class="pre">x,</span> <span class="pre">lo,</span> <span class="pre">hi),</span> <span class="pre">x)</span></code> assuming that <em>a</em> is already sorted. Keep in mind that the O(log n) search is dominated by the slow O(n) insertion step.</p> </dd></dl> <dl class="function"> <dt id="bisect.insort_right"> <code class="descclassname">bisect.</code><code class="descname">insort_right</code><span class="sig-paren">(</span><em>a</em>, <em>x</em>, <em>lo=0</em>, <em>hi=len(a)</em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.insort_right" title="Permalink to this definition">¶</a></dt> <dt id="bisect.insort"> <code class="descclassname">bisect.</code><code class="descname">insort</code><span class="sig-paren">(</span><em>a</em>, <em>x</em>, <em>lo=0</em>, <em>hi=len(a)</em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.insort" title="Permalink to this definition">¶</a></dt> <dd><p>Similar to <a class="reference internal" href="#bisect.insort_left" title="bisect.insort_left"><code class="xref py py-func docutils literal notranslate"><span class="pre">insort_left()</span></code></a>, but inserting <em>x</em> in <em>a</em> after any existing entries of <em>x</em>.</p> </dd></dl> <div class="admonition seealso"> <p class="first admonition-title">See also</p> <p class="last"><a class="reference external" href="https://code.activestate.com/recipes/577197-sortedcollection/">SortedCollection recipe</a> that uses bisect to build a full-featured collection class with straight-forward search methods and support for a key-function. The keys are precomputed to save unnecessary calls to the key function during searches.</p> </div> <div class="section" id="searching-sorted-lists"> <h2>8.6.1. Searching Sorted Lists<a class="headerlink" href="#searching-sorted-lists" title="Permalink to this headline">¶</a></h2> <p>The above <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect()</span></code></a> functions are useful for finding insertion points but can be tricky or awkward to use for common searching tasks. The following five functions show how to transform them into the standard lookups for sorted lists:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">index</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">&#39;Locate the leftmost value exactly equal to x&#39;</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_left</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="ow">and</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="n">x</span><span class="p">:</span> <span class="k">return</span> <span class="n">i</span> <span class="k">raise</span> <span class="ne">ValueError</span> <span class="k">def</span> <span class="nf">find_lt</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">&#39;Find rightmost value less than x&#39;</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_left</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span><span class="p">:</span> <span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="k">raise</span> <span class="ne">ValueError</span> <span class="k">def</span> <span class="nf">find_le</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">&#39;Find rightmost value less than or equal to x&#39;</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_right</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span><span class="p">:</span> <span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="k">raise</span> <span class="ne">ValueError</span> <span class="k">def</span> <span class="nf">find_gt</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">&#39;Find leftmost value greater than x&#39;</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_right</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">a</span><span class="p">):</span> <span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">raise</span> <span class="ne">ValueError</span> <span class="k">def</span> <span class="nf">find_ge</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">&#39;Find leftmost item greater than or equal to x&#39;</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_left</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">a</span><span class="p">):</span> <span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">raise</span> <span class="ne">ValueError</span> </pre></div> </div> </div> <div class="section" id="other-examples"> <h2>8.6.2. Other Examples<a class="headerlink" href="#other-examples" title="Permalink to this headline">¶</a></h2> <p id="bisect-example">The <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect()</span></code></a> function can be useful for numeric table lookups. This example uses <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect()</span></code></a> to look up a letter grade for an exam score (say) based on a set of ordered numeric breakpoints: 90 and up is an ‘A’, 80 to 89 is a ‘B’, and so on:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">grade</span><span class="p">(</span><span class="n">score</span><span class="p">,</span> <span class="n">breakpoints</span><span class="o">=</span><span class="p">[</span><span class="mi">60</span><span class="p">,</span> <span class="mi">70</span><span class="p">,</span> <span class="mi">80</span><span class="p">,</span> <span class="mi">90</span><span class="p">],</span> <span class="n">grades</span><span class="o">=</span><span class="s1">&#39;FDCBA&#39;</span><span class="p">):</span> <span class="gp">... </span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect</span><span class="p">(</span><span class="n">breakpoints</span><span class="p">,</span> <span class="n">score</span><span class="p">)</span> <span class="gp">... </span> <span class="k">return</span> <span class="n">grades</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="gp">...</span> <span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="n">grade</span><span class="p">(</span><span class="n">score</span><span class="p">)</span> <span class="k">for</span> <span class="n">score</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">33</span><span class="p">,</span> <span class="mi">99</span><span class="p">,</span> <span class="mi">77</span><span class="p">,</span> <span class="mi">70</span><span class="p">,</span> <span class="mi">89</span><span class="p">,</span> <span class="mi">90</span><span class="p">,</span> <span class="mi">100</span><span class="p">]]</span> <span class="go">[&#39;F&#39;, &#39;A&#39;, &#39;C&#39;, &#39;C&#39;, &#39;B&#39;, &#39;A&#39;, &#39;A&#39;]</span> </pre></div> </div> <p>Unlike the <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> function, it does not make sense for the <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect()</span></code></a> functions to have <em>key</em> or <em>reversed</em> arguments because that would lead to an inefficient design (successive calls to bisect functions would not “remember” all of the previous key lookups).</p> <p>Instead, it is better to search a list of precomputed keys to find the index of the record in question:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">data</span> <span class="o">=</span> <span class="p">[(</span><span class="s1">&#39;red&#39;</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;blue&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;yellow&#39;</span><span class="p">,</span> <span class="mi">8</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="mi">0</span><span class="p">)]</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">data</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">r</span><span class="p">:</span> <span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">keys</span> <span class="o">=</span> <span class="p">[</span><span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">data</span><span class="p">]</span> <span class="c1"># precomputed list of keys</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">data</span><span class="p">[</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">keys</span><span class="p">,</span> <span class="mi">0</span><span class="p">)]</span> <span class="go">(&#39;black&#39;, 0)</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">data</span><span class="p">[</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">keys</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]</span> <span class="go">(&#39;blue&#39;, 1)</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">data</span><span class="p">[</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">keys</span><span class="p">,</span> <span class="mi">5</span><span class="p">)]</span> <span class="go">(&#39;red&#39;, 5)</span> <span class="gp">&gt;&gt;&gt; </span><span class="n">data</span><span class="p">[</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">keys</span><span class="p">,</span> <span class="mi">8</span><span class="p">)]</span> <span class="go">(&#39;yellow&#39;, 8)</span> </pre></div> </div> </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="#">8.6. <code class="docutils literal notranslate"><span class="pre">bisect</span></code> — Array bisection algorithm</a><ul> <li><a class="reference internal" href="#searching-sorted-lists">8.6.1. Searching Sorted Lists</a></li> <li><a class="reference internal" href="#other-examples">8.6.2. Other Examples</a></li> </ul> </li> </ul> <h4>Previous topic</h4> <p class="topless"><a href="heapq.html" title="previous chapter">8.5. <code class="docutils literal notranslate"><span class="pre">heapq</span></code> — Heap queue algorithm</a></p> <h4>Next topic</h4> <p class="topless"><a href="array.html" title="next chapter">8.7. <code class="docutils literal notranslate"><span class="pre">array</span></code> — Efficient arrays of numeric values</a></p> <div role="note" aria-label="source link"> <h3>This Page</h3> <ul class="this-page-menu"> <li><a href="../bugs.html">Report a Bug</a></li> <li> <a href="https://github.com/python/cpython/blob/3.6/Doc/library/bisect.rst" rel="nofollow">Show Source </a> </li> </ul> </div> </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="array.html" title="8.7. array — Efficient arrays of numeric values" >next</a> |</li> <li class="right" > <a href="heapq.html" title="8.5. heapq — Heap queue algorithm" >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">3.6.7 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> <li class="right"> <div class="inline-search" style="display: none" role="search"> <form class="inline-search" action="../search.html" method="get"> <input placeholder="Quick search" 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> <script type="text/javascript">$('.inline-search').show(0);</script> | </li> </ul> </div> <div class="footer"> &copy; <a href="../copyright.html">Copyright</a> 2001-2023, 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 Dec 18, 2023. <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