ࡱ> UFNOPQRST`!uj?Ћtդ SxڅKP.ikӀAĩ *TPСdՀB -HN]KOppp!U w^i{EONYs i*'%'uB]EOcwo(o'ېrߕv6%Ygx݇sQC_(*]Cُ:=1+yTC1.s\X^eym|e޵a. +/+ IAk]@Zʤ}L4OCլ.~'(rM*]yqAg6-UPzHTm0xuzW^`!fWy%7n܄ٰ@ xڅK@߻k&6)tEhn:N.R!`[ ' \ Vwx?⑫ !}.&}@YW=&{AYS /I M՜Y،j%'$aޯv\+|oQcQzPw[Ζ{l79d]c#Ņ=s˂Jks^P|\T<+f8c ޣ_gޒp<~nҩ5ȾQL34T# C(`Bu{."=!J~SO'9/).*.v^RY߉QENOCEֹ0;O enEv n'^`6 EBrN֡;>M*t?܅r`!fBr@u1U ^& 4xڅkAd'?hK)"bsY衍'R!PmDE(<ϊ^qL9}; bphE批Us3efβY̫S>8{ͺSpJ5{fdaӌ nu]Vy]!.Ϳ2\ ܮ`f.HR~? hlwO& 窕Qr+𤢼_bX/_V\Sx?R*EJb?-zx`?-HK_UW`'_8`Կ`7t??3X8k{#p2x0M;S;O&8?WNR(h~i~aRZ*/kq?Z|8nތ'7Xn9A |veAqNn`! ԫg(ШLUxcdd``Nfd``beV dX,XĐ i A?d>c@P5< %! `fjvF ,L ! ~ Ay 9W^<8 '*ߊ@E Ma`$^qp~ |* *?-F0 K>TΟ \@7߁]fW1IEA,! rokEIQ".hW#6F&&\6t_3 f_`!KݛD\;44)Q^k+xD(fkw\ X=C>+,.FD{l+;-镌aC?*m؀<1W-zd=(OZTJ.烸Ҟݴ̻Qϼ=QmWoڳmb/2ڳh_j[{v7-%a^+~K&(&5Y/s"ڿ@&8r#kZbŦgT08?Q&ǑG!|IxOs9Hk9;^S)Պ+ś*aef*=+/?"kidfrJdt.WaxP;Vpcoy÷eVT _DΌpfF= Voo%&|z/F^@3=uב`!qMZ*L=LJ@  d?xcdd``ndd``baV d,FYzP1n:&f! KA?H1130bnĒʂT`35adbab Qp()J:rٗ810I] Hq`rgTWBSV4$ 2/$37X/\!(?71y``&e \Ps13TUB->(rFNsQ LV 梄 F sq5^N`UrAS 8EAtA```#RpeqIj.H p,CU`!os7Qs#;葔 P. =xڅ=hAl^6/$"&Q"%G"AS) E"b)`sFFz w ofv; ao@43O)]ڕSfWC+J(#zv +0 ]c=3ckZ}5EZYjih46Rmf9@H9oyf /=ȸsGS;~Yvclα؟X,(9JO: hMSoWt_nEƽh uX؛:Ӽ;>d+u|qCaC":>oR?aG|Q~ģeGXOzKTx\?HO=n m#Ǐn&iIhx,Xw9p] \?s.R=2fsHzV^/q>RIϓzٝ4/@- {Ϫ0hy'c!b{Ո ڔ`!V)atP1 `:TxڕJAƿ5)갰ň se"D1M*OsXX-| esvpXns3̎BMVa Nj$IIJb 4+Q] +.a <+>Wc}J6Ͱw;Xf"~5 Ξ &6m=bS iWE/ɤZ.8FNCQ&F |̌ zF1k^nw/6QUuPNG  IHDRsRGBPLTE@@@@@@@@|V@ VVxVSxV3V2VVš1VtV@PMVp|V pV   =lV`ƒVl=V@V,,@VVV|V,@?V?V @VVPVZ@ZHVLeHbB` t  O Tz".Wg?BW?JGW?LBG/N B2?WBld?W_Y fj^TOM|GF֒ƦƸW*"M|GF*GV2)R040W4WOMv"2&B(R?(WR??OM&&":ROWROOOM$PWJZOM6ZZ$.r..$Β$ҧOMBB$J2&""%%.$a^ pHYs+IDATx^\v гnI\@SC ԲK p}  aCqRi|< šGk}6.>.p64qaA6ma/oa*ȘtF‚L‚L“:}=’ҹHb8Y*ij[POc-6Jmo[`-ꡳ?$m4tS !R3C x3"_f apym7*؆_*!Dy)*R+r)eǪ9J*=z\qXM^`@+Tx$w,؆_\\Z*AXQZxQkDq8|"<ߕ۟x73y)RanO N#}iq(vpNӽJ7MΥ^OO*>0Ġ̱cT?Ƹmb` aFsp8FKr)5m#D66B4@oά R~Rit-CاNJBx}&38̵5BxͳӮš8s&Rq4Q*Jc4񷇏>""T'Mh2Jf϶dV>n&~jTI%)$IJI$RI$^ȐuU-WStG5@S01 {,!2O*TBEysF@ 6hJ$nU|ļ4ks]ul?"[e-hkjS~jTʩ$O}+dvm<~wv;?)&;L?`O]>z_TUz^ WS'URJ?-?kig-߬?G6Gÿzo_ZIj~wܑץC?T_z=T7~g 0ݿf=ubHj_qwwGџa۷tWowޟ[zԐSzzэ'WoxA۽KП}oz?qI=Ÿ8BIM-~L<-~L0$-~L0$,qKd+J+J+J9,qIW-iHw2PAJ~'<'<"#>$GE$$GE$$E$#۝E#۝E$CʧNDND7rGszHRHR7rIJJ<Lsz'Lz'LLN8LNzLNz4O<^O<^O<aPSFPbPbPPPLQg7rR87rR8|QSTTTmUUzU?tUetUeUX`IZ8IZ8[<%V|B%V|B$[)_\)_\+F^E+]un,\?.UZY!-Tɭ-Tɭ3P-@Mz-@MzA<A8F>%A@>%A@='7cG:7G:7F7fwFt6`Ft6`G6܋G6܋G6܋@6>,->>,->CJ,G./G./G\.F-F-I:->J^/5J^/5J^,:LA+GLA+GO *P e+JQ]-,R4)ٞR4)ٞR4)ٞXh*Xh*Xh*ZlK,nZlK,nZlK,nZ.RZ?>/5Z?>/5]f-`_K,_K,_d-E_d-E_d-Ea,nhT-`hT-`fT1;a4ka4kd+Q47f5)f5)a0:2Vq}8Vq}8U/7;Q;e*Q;e*RCI-{H:I-{H:F/EG|?/G|?/8BIM(ICC_PROFILEADBEmntrRGB XYZ )acspAPPLnone-ADBE cprt$desc dwtptbkptrTRCgTRCbTRCrXYZgXYZbXYZtext(c) 2000 Adobe Systems Inc.desc Զ RGBXYZ XYZ curvcurvcurvXYZ >EBXYZ R6 XYZ #bnO&File written by Adobe Photoshop 5.2Adobed            O"2 !1AQ"q2BRbra#3C!1aAQq2"r#3S$ ?T om}DfzDx|ls|euSM~ycs>{ z%M5v[Ea%ȸvu^"3ʉ-HT\辋ֻ#5K׳}v_LLxD{ˑn7vk=L0$W˟^{g?&IvX3[D|V&\9s F؞KթEeD¢ɉUj‹;o;]Ԭѕ)]{vבfN?svFo՟9[wԤږُ]𸏨X WV[6xbf190')Zf/i,ynm_}L>6DG?b^ORi敜O 8y:[-fb\Zfּb'Yr߶^w[y}'ksoiKϺ&3=OLs}ٙ77_l_]|vkOUn&#vզmDzG^f1co7^̊/~\6~U6b>d)vq#LCvyǙ>ng\c_:̹34m?gu߿y~q⟵6k^vY9xW^}x\zMןcmګ?yiDZq5wG̘{qOWO0ɞMxv#u0{~egMc%ٴa[JOm|.mb68WFOFo՟=_[L=y{k3bbc1'a[=;ͥ&Ե6L}Omf5KDŽ}۵fS]~FC)Y"2TDVDFg3lԥZ=Xuq9D7]ݝ>8}3>}gfp 3(|[ucykX:kb&&&3bHF#ؗ㧱mZ?+i1+kcmFZԭkDBl&"f&c3pv"&s:3IVz+@Tw-LuL*jTLJ*/H To=ş >k>?춞65n&GkvN,M|f1lhv~8v4q}r3wD דg#"r+&`ӲWdYuD=6mq ul|8XI0#8GtТpe Tj[ȤxL~/<_LmkJf>Kjū51o5z|=߷}7fmnq|ˮHlʙM*ګwIR=2WTnm/cgF,拀Х5z5g>.{b+WtV&vۖه/]&+Ek6LK8ȾSa0U8K=E94Zr^a!k>ii?N!<xn8_r9մ|wnG\N?ȶ'XmXC4ZVNhǶS. xI!͊=]xi[.ujg.sp艉v#*ϑhyon\L-&D%xP5+C8Z+) CH%U[aemyHZzsSbՔղ)mQܽk9LJb )dfu>Kef Sdj&6uO%L fr%0AxZĴV"W- D^a04 4?QK^s9f@ *Ʌ+9DL`mxERszv3.{PJ @ b !`IbWW{h5aʄNE"VGlYX-UՈ@JaornE'Zʓ^Nm iN19VeFWىg;ai;e,քJkVՓLġ%ULxj.z!::"0l`@6! !Fp0aya*J ڙ־ Dq_\a1:6ڝVόʸjWо9_m遮QDKM~ 5G&>!z^DCḻYLH JZ"-5R{Aljt)@UMu/e - 0,&#2:B"sٵKlj;"ц7Sj9܍.ڞ|NYz6JG0n)f\XIC\TB5ꊵu\DDF 08JŹ#\ZqޥEf9ԙlqmV;6lAMmmV΋v垵zZ;`CU+hF+DJE0̂Z2 !k!%0|NYa}YV쪥"rz)^zi-D5t"g{,eiHS]s9l̟;Dye~r=FmscXҵȷmX?{7>WfWa/T^Ҁ6?Twehˢc,VlvVzY)J.BY[(c(>?-;gE,=w+ӟou?Kl ^&?{sӄ TG|)x_|ǩhrw߅Kkn#1'm#tzZoTƚd T=|wuf*j2^"?D՟8"[ V)XcYy]UM&wW̗ ?TY씢xZ%9iKnK]r4XEErVl d)ղdh!*2@ޢƷZZjc:|>5f?n\\c<vJnϦ=vJL{;?^mv[R6?TC-lJ95sV~W"L/ˆ25Z.bǒ768rZbAXD̮QyصmZkQ%z|WDxtt+S٪Xg]cΙg1W{~3ΆY T)o\4(T`J a NX 0kV g_>zfr;M՞Zq?r:qXm4IoXmO|~gtEc?q魶Kf*(TL7"2v#26&z2OqRai3UL09FvHZژ hZ!X^$ )NZ>wԼͭմ/YO}<>#IzÕsmyʹ['ZgXȷmX/x딠TH2o-U) EHPA|gLHNU''r "E,zO?NWY|vyv?dcpz{GZ|vOJFӣ^b:i[-̭»b/Y17j19N?z}xsqEK9Zubu<_ J[\kg?jguin>TH!_E"-tڎANNR0$/=OYkXYcajԎap1;Z"S{NՅN0Zb1]>ϱ^"?{OzTK; &\ۥ/͖v\]Uܙ;&793)IG}v[. v^Mv6Dz62*뎨Zj=hֱdB[Dʶ_v KnRwKuvLl͕O1x.Qgע>Oo/Ϛ~UcV>t|-YkG}|NTkZֿV"">&vCOE0(LV!Ϸ{]_+_zuڷo^DtS T)V&TL-YRe1$Vz܌D%NA(*̂=2h峁B[0+($A1+EAr46BZ!y/J^>f'JOqDZmIfY?Govmvzc¿%ڧ?컚3?T69Z+xfL X2F BEEf\L j$Y^ZXYBe D-L'&~q1Gñyޚ o">?tGjpݓ6^I`=5TH2kxg0eQfȴ"Bi  \ W2dʝ229ؤ-ZVK $Q (BQ h  )d"Y6c>7-mof؋Wl{L8ѯU5Dž+!i<ŦOňţՇ}dY~T `T "eYdZYҬ5PeL-XAzWAK2X M e~w3~XZD `\ B BE$L- -_ u2׭kDazq)19"~tޯ{ԼMvחV*wg,w^-mÏDZo?Zߝ=/n>_GtɎ6?TBT9T*'Va\[ DdU01*[0#*lb9/9gmjuZUω3%e B&: VZu6F53UKuBpQ.b !l!% @@)H:!Ϧﯢ%dW˻=b?W3~Gw'_<5W~w߅KRcg׈4|-׎^5@T0+L Q5kf eQ!8F Fa]9\JuV>͘퉅/jY|5WeaGV.}qѫ=~ "R 2%[әrުIq W(RU0޳+hcαyyެ~U//1ˈ/lEm>GnJV|""#腞wrxUԘx^chz.u|PGTZ3Qz Q0JL"e5WVqts:e϶ahZ.݇a}~ h/ຶ[brb]ՖsǗ72`( N$+cJN]ZH VZ!.D$?w3]h-w㯷zͦ>*^Y~>|..0|xt|7xEx^E}j~=(cTZեf֜VD8>oͫKv^&b)n1}3ٲ18Ky~iΈ3Yſٶu_MXͦ"=>[1mkG٧?7Nُ=?ξ79w^jh!}nN~cQOL">;!kvpkZ~U-}3̸N4rf~eo1Ov~^7+4^/YxqԥoYۤ>]hf|/Ӽ7>fbqo} Sqc[1}յq_HSVGq.7ywzceߘ ߷NԼ[ژ+\n/93?2R+1=+\Zj~Um~]4o;i6Y-q|~V٢zϳ_f:mHb?m۪ϏMi~-~m?ɇ[o;gFcW,/~a֘ڳ=5vLjpۇ|]]m:O/?UnGv1_gӓmߢ^zM":Mӷw֟Mgϻ/pj;11>awSL<ޟikeszTOs?N[ox鮷b1ξoX$~؎8|7yGK4_?gVɏ=?|tzw~]Qr~]ۧaR"~ [-QllgOXUiG}~b?2zroõuyr~7}-liVN٢h鿗қ/4foZv<ݞQz/=?\L[|ۯ\geHb.diçyuoͲqe/iwc5o۷ۦ> 4OMǿ0yhZu ߦ-/kˢ:ɟwo+۵t[M筧-d=~Wx&c6̵E5 <ɦkL~o9|>cO5#K;v-\a%>_gysjƸͧvj-1Z}O.18m_RqiG1.77ʬUbmcCAĵ~ ^Nspe7Lkqݲrp>m^nf+zBf"33>El:tEogNُuKo.јͣqlG'ղCet߯}~b?/~ޒk84ݻi}YS?xOS1ُgoi;۾~]9NN{kfoֹۻuprxܽQE>1j:h{1gǿMsouϏ3n}ralo/ӾvOa>}M7an7-h#wogMyv13g_/yf>\./SE1jτG۩O3}yikeszF^z,uܘz}KMq}#4ŦģODןlV"=3k[lW'ÿN]&6Dg欲 nf+7S9S1ԜwCnLۉ|?31G^{ղ&Y"=y_otZz~9}mӶ"6W1;;uGm쭵l1Cn퍔ʧ|9KoM&""f>9;۾#?.󘟢ˬYb|3ϙo>|gw3aTݢJ1LB؏zLL2[+аV^J"X^!(zEgjǽgԔB ୼QY%}ptc Q 4 z%ɔ;T몞3ս"x$MusDZ}T?O_W~{c_Xh.kwSSo k[[Kcwu~_ȶm0gS"[uϭ[6=̥kz;iis4auMwogZ*`}uuT[o5wMa.[\XHcEqU7f+)Nt|qJ6qEc79t>K?$Nʽ@5"԰v5e@6 kq]S.7߬?"\L5lҫ ~ \LJGI$ՊI$RI$I%?U '%FecLY麧7c(Wgߢ 5jSd #u[@ź'#=E:LIֲ^nP˻;8 'z'ԞK(c7 YۻE[FzDDu $Jt)$IJI$RIUʶa[[cCv17Y&UYcsH$j?t%$SefbYӌحg~7~+mվV[zlvG5? t9拫nc5߹ s=oWekX{+~Xi1}t3KAq$v̪umTjΩf_|+3CZ뾣mٮ]S'#u{}1ߋK+UbVeXn 1mZhh2=<:I]Wpխ2Ct~|t=ZI$!I$JRIX@LH@SiSŭ"Te5"5q(9@ Ξn LxZik<c?5?TI%<K/*uPz'=߻ͺR=KYrksYV5]>絾,2b-kf s齟?=_ &+emXap?NS3bܨUO11dǙtuO =[߿J68&uВg~ݶC Wt솽Z}[ n}k2r?juVkF>A&IWm mPI$)$ph$^ݏ@Rc nikK+j *0 `M&?w0^ncH?ՃVZ&uƸ ={/`ͲO;}?v H^#STI%>yjf&u^DV'{kko8~-!]Am[뷿zWQ[2Jƴ]`;+c]ޟoWoROzNV>QeTcIvd` I*ikk-kYf/c=z?SԻߨyٷ{w6{\-hks+~DгCw:M$?~[?q;UI$Ŭ-t3]1BΦI9n8FRͻ8V{bZy)[X854L%oM)zo~F0oXI6Y7SlwTH']XƳz65cZ`OTʩ$ڏ=[}yw?֘Sq~'zkmh ,UϸՍ?*Dh;}}_D>~z4vϩmSϡq?~OI/7H=?SԘwO۶o|ؒ~ H=~o i=w:lOg*$?G;7؏nSv?' }i~־WlI4umO;F5ݳ۽] !_у;z?A?g>A|=?8BIM-~L<-~L0$-~L0$,qKd+J+J+J9,qIW-iHw2PAJ~'<'<"#>$GE$$GE$$E$#۝E#۝E$CʧNDND7rGszHRHR7rIJJ<Lsz'Lz'LLN8LNzLNz4O<^O<^O<aPSFPbPbPPPLQg7rR87rR8|QSTTTmUUzU?tUetUeUX`IZ8IZ8[<%V|B%V|B$[)_\)_\+F^E+]un,\?.UZY!-Tɭ-Tɭ3P-@Mz-@MzA<A8F>%A@>%A@='7cG:7G:7F7fwFt6`Ft6`G6܋G6܋G6܋@6>,->>,->CJ,G./G./G\.F-F-I:->J^/5J^/5J^,:LA+GLA+GO *P e+JQ]-,R4)ٞR4)ٞR4)ٞXh*Xh*Xh*ZlK,nZlK,nZlK,nZ.RZ?>/5Z?>/5]f-`_K,_K,_d-E_d-E_d-Ea,nhT-`hT-`fT1;a4ka4kd+Q47f5)f5)a0:2Vq}8Vq}8U/7;Q;e*Q;e*RCI-{H:I-{H:F/EG|?/G|?/8BIM(ICC_PROFILEADBEmntrRGB XYZ (/acspAPPLnone-ADBE cprt$desc dwtptbkptrTRCgTRCbTRCrXYZgXYZbXYZtext(c) 2000 Adobe Systems Inc.desc Զ RGBXYZ XYZ curvcurvcurvXYZ >EBXYZ R6 XYZ #bnO&File written by Adobe Photoshop 5.2Adobed            O"2 !1A"Qa2BRqbr#3CѢScs$45!1AQaq"2RB#r ?D@NwZצJTƼ _њ`hFLʾ͘r4f}n.8#;>-)wQ8iZѢwEXf&+|: ɘZ[{Ea]Y|o{ct=Mo5[7P\5206tꟻWB" """ """ """ """ """ """ """ """ """ """ """ """ """ """ Nf C$s8)[t+&6QifY<n7Z ݷq.({d2AJ8"27=o@@K3o4Q:h-ٸ%A 0{fq5qo5i׮{I]>փ~!Dghjnit9Uۖt׎g(߉»տ4̼#,6q{Fm߿o6 \G&?ّ1ٿjvFd3h\ V喝`2ᛇgέϠ{[zލ,Xj%u0`l<"n ’(Svl7g%Mq Jʹ5"zH"`ݰ|- W.@IoP-0c;T%ť)ٺ[I# Ne~iuxZWd1jP`71!AQyEN bEjǰ|NL 13rh ֘Jb+MIl8 Mn 6n{Nll (H6)"pHP+ALk.F+b)25k{.&\؉F7#^oQIs_TJ /x"b;I8ͫKV 76,PbqUJϯDU%BEt`(O̗,T >VPK`blC8 exuJDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@n^FS&9U|%Y\D}=o*ap5;wr9zUm]p!OQ[O~f"b:{9 LS/'4V5ڇyh-1΀ Rr}Q-z5~N5Nd}Qo~+MQuM W/~y[M-{BFOQѦ0e㺻p7Ɵz놷r~ILQ.9e5^ٲmb3WK1.OAt^˧M:A$ Iѽh 6u{rn0Qvl :eHkuu[2WT,Fz(i5Vɵܴ"Vdv/4$ݳ!e8B@Q30|{\1T5N ÿ3"). `¿l Vpkd *+e)\FSPd#E;B ~*WnMks71  MHMFRvjIp6WE*ͱ XA*7E@5k:@ğHLJoJ22PaJPLːԜ@?fmWa`h6Nq@ 7}Rr6A@~g*4s +#Y핦mYEk6OtԠ=mkTnae8PVKy[J ai۝lۺ|5 _BB" """ """ """ """ """ """ """ """ """ """ """ """ """ """ D@NOnIŲm\nZs޸OͻLv 8#CZ&Rd?Nu(wǤ"'D""" &;Rͧ*)fd`xOuu-.e5Fkjrl.gO>;i\q=5R+*Ir7ܞLTq or-j>\(pan`T́CόJ*)=(7m̵$0 dVt:OqPdžzG9T5*6w5=$1{NzvNĺ2:}u۪tVEsu|4l[n>\;Dtmkfm]w\5*^nV:INbnlM7k-I8a =>֒7?Q*MA?-,l.3o۸MV4Z! qMR5ش>/Selp8n|xs7O^v,~e&|lL&PӆLi3WQ2d(CK/Z5ێN=θ~R»Xb&ỿ=FV.P?nZm7*_*=igލ AFa83UxQ`hi;f1vy;6W5PRpdqԺ@Fe8+{hu} W43')ox'Wm ʬ{4EBԽT;.R-t3z""" """ """ """ """ """ """ """ """ """ """ """ """ """ ""D@O;yq+OE8~[o#'g.6vrᚤk:3eg^kMDH9Ytζ.[e 6);i]zOy}P+K!ne+9ʍ< 6'vhIeƤJ 15g!a>e5h EfjMWl jS@vI C*+FVM@ƃfhPܼہ` hmҩ$Rc÷Fط^ݻu 2NY P2)o鵫spМ{ϼ 1SAQüff^q6cZKڔkV؅vTҹW̫9:=8^:NP~2ëW Eԓq郟BMCM9K~K¢M{>imv؜p/YEΤՀsĞ%vة497G`kjSJS;64`6 J0l , FF"}g^mGNsFb%A8OeqٽM5=8h1'[~ ߣnlz(""" """ """ """ """ """ """ """ """ """ """ """ """ """ ""D@M>c2WnM}uv f6ǭЏ?5kuԯҼSO%cԐDbHիN9>$u(v0 >suԩTž }3woi/޻&U"N #}+ͮZufLFG]&`VqLTm& )UÊc=2e'ybme7cF8Z}-Ȭ]:Rݹ|\ "Ǧ\j0f3}FFd=S m$omwnYr0#wJ?Z+5Bـ;'}dze d͞yizh}BM}s!طKO=YӮ[=D@NoY׵֔Z\\m/ORhN{=Xb@|0ی͖essk&OwPjwh6Pi@p5vJ lZ'5"T]Dde=Nݺbs5:*od;ed߆,~p@z]骗iv#+S;:]wU؁Z*']c]FH5VOyЙVIfO`X* MR b)_1f0۶ϴwXLz\6=4W >Y R"vmnk[odon#n \L׿l4ou+€ f/if庒ٱ4A# Ԍ%cָJ-; F{{of3_̵q(A8vIqF=ؓ2;㘉KzuD~׹ZՔX]Ù]QbiLAe1HTt*psXsӷDo)]""" """ """ """ """ """ """ """ """ """ """ """ """ """ ""D@DDD@DDD@DDdoty}6pT w41ƽ ?Q҃mۻ^<r,io nY]#=$*~D櫥8~6YP`n햽pd(1*ɎF;RŇ ԑ<~Iϸtmqmj+ӖK޿TrޭYsȲPF<4">YvL$n익{֥XE|M u7m:ʖ1ig˜pϪ^ުەejAKre$JfȦU8;i'h|'7EԵxTT[f[\L۹f8נ8 1^y_*R Ҵ߻u4wZ+M圔b/̠NTEih e襆J]ֻ j673Q[f=%{a7q axW}g>mv& f`?rUìe.锡)_ouT|f:Й}Vq3Cr.6+?ZmS@"*/Rs?/Ȓma:c WMR.ul^Q.@hʣ) qj1M+0&;6n+!fTO5ڥ0sP(x]U5u4uʵxwgM}S-dn"->o[:ky>k]uH]zs.elr}?5m۶KGbҲQW2Rs7׫[JQ;!?D@DDD@DDD@DDêf]=Ҟ GƆfvwGh۸nn@K Mu#Ziwkk6U,?4k0 E~ٲu諸e*һX~Vt֤;4FZlPhA%Db3Ss囜aV+F`G4j]αѕ"o-rhj:SlKNSl(6ف|^{ۅZ_4g7=Af$b6ea{ >Po8 EE#{";_ꮵ;Er.r4v9ֺ[^ /i#$AI5OgLKCükYɠ"Y7KZۦ.>QFūvr f'gC:{ f#<+Ko£50fFrͳu@kZ}q˛mUkSVaAPuwLD!2.]2F3C@qCweU9Z Ysxt g|%sRs4WR-ݴ=Y,֗AudrRH$%X $J>RXPh8Z/hRUnfu]e³}.-Q\N_L峐 [I=ۇK3oueUUn9!e. f&R--_ߙt*n2֘N5V]qUOpA~ uK/]gOa[OBijʹZN}o[pjҩ"7i7#m5B׃"=fF{ke*[ZSonk맛|F[2V L<#7-*fn q/Pc4pĒyyjj˓f{\/M+eM7>۶_Z=|ScZuN]H~.Oli5su͜ H%}+m&R(1937 ڜ>LH+8*ݾOؔ vz[4q{.fR(oeXDqhz=eTbQpgoLݹݶr8 &-yeU_'[kKq*kE8>jduh֦żs |Svw>`%;\I- !Wi&ຆW㊜ǯLL{PLQft>DJfzR2۞Citܣa@P=ƙhp8KO{58P68kJXVdG$RLs1o^L[S|`w74RrF* F04*63XeR.k/9d9#  bKp \؜7[+d́CPg{io=LzF{6e8}`ұҵW^ޥ͐h(3/+ljI-5IUT?1-n'$ҕRqͪǧiCs.*4 )ƀNgY.FӅSlkKoskខR*?dr|peϑSʛpgUe'v[m Tr!ᾯ93&Z̺mY=Դi xZvӶ"' ST6Wl<4H!YחM4?D@DDD@DDD@YiQ}[*d^uª͍?շj 8֣|>dfDXfn^Że{3ZA<߳F}3Z42@Kf<ƙsO7ͬNIlN56xz[5e* cE溭3^]*703'vq틭\Nfڶ{ 6Wm.kff!t ? U l]B-8 duܥJLFL|M[onJ޺ʥ^,M>nY( + er׷3xtgykmHD2`;+gEE*Vk6[j25tw `֭Xb jW^0ᵵjF#ݳöu4#*yfÇNr TW#\z,uj`KyZ\SK2`m_ JOjjַܸfi=}1-yp- ъyNq9kUϜpP Ӟ^] ᧗iIٰu Hۿ3~٢҅C()Ovl][XT%ͅ6QrApU@a4#hEZV@p;O|0"z\˗qc Ȇ $T}<ܿKylY{vVU9l%- 86U̧qy{,q7rxqIc5=یlmHP=׷zvMXx9yx vʬ@ͰUDE袶֡ES}3[mԄD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DD{3\;}@/gLoqY=mŔޜot'm\;'J^56?D@DDD@DDD@Nuy 7_@'tMi-.c6[n;3\[Z:F>Yߚg/Lоk;x~7V.2GM;w̓j4kmŋLR qMikcwSd3& <7yKb[sua70_reƦxfZzk 4A@(F%3Fv\+L:jlKn DzFIsP1d)s}~OyE`lP\6k;A%[ Likvsb&If?zju[mR 6o%}s:nrup]ŰQqRhEO#"й\k牙7U+05iHQkRIߛ6b+B SioY{7)qKw18uSqTrJydNKmu7o 8-msoٹi7۸<Ɣ=Z^&-ЍI(xje ဘs EF +:]4Q"l|SNŀu(훪PEI*VZ6T6۠#J?N,fȧ9 s%\Vn?]r;yFk,EٺN5~3˵ʩ|Pl2d6 o "U&n*4FVB;0gƽOss F7 g;]}6O5.ΞR2C_2rY9( ƾǙx'FжH*;FiuPX  +.~Wl5| =Yԯ)T%8˹yM1Ζ:wz.ʼn\]:ܝ=nWUKmZfai/N-Cp[E6֤2S,۴͟KLҋқqEbf=72[+(~UoT]4ece*H8cIr~ƒ8~'tQZ$->`~KP² m$B0,j}euűUV#2ny{=Qp5kmRNUg^]fJ1=̑ ~ѵrż9~zq˦5P {A,۟Kޖ4G(Kl+MߚnNbw:K""lD@DDD@DDD@DD{\\-h wTznmNal2(rT9g^}[kலD,›wMmGTlZWzN-i쪖P W< sdxu۶_1ܼlX?"P:"]9@Qu$` 4>Y5ljt{1y=vli?.JώjSnSm7ˉ5΢o6콼m 38e4ujmLqFVdQggp+{>t<<4[|\san9d8W.;i̜.UqnT_>^9鴶Rۣ%otLq2oy*rjяJ턻Et3oUU۔z{v[ z iU ү[uZ M WoNWO{ ׉lPNSMʰ-epRlV)P="+ky0tsPAPrֹ9r`ʠTj?2z`p8D幄=={..!«u{%-?](gb^e ')VK[@d\yӣZRz`uF9%|q4ۑӺν 6m[m[%Z0Û3OMwWv(`% r72ŭE\`-p T7?U2z-׸-S1`[5s\f[[4[F 덻vכU-Jx9\Ԭsܩu$6mmcM~gJTvH.@;N 1?E%Ȯgfڈ6L.\e@Noܞk`t桲qr{tF]R*xdr3ksis !\3;1_z:l]8QOSnwCܪ%.\+/iU yZ*ygPZ% 3 mi-[qVڃShQk[ŕӋ޾] ֲaN'ON_ ]Gm8 7T5|չ̵x3,4r5% -XvM nN=lzmTjQĚaq\ǘ`iYYduԺ W=%˦L+-W#RrQe8yzni0 gP*sxk9oʹ .( J8?U6J$^屸Ç._$>IcUd*[vzx-~%*7- 9W//ß5:zijV@Y3yŹoYc=5ւgS6sΦX[ o턹_f7m̠ܵhsLQUFvbtuHƪGfLq.iD\6ص!ݚ/0a>IkuqPPT 5fQ}K-74qi:-FneFloi*~QeuE_V%ħӞw’+E qvi3(N;l~]%Z"O.V3(5;>߸d"tkFS˚ܝ;cxWd;3-~Yg.(%G&>.V= iWuw4J5(W%mgJuJDJ?D@DDD@DDD@DD&UA@=sM\po5+Y[vTݸWnV>l`v 5.I1\ 9p4v)鴕9UAc:Ż/d*Eٔ/G+BR]`P[)#6:}: V85-22$(@'NQtou4|W)O6g+_pF l;(|9x`xEEf4To35Val@4:li5 2fMCerݲϪmf)shώzվa9AnSH`K&S xԑJl+pMdoڗ˕Kp6:wHkS) B3Zx1.'f欨-ww†T+YW޹ѕ-rZB޶–|[+u"fs[qaƕ>YٹX<|[=-9{xr5zKlPqqzi`IƤ+]3j5bR ![i44Ukq0*<u3ۭ~aʢMu~[)@,1ˊ׍?ԕ}/Hچ*gu#yzg*9-S9H |E,ZN\@˂i2wFӳE%8֟=oG hp_*y^'VMg=!+`l-jyNߏwb"{Y""" """ """ """ """ """ """ """ ""D 5ɑ^ddff0E"$Mdyɑh""ypzlfV]c= {)HVR϶gKygaqNK7ڤve?X3/Vm%HD@DDD@DDD@DD1!d\X ]O"`qg-N^Wv>\Īe68OYw %𘮅;p4ā33.{ohjQh۸!;S974j*X-\ I'ޞ(vaf@s(4s|!u}SYv3jfTalֿkׂ٠`NV~]!Ƹɞ?,a͟Iͽ҅/trK ԮKN)]0\9л280ZP ? 2)J ڟaf je<ΒUn14NzfPW)?#4< IH+@s\=b .]pJOEf[A%h ^c3 \`hhO0oFWwGJQ0t3\{(^9vfʙ\gg,v@Bݙwt~G*\d 3"sn[.ZӬY7$m{NClV86W/ޙֺyvP&>['\1>Uk30KJW  oߴ*.nO^*..e*8 `ry睛Z[vߚg>9=^7^ž]<5NcFƃ~Ϣd5+lTS@۴l†#Z=OlZlCPqc<Ql{?oML؛dۯhk=JD 7&y`2歀ҌҙV_c ʯ0c&ˆٌYrJ,L0ˡ`c4ǚUeK!52[VY=kVۍHD@DDD@DDD@DDh+&Rs-W.`V(^?[xHZЅ@f޷Ovơݩ5/cԃ\K vZmDld\N'~KںuW1ħei$U5̯e [2>eִId QEڶye[j6WP-|2G1xz-mLMZ31O?TZ{tE [o~bVUvP O?m}$D@DDD@DDD@DDD@DDD@DDD@DDD@DDD@DDD@Ln&IG%$R\YDDLDI"Aa,%Di$-T fd A3u6#iV'z;Wޠ:!@cLw8Xi)u U"dr]f <+_DMm[0DMD@DDD@DDD@DD(K+vWu1m-T;,䱩'>C ,v*0\D5J׺XSh?SQA&\c*V5z3k4{n%YOq!+fq }~N‘l+\pP(-ڞ֚qY׃`YYǙg`{pqem&Ky2A4~^vlSOtmUAf+F?F<~^u7,tăZOlS{iZo<'.EP@tN-XQm -=&n=A{cXP PcRWGW;da4zK) ^nS.cL kIeF+)5fDGq߶TW(ɀ1tfFN? m$)4 '=F[zDN&\Eq?DLlEgw+qY҈d -"Wgz:t%""tD@DDD@DDD@DD2 r4F$+\T^\:DSi;p1<=g{X)d%ei9*X p }@4j@ZssIew mVS5Wf7Hɶs\]sY{SSL6БPYO!K76o[ pY@L[ߌOز(0 RW&V<<*5~ӂQ1%aپtl ꐡr5i931؃&"".5_!p%lK6տpl*)K(%f}%2o4$ $l `@ȃ1+Zهg͛C`ֿkOMJ2]-r!6ܧcl}bWb"' d(Iܬ0ţ c$(%k&LH""AHYYZȬ +1 0dI9$r3s*lI I7z >f>,v}gU/l_Ә-Xmv":i1d""hD@DDD@DDD@DDuŻnbcL(qh|}Pռ)S8g[tBj.e*{<rOlٵJ0cZn=+$;Wdc1-]lΫ\( p VɸKrm71,J>Ojv:Xb^➿u}%==I˪IB o.v_?x}N7p" 2Ttkϔ9-S-VR29a@g|Dօ=3Z35oYm+Sp*UntB(8KJ"],7[CmXXaJbF<>Yr0ԱkE? Fe[P6XV %@\6$H 7`TSAd`eR'O^ bC+M(L3ꭺRs -cA1adlʲfF%IZL")D9ebXDD"V)")$I#DLZHlճe? '8wWfRPU(c9Itc5ӭ<`qw7fLM*6Rۊ'>:Y4?D@DDD@DDD@DD 9IycӬ0҈ Ē|"bEbQD@DDD@DDD@DD|9p'$2,ƀ vmQS)͖a;=p˖ {ɕ^F'gSaɍ9iS?I"OR0r7m'3W3ksՖz3_y^]u-.B,-yroP5iM+)4 g\Tx xi]UeA,8o䥫;w59y|NMF]K.X%R~',ݒ<2 p FWQV]kE-P Y'%|+pxtζkhn$퐽;LV[4=|9wp1ULbM_6T5gRU.{a-{AV\1ŰRT4qbzEf^af#) B9to_k2*e_6F id[ԥ]Sr͚O*D/nUIsBś::vH 1Ll{ޔ:\;XbHn~Y"zЈd^$"P\cֺ pM{YwQR`DK0)&X"" X5&D{f,d9MeȂnr2Y T$B"% ZimmQ3"DE`EfU>VZLۚ^,ڴLmTtbr ӳoG_DDD@DDD@DDD@DD2*pY[oB )-He$wsoԭW-m[͙+x/=vO=5}6fyUP _I |(`Oi1zSM&. /e)v.=mP`3NEwT\ \ntq|3nϸ^3:۳lT-s3O K`}& z56 iCL͗?gu"e Oy5yWT HݼLͺ`xE 9޿5Bs2[8iSb08GxH5RHwu ҵ[Ms*j՘Qt߻vХШ*4 ]ԫ[j$,د97:*k«k·Y&Ŏ}Mֶ7ˑ/7ǠW[[|.3Ne_/%[a'&R*+<ݞ/IL 0  =^JA -OMdX:`@g=h;Pfq@͋v3K`ae] q="dbI%Xa͖nYFdƚtZlrifPN+Y` OYkIEe`qό]ь3#2MNyb{vΟDՔ*;FAmSZeQν;zWB" """ """ """ """ DeE0A\.\<Ɇrj&30heHl\I&3T,ȶDI,ciM``dXMgaIL%X23"j̉rr"Zk%ٔ83ăpKrf+(%^׹vl"a2'rDHD`(8@e'cW[KooE~'B8tV_ D&爈4GD@DDD@DDD@DDb巶RHR@@v>&AP p}sz2Z{A2 WQ?I2@ +,(v6N'&ٲ"0˳/'l)9}z jd-_bVӍ=}I̢yf='*րJΟTjVv3Ҵ\¥]9nbޤNL1Un8YƹhjR*6ض~ 1nzf/u4:luB ?~YGcd+W|3ݿE|R-4U)bA(.) =zpXkhUo ,"^<OB7uib/eʹ3+Uv jil@F M'HV\,P-.grֽLj AqG#36M)C] ɛ0>3]JڻB@9֘7w̯uV\qm H(Iʹ³tH%A^g= b.|mUօ m+R%Iׁ݇v);Dl|j5+;05Cf!N>eԝBƤ\z҃arpܪh84s=l-) A%c_sCo‚l}#[v.åp .TiDOj*ҭamKeA&E5ɒ Y&3.iX$ 25+129 d322..2 `S,Ε7LS"_jaspBdIȈV@BhuM>u[@qA4?vRxJ9.>mw Iү|jmZ""hD@DDD@DDD@DD2 q=âjV ǶC)8ǸLZÒˊAUZWdO锺ǖAsLN xm-.帷Iwp7ŚOF}..RC_<֭֔imDZPPOyv.•#8zzs?Tzm:)vaLۚo[XgR prVHzGn(FSP{q3VCԦK኱NWLw pmXp>`YOQt*qS +,nQ oM0>\.-Pơ[f_/5tKZvnUY[22ÏY;"UPO8!ф{QuTn̈́17ޜޙr2&F |6IekI̯uS+.+|kh/ (Ŧ6)x[  H 858t ^&޼^\wVIuvRW`T04Z>xdl5l1f TZV37ng`7zvO<$1I>ffMFET64WX6Y-[MO]^5Z3-m vFΪ'0t9H'3nrj/|ʝB{1Gax#Ʀn&qPV_,tk]CjÛn} Km88gteӹ)|-O>u/Mro P&x folF5+z"'i$3@eecZY"D"ɑ&DL$D#Y&X&Z 0%f6;L.fhdL d$D H5zC@\ۤuGIU(9.ĉ3O) -6cXHD@DDD@DDD@DD3wRPŬjy6 uW]gU|50kϟnZһL`pJ8&U8eL8vRV\Rj@s+ҝj-`VǛʫ7=_Oa2/ʁ#5_˞{I-̵(ͶQiJe$ ie4mqe-\㖣kвrٙAi̻k-= I*Wɓ!24muHcMŴ']uܳ̕s"oD@DDD@DDD@DDAEu,@=s*-h }NUI~αTn8l=ُ{fK#6$ TDt0= #Tw~/0U8Z[Kr}K.N-P2v{^{Mzf嫷/0F^nf9e wzzzyןд QP .Wr44UchiŗէEF[µjOfk6@o1P )氨 ի[Úl\gP$6;ol*{ݥQmu3Sfޙ9Rhx6|j 6pSfgT-6/lfcp`+@1 唲5hn% ein야PyvLRX0 k55 @xԚI9$2"LƇyRi`rR9I>nMSaF<9i8xc2жN@~ܦ@@|L*Xbdv( B? l-Z0#Qn:m r 4èʇ>\1;#,Fw5P+'m6_U>r9j% kB1sye,S.b m'ni35ּ$nV7p_ݶgɇߕ0Rŕ{c) {>k힏sJXs 0a7yv5IxNts]YSG5 =  -(Z2!#.L1V8J($LQei"S%%ZySrUg;̑bVOj2f&ELV^E$&D2 +A2$H@R6D@2ee,Tկoݝk)9[:U(5}2p\$rq}uMzmޝӮˤ1"&D@DDD@DDD@DD2 sz5F\,)+["W;4bi明=iSZGA;H2glf +3@j6@ZUl]S@keO;N~\7ͳhd9-[?k}7Tt7)h$^\8 @Rd'd ֠*+Jͫqo5l̸ ښ H)39GOOtl?"[ @.^|Yv]KcL+fm^P裇l9;d[|'0={heI5'YG4~oyg.f3 ww|d0)IuvI F2@&Xt>"T8R̝h{ND} կVJ㏗5<3[V,$PPmTXo)@Mۢ_oR=DDD@DDD@DDD@DDD@He7QXLdKE")-d-!eYvM{l/m5`j.L#lƳ&HIiKrQ13$f6n[3g+9V*E%RT"ID"LRٱmk0*ͻ+oX 4$Bp=ZqQ5mߜqN.F(Txf{eعeo̲/Y؁<~s7hDVqYj7ra޽h\? #E:zakSzlO^߉>uN-w|*~VM>tZ¥Ny{njme.pd5jLK۷#fcG8&عי;H GyS ]8;4cJQh?R\u@w Lk)/f٨7fm*1[*j|w4Bپd2ثQM&ާM\;]lm7&tf\̞]ݐ-cItw[ m8|+itm# {~lXlќJcS&{g8:ڎjKtаmNzn+ Aa' y77J2\;wT<ukuNU;ioofʹK`m^ Jk휻}XcS6kJ?ox,L; kl_Rޡq`p#sۤifSZzNy`eM3V5۶\\Uu=.o0,بN kgWq0El pna޻tqt^#DqiK=Qpk-G웶9wmI&ϹtNiq^yٛi?TO1 2e>"}3 ElW#YӖ6Ը>L̲^8U[,`v㹖ZYu@6 O-su[m4ZqYoqwzL;:ӓspښ֬W M6}jfF0yę8Fiu 6G;>mFO-ܵٚjj=}o[=4,vLCҹf#S% @.qO})}ނ;tlɳ{ ~=sDs:&B#n5;8oizV9EYNf-Xl̓ ]ERi4w[e~5CF/=I`IwvҮӫ8,@;i9^ YGc6ޚڍ=5ƳtR2Yg#zj⵶P E+>;ehz#+摬g. P*~[ݳG5piuɌb|:߮ҼNej<5˛ynO'M~GqvND@DDD@DDD@DD5;h+IiNPAa+Z]sLh)ҹPM]y|el#qzS>vқHƐ)d]I,O*p&CHǶ0HA?dc$@k%P#]iJ@p)f9}RLk8듘MNp(r qT!p$/XH55 n>DNP4f5FcA^8A;3b >1jȋP¿^*nVRh{' aM #MwluXYB06<_OiZn†v}jj[Na(.)ӧ>S"LO{(1)&"E$RL@DD")& E"L"$"Lc ]0˅ &"4lQDYn3Lw퍼 6+P9X] 4%IhdZ0l P14"ZcriAc!dLl f($3b"$H")& Dh귳l̬>_Ꞿp=ɦ췖 kebL߮tXYum]<,t-=0.][jzsJt%DDTf(  L  ;lQ_ Equation.30 Microsoft lQ_ 3.0 <lQ_ Equation.30 Microsoft lQ_ 3.0 >lQ_ Equation.30 Microsoft lQ_ 3.0?lQ_ Equation.30 Microsoft lQ_ 3.0@lQ_ Equation.30 Microsoft lQ_ 3.0AlQ_ Equation.30 Microsoft lQ_ 3.04llQ_ Equation.30 Microsoft lQ_ 3.05mlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New Roman$D 0DD[SOes New Roman$D 0D DArialNew Roman$D 0D"0DWingdingsRoman$D 0D@DўSOgdingsRoman$D 0D1PDwiSO_GB2312Roman$D 0D`DSymbol12Roman$D 0DpDNSeLwil12Roman$D 0DDeLwil12Roman$D 0DDNSefNl12Roman$D 0D C0.  @n?" dd@  @@`` h@3JG$e%^a,"  5 v  7  )   2RG /" !"#   78 9;< =>?    5STUWYZ[]#`bcefg hijklmn p q rs Ytuv2$uj?Ћt2$fWy%7n܄ٰ2$Br@u1Unb2$ ԫg(Ш2$KݛD\NO( vcR_ proc factn if n=0 then return 1 else return n*fact(n-1) 0GMf@ 7 cR_ proc p1(n){ if n>0 then if odd(n) then p1(n-1); print n; else p2(n-1);print n; } proc p2(n){ if n>0 then if n mod 3==0 then p1(n-1) else p2(n-1) }&$#G8 R_Qpe>NO( *O1 6XNQpe 6XNQpeSR_0W[IN:NN "   g g$H9 R_Qpe>NO#$O2 FibonaccipeR ewzpeR1 1 2 3 5 8 13 21 34 55 & y:NFibonaccipeR0[SNR_0W[IN:N H " gg'g2 7J; R_Qpe>NO#(O3 AckermanQpe S_N*NQpeS[vN*NSϑ/f1uQpeꁫ[INe yُ*NQpe/fSR_Qpe0 AckermanQpeA(n m)[INY N H " gffgf g fgfgf'fgf'fgffn   #K<L= O3 AckermanQpe A(n m)vSϑmvkN*N fO3 AckermanQpe [INUSSϑvAckermanQpeA(n):N A(n)=A(n n)0 [INvQQpe(n):N(n)=min{k\A(k)e"n}0sS(n)/fOnd"A(k)bzvg\vk0Z fUwf        n\ MRbvQ*NOP[-N ,gwQ gkf>fvR_sQ| V [f(uR_QpevcBl0 (W,gO-N Ygp(n):NcktepenvRRpe RN~b0RR_sQ| VdkQXRN*NSϑ\g'YRpen1 N'YNmvRR*Npe\Oq(n,m)0SN^zq(n,m)vY NR_sQ|0 D " d'~1  o] h(3) q(n,n)=1+q(n,n-1); cktepenvRR1un1=nvRRTn1d"n-1vRR~b0 $5HbQ R_{l( (uR_Blv3*NBl vcmSĉ!j ĉ!jSuSST '`( N9eS v㉳Q gQS proc fSpeh if R_QS then {USS else {USScall fSpeh {USS endif endfV#vW#W( cSdT O6 HanoiTX a,b,c/f3*NTX^0_Ye (WTX^a N gNSqQn*NWv ُNWv N N 1u'Y0R\0WS(WNw0TWvN\0R'YS:N1,2,& ,n,sBl\TX^a NvُNSWvy0RTX^b N v^N c T7hz^Sn0(WyRWve^u[N NyRĉR ĉR1k!kSyR1*NWv ĉR2NUOe;R NAQ\'YvWvS(W\vWvKN N ĉR3(WnyRĉR1T2vMRc N S\Wvya,b,c-NNNTX^ N0 JP 'f'  !  eUhY 8n=3 t(3)=7 n=4 t(4)=15 n=10 t(10)=1023 n=16 t(16)=65534 99fVR_\~!Op~gnpf S'`:_ N[f(upef[R_~legf{lvcknx'` Vdk[:N{l0Ջ z^&^eg_'YeO0 :pR_{lvЏLHesNO e/f9v{e؏/f`S(uvX[Pzzk^R_{lY0 zeii'4''+ ' egWR_{lve YBg^Rg ( TR_QpeBl {USR__Bl master method ce zvyr_e zBl Z$ $ iX public static void hanoi(int n, int a, int b, int c) { if (n > 0) { hanoi(n-1, a, c, b); move(a,b); hanoi(n-1, c, b, a); } } T(n)=2T(n-1)+O(1) ne"1 0 n=0RZ#Z"t M09jZ{USR__vBl 1.T(n)=T(n-1)+c1 n>1 c2 n=1 2. T(n)=2T(n/2)+c1 n e"2 c2 n<2 3. T(n)=2T(n/2)+(n) n e"2 O(1) n<2 $$g %J@= 2p^    q_ Master Method(T(n)=aT(n/b)+f(n) ae"1b>1 f(n)/fN*N^nۏQpe case1 >0,Of(n)=O(nlog ba-) sS0<f(n)<nlog ba- RT(n)=(nlog ba) case2: ke"0,Of(n)= (nlog balgnk) RT(n)=(nlog balgnk+1) case1 >0,c>0,Of(n)= &!(nlog ba+) ,af(n/b)<cf(n) RT(n)=(f(n)) b (Ggoo2o goo2ogoo2 g  g  o  o 2 g  o  g  o  g  o  o 2 g  o  g Ggggoo2ogog    r` O1 T(n)=4T(n/2)+n a=4 b=2 f(n)=O(n2-)S=1 RT(n)=(n2) O2 T(n)=4T(n/2)+n2 a=4 b=2 f(n)= (n2lgnk)SK=0 RT(n)=(n2lgn) O3 T(n)=4T(n/2)+n3 a=4 b=2 f(n)=n3= &!(nlog ba+)S=1 N4f(n/2)=n3/2<n3 Sc=1 RT(n)=(n3) -ZZZ" o g  EME E gog   $g$$o$$g$((((((( (((( (((,g,0g00o00o020o00g0448g8<<g g        E  M  E       &## $!%"'$(%!*'+(,)-*waR_ z^vl ( (uVb_e_cgbLh c!k^QQ z^(WS_MR(uB\ N[EgbLvS v^(u gT'_hfSgbL!k^ [ z^-Nvk*N(uSQQ[E(ub__ (WvQ NS QQ,g!k(uvP[ z^[EgbLvS (u gT'_c:y0 (uP[ z^gbL[ gT'_cTvQ N~h Nb_Sv

0 then { f(w-1) print w f(w-1) } end fVZVM5263748596   0` 3ur3f}}` zwf3cc3` 3f333` 333foo` cc33` bb33f` ff` )))f}}>?" dd@,?vFd@ U vP@Z`vU n?" dd@   @@``PR    @ ` ` p>> 0(    6x "  LUSQdkYkHrh7h_     0 "p  8USQdkYkHre,g7h_ ,{N~ ,{ N~ ,{V~ ,{N~    0 "`  f*"0 C  0h "   h*$0 C  0  "   h*$0 Cp  JA ޽h ?10+"` cc3380___PPT10.~F: Stw  0 TL@(    6\' " 0  LUSQdkYkHrh7h_    0?" "    NUSQdkYkHroRh7h_   0D" "`  " f*"0 C  0TI" "   " h*$0 C  0L" "   " h*$0 C`  HA ޽h ?10 cc3380___PPT10.~F: 0 6.( g   c $' P   ' R*     c $@F!    ' ^*  X  C    '  c $'  @ ' 6USQNkHre,g7h_ ,{N~ ,{ N~ ,{V~ ,{N~    s *' `P  ' \*    s *' `  ' ^*  B  s *޽h ? ̙3380___PPT10.q [R p x(     c $̮' P   ' Z*    c $p'    ' \*    s *4' `P  ' Z*    s *' `  ' \*  B  s *޽h ? ̙3380___PPT10.q_[}  0 P$(  r  S Y" 0 " r  S HZ"   " H  0޽h ? cc33___PPT10i.8@۬+D=' = @B +}   0 p$(  r  S "  " r  S P"p " H  0޽h ? cc33___PPT10i.8ЦYI+D=' = @B +    0 pPh(  P~ P s *"  "  P s *"T-v<$ 0 " H P 0޽h ? ̙33___PPT10..I$;+=DB' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-6B'blinds(horizontal)*<3<*PD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-6B'blinds(horizontal)*<3<*PD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*P1%(D' =-6B'blinds(horizontal)*<3<*P1D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*P1A%(D' =-6B'blinds(horizontal)*<3<*P1AD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*PAQ%(D' =-6B'blinds(horizontal)*<3<*PAQ+8+0+P0 +   0  (  r  S ж"p " H  0޽h ? cc33___PPT10i.8+D=' = @B +    0     (    Z\"fԔ ,;N z^ call A 1 &0 E  r  S ",u "    `"3Ԕ5/3  dP[ z^A&0 EB  Z0"fԔwP  @;N z^ call A 1 call A 2 &!0 !E.     `"3Ԕ4 2  dP[ z^A&0 E   Z$"fԔ  0;N z^ call A 1 &0 E  (  Z"3Ԕ m S  &P[ z^A P[ z^B call B 2&0 E.    Z"fԔ 0;N z^ call B 1 &0 E     Zp"3Ԕ% cI  P[ z^B call A 2&0 E    `"3ԔcI dP[ z^A&0 EH  0޽h ? cc33___PPT10i.8`bI+D=' = @B +   0   . (  r  S D'  >l Z*  Z*,$D 0   `)o Z[S(0 G    `"oV* ZSS(0 G B  TDԔMVMB B TDԔ2  Z$"oZ E1(0 G2   Z,"o E2(0 G6l  l Cq=,$D 0    f0o Z[S(0 G     f03o9@ l fSS X(0 GB B ZDԔ|g|   `09oC"?6 d0W@WX(0 GH  0޽h ? cc33  ___PPT10 .8aV/+Dp ' = @B D+ ' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* Dd' =%(D ' =%(D' =4@BBBB%(D ' =+4 8?XCB ppt_xBCB ppt_xB*Y3>B ppt_x<* D' =+4 8?`CB ppt_yBCB1+ppt_h/2B*Y3>B ppt_y<* D' =1:Bhidden*o3>+B#style.visibility<* %(D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*+8   0 F>(    S O<$  0  H  0޽h ? cc33___PPT10r.8PM+|9D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* D ' =%(D ' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-s6Bwipe(down)*<3<*0DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0H%(D' =-s6Bwipe(down)*<3<*0HDD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*HR%(D' =-s6Bwipe(down)*<3<*HRD$ ' =%(D ' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*R_%(D' =-s6Bwipe(down)*<3<*R_DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*_o%(D' =-s6Bwipe(down)*<3<*_oDD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*ox%(D' =-s6Bwipe(down)*<3<*oxDD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-s6Bwipe(down)*<3<*xDD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*+8+0+0 +   0 "w(  x  c $_pY    S/f    #"."????q <$@ 0   Z $o?SIfV M1 @`  ZP2o?S<fI V  @`  Z`o?S/f< V  @`  Zo?S f  M1 @`  Zo?Sw f  d000  @`  Zo?Scfw  M1 @`  Zo?SVfc d000  @`B   To ?S/f/~B   N1 ?Scfc~B   N1 ?Sw fw ~B   N1 ?S f B   To ?S f B  To ?S/S B  To ?f/f ~B  N1 ?S<f<~B  N1 ?SIfI~B  N1 ?SVfVB !@ TDo,$@ 0R "  `oC"?6 ,$ 0 ngbL0RQSagN _YQh( 0  G H  0޽h ? cc33H @ ___PPT10 .8 + HD' = @B Dw' = @BA?%,( < +O%,( < +D' =%(DV' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B+checkerboard(across)*<3<* DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =-6B+checkerboard(across)*<3<*!DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =-6B+checkerboard(across)*<3<*"+8+0+"0 +   0  (  r  S    x  c $q   r  S <]   H  0޽h ? cc33___PPT10i.8 +D=' = @B +   0 |t T(  T~ T s *>/    T c &A  ??J 8  $D 0B T  fGH_)X?#" `" C,$D  0 dLuagN&0 EB T  fGpH)X?#" ` & ,$D  0 dR_e z&0 E T Z )X?" ,$  0 bLuagNNR_e z/fR_QpevN*N } R_QpeS gwQYNُ$N*N } Mb(W gP!k{T_Q~g0&20 2ef 2r  T S n   H T 0޽h ?/ TT ̙33___PPT10+D' = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*TD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*TD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*TD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*TD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*TD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*T++0+T0 ++0+T0 ++0+T0 +   0 ldX(  X~ X s *7)  ) x X c $7)?  ) B X  f :)GH<)X?#" `` ,$D  0 dLuagN&0 EB X  f=)GHc%)X?#" `0 P% ,$D  0 dR_e z&0 E X c &A  ??y 8  $D  0r X ZB) )X?" ~,$  0 ,{n*NFibonaccipeSR_0W{Y N public static int fibonacci(int n) { if (n <= 1) return 1; return fibonacci(n-1)+fibonacci(n-2); }$0 EfD  XB X s *3޽h ?/ XX ̙33___PPT10+D' K)= @B D' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*XD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*XD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*XD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*XD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*XD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*XD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*XD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*X++0+X0 ++0+X0 ++0+X0 +   0 B:`(  `~ ` s *z)  ) ~ ` s *t{)Y)  )  ` c &A  ??8  $D 0H ` 0޽h ? ̙33IA___PPT10!+r}D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-6B'blinds(horizontal)*<3<*`+  0 4,d(  d d Z) )X?"'6 LO3 AckermanQpe MR2O-NvQpeSN~b0Rv^v^R_e_[INh'0 gfGfgf g D    d  ` )X?"11 d c &A ??m 8 $D 0 d  ` )X?" d c &A ??`3 8 $D 0h d Zܔ) )X?"s  ,$  0 6FO,gO-NvAckermanQpetSel~b0R^R_v[IN0&0 eH d 0޽h ? ̙33___PPT10h.Iy+PD' )= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-6B'blinds(horizontal)*<3<*dD' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-6B'blinds(horizontal)*<3<*dD' =%(DS' =%(D' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*dD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*dD ' =%(D' =%(D]' =A@BB BB0B%()))D' =+\4 8?CBnormalBCB boldBCXBnormalBCBnormalB*3>+B#style.fontWeight= `B<*d+p+0+d0 ++0+d0 +   0 h^(  h~ h s *,)' )  h0 TA ? ?    )H h 0޽h ? ̙33___PPT10i.I>+D=' = @B +x   0 RJl(  l l s *)<p<$ 0 ) H l 0޽h ? ̙33  ___PPT10 ..IE]+=D6 ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-6B'blinds(horizontal)*<3<*lD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*l2%(D' =-6B'blinds(horizontal)*<3<*l2D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*l2h%(D' =-6B'blinds(horizontal)*<3<*l2hD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*lh%(D' =-6B'blinds(horizontal)*<3<*lh+8+0+l0 +   0   pp (  px p c $ľ)  )  p Z`) )X?"',$ 0 R={r1,r2,& ,rn}/fۏLcRvn*NCQ } Ri=R-{ri}0 ƖTX-NCQ }vhQcR:Nperm(X)0 (ri)perm(X)h:y(WhQcRperm(X)vkN*NcRMRR NMR_0RvcR0RvhQcRSR_~[INY N s0 e%-%-%-% ememe%e %e%e-e%e%e %e    p Z )X?#" `S TC ,$D 0 S_n=1e perm(R)=(r) vQ-Nr/fƖTR-N/UNvCQ } S_n>1e perm(R)1u(r1)perm(R1) (r2)perm(R2) & (rn)perm(Rn)gb0 d\0 %e% e%e %e%e%ememe%ememe%ememe%e      p N)of p,$  0 FN!(0 2G fH p 0޽h ? ̙33  ___PPT10e +h|7D ' "= @B D\ ' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-6B'blinds(horizontal)*<3<*pD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-6B'blinds(horizontal)*<3<*pD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*pD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*p++0+p0 ++0+p0 ++0+p0 +!   0 F>``(  ` ` S Z Y<$  0  H ` 0޽h ? cc33jb___PPT10B.u+|9D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*` %(D' =-s6Bwipe(down)*<3<*` D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*` 7%(D' =-s6Bwipe(down)*<3<*` 7D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`7C%(D' =-s6Bwipe(down)*<3<*`7CD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`CL%(D' =-s6Bwipe(down)*<3<*`CLD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`LW%(D' =-s6Bwipe(down)*<3<*`LWD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`Wb%(D' =-s6Bwipe(down)*<3<*`WbD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`bm%(D' =-s6Bwipe(down)*<3<*`bmD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`my%(D' =-s6Bwipe(down)*<3<*`myD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`y%(D' =-s6Bwipe(down)*<3<*`yD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-s6Bwipe(down)*<3<*`+8+0+`0 +   0  *(      s +0e0e #" 0e,i  H   0޽h ? cc33___PPT10i.8.+D=' = @B +    0 $5(  $" $  60e0e )X?3"0eT    $0 \A 4??H 4$D 0  $ N 3o  ,$  0 E?(0 2GH $ 0޽h ? cc33___PPT10e.8`g+F:D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-6B'blinds(horizontal)*<3<*$D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-s6Bwipe(down)*<3<*$+8+0+$0 +#   0 h `  , (  ,N ,  G0e0e )X?3"0ePs <$ 0   , ZP )X?"s TY_,$ 0 (4) q(n,m)=q(n,m-1)+q(n-m,m),n>m>1; cktepenvg'YRpen1 N'YNmvRR1un1=mvRRT n1d"m-1 vRR~b0N0 .em emem el$z v q  , Tp,$D 0 ,  f[ )X?"v b  V`(1) q(n,1)=1,n1; S_g'YRpen1 N'YN1e NUOcktepenS gNyRRb__ sS10 ee%-eH j , c &A 5?? q  5,  , Ze )X?"T,$ 0 `f(2) q(n,m)=q(n,n),mn; g'YRpen1[E N N'YNn0Vdk q(1,m)=10 40 ee%-eN6  ,  `oGHj3o   ,$@  0 r S+TmvRR&0 E(  ,  `ptGQH 3o  d- ,$D  0 d NS+Tm&0 EH , 0޽h ?/  , , cc33___PPT10.8H0S+f kD' ~= @B D:' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-6B'blinds(horizontal)*<3<*,D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-6B'blinds(horizontal)*<3<*,D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-6B'blinds(horizontal)*<3<*,D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =-6B'blinds(horizontal)*<3<* ,DN' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* ,D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* ,D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* ,D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* ,++0+,0 ++0+,0 ++0+ ,0 ++0+ ,0 ++0+ ,0 +   0 0:(  r  S X     S  G  "p`PpH  0޽h ? cc33___PPT10i.8A,+D=' = @B +i  0 PH(    6, P >!   ZȤ )X?"/! H"0 P% |  C A t21@ E ,$D 0H  0޽h ? ̙33YQ___PPT101.N Z!+r}D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*+I   0 ph`(  x  c $Z   H  C A t21 z  H  0޽h ? ̙33y___PPT10Y+D=' = @B +N  0 H @ p (    Z )X?"i,$ 0 N(Wĉ!j'Ye ~b0RN,vel VdkbN\Ջ(uR_b/geg㉳Qُ*N0 H'0 P0 '%G (b  T`)X?#" ` ,$D 0 S_n=1e k{US0dke S\S:N1vWvNTX^avcyTX^b NsSS0 S_n1e )R(uTX^c\O:NRTX^0dkel\n-1*N\vWvOgqyRĉRNTX^ayTX^c 6qT \iR Nvg'YWvNTX^ayTX^b gT Ql\n-1*N\vWvOgqyRĉRNTX^cyTX^b0 1udkS n*NWvvyRSR:N2!kn-1*NWvvyR ُSSNR_0W(u NelegZP01udkSNQHanoiTXvR_{lY N0 H0 P0 %et     Z| )X?"K |O6 HanoiTX$ 0 P ' H  C A t21 XT  N$)X?#" ` ,$D 0 < $=0 =c( =  TH )X?#" `U ,$ 0 "public static void hanoi(int n, int a, int b, int c) { if (n > 0) { hanoi(n-1, a, c, b); move(a,b); hanoi(n-1, c, b, a); } } &0 e"   T\8c)X?#" `  ,$D 0 p`YgTXv*NpeS:Na,b,c,dV*N s\n*NWvNahQyR0Rd yRĉR NS BlyRekpeg\veHh0&90 9eZ H  0޽h ? ̙33___PPT10.NPq+k2DB' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*++0+0 ++0+0 ++0+0 ++0+0 ++0+0 +}   0 $(  r  S    r  S p  H  0޽h ? cc33___PPT10i.8+D=' = @B +   0  <(   ~   s *$   ~   s *p  H   0޽h ? ̙33y___PPT10Y+D=' = @B +}   0 $(  r  S T   r  S ,p  H  0޽h ? cc33___PPT10i.8n+D=' = @B +:   0 D<(  r  S |" " I   `!o psX ,$D 0  T(n)=2n-1F 0 C,K,C,2   `!o A4$0 CH  0޽h ? cc33___PPT10v.8``o+r}D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*+8+0+0 +   0 :(  r  S      S &p  "p`Ppr  Z7ԔC"?* N(0 G r  Z:ԔC"?  N(0 G r  Zr!ԔC"?[ )  N(0 G H  0޽h ? cc33___PPT10i.80n+D=' = @B +   0 0e(  0B 0 B@o \ T( n/2 ) + T( n/2 ) + 1 (n > 1)X/ 2# 0 BGov\ w 0 (n = 1) 2jr 0 BoJ/ 0 Boy t" O1 T(n) =  2 0 BPojf  t T(n)=2T(n/2)+1 =22T(n/22)+2+1 =23T(n/23)+22+2+1 N2r=n =2rT(1)+2r-1+000+2+1 =(1-2r)/(1-2)=n-1 4" T( n ) = n - 1H 2$          C@V!:H 0 0޽h ? cc33___PPT10i.S<`+D=' = @B +;  0   0 +@b ( w @ "@ BioDC ,$  0 P Nc_ T( n ) = 3 T( n/2 ) + k n = 3 [ 3 T( n/22 ) + k (n / 2 ) ] + k n =32T(n/22)+3k(n/2)+kn = =3rT(n/2r)+(3/2)r-1kn+& .+kn =3rk+ (3/2)r-1kn+& .+kn R: 20 ^ 1       !   F + #@ BoVR<  N  22 &@ BԂo n3 ,$   0 &= 3 r+1 k - 2 k nJ 2   '@ Bo ,$   0 ^x= 3 k 3log2n - 2 k n 3 k n 1.59 - 2 k n = O( n 1. 59 )= 2      bl D *@,$D 0 @ B,oDC  O2 csQ|_ 2$rr @ BoJ=  @ BLoD_E Z" 3 T( n/2 ) + k n (n > 1)# 2# !@ Bo R k ( n = 1) 2 )@ Bo6 @T (n ) = 2 H @ 0޽h ? 3,,___PPT10,+JD+' = @B D+' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<**@%(D' =-6B'blinds(horizontal)*<3<**@D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*"@D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*"@D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"@:%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*"@:D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*"@:D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"@:x%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*"@:xD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*"@:xD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"@x%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*"@xD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*"@xD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*"@D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*"@D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*"@D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*"@D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"@(%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*"@(D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*"@(DN' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*&@D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*&@D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*'@D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*'@++0+"@0 ++0+&@0 ++0+'@0 +  0  4j(  4 4 B(o F  2&  4 B|o9F U  2 4 Bo h O3  2P 4 BPo `T( n/2 ) + T( n/2 ) + (n - 1) (n > 1)b1 2) 4 B`op T 0 (n = 1) 2jr 4 BoP  4 Bdo_Pl AT(n) =  2J  4 B8o 8 n = 2r  r:^tepe 0@ 2 <   4 Bo/< N gT(n) = 2 T(n/2 ) + ( n - 1 )( 2(   4 B0o 9 T(n/2) = 2 T(n/22 ) + (n/2 - 1)@: 2'VM  4 Bo  ; T(n/22) = 2 T(n/23 ) + (n/22 - 1)< 2 . 4 BoO \  > @ 2  Q 4 Boo |  ? T(n/2r-1) = 2 T(n/2r ) + (n/2r-1 - 1)@ 2  pB 4 HDo   4 Boo @|  <+) 2  4 B o ? 2 22 2 @@ 2%] 4 B$ o  9 22 23 + 22: 2 ^ 4 B@ob o  L 2r-1 2r 2r-1M 2 4 B "o P  f T( n ) = 2r T(1) + rn - (2r-1 + 2r-2 + +20)B 2  4 B.o  ; = nlog2n - n +1 = O(nlog n)@< 2&H 4 0޽h ? 3y___PPT10Y+D=' = @B +:   0  4P(  4r 4 S p6    4 S 7p<$ 0  H 4 0޽h ? cc33"___PPT10.^<0+A~D' = @B DQ' = @BA?%,( < +O%,( < +D' =%(D0' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-6B'blinds(horizontal)*<3<*4DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4(%(D' =-6B'blinds(horizontal)*<3<*4(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4(Y%(D' =-6B'blinds(horizontal)*<3<*4(YDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4Yw%(D' =-6B'blinds(horizontal)*<3<*4YwDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4w%(D' =-6B'blinds(horizontal)*<3<*4wDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-6B'blinds(horizontal)*<3<*4DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-6B'blinds(horizontal)*<3<*4DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4 %(D' =-6B'blinds(horizontal)*<3<*4 +8+0+40 +!   0 F>08(  8 8 S T<$ 0  H 8 0޽h ? cc33  ___PPT10.`<u+=D~' = @B D9' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-6B'blinds(horizontal)*<3<*8D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8-%(D' =-6B'blinds(horizontal)*<3<*8-D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8-<%(D' =-6B'blinds(horizontal)*<3<*8-<D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8<Q%(D' =-6B'blinds(horizontal)*<3<*8<QD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8Qm%(D' =-6B'blinds(horizontal)*<3<*8QmD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8m|%(D' =-6B'blinds(horizontal)*<3<*8m|D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8|%(D' =-6B'blinds(horizontal)*<3<*8|D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-6B'blinds(horizontal)*<3<*8D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-6B'blinds(horizontal)*<3<*8D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-6B'blinds(horizontal)*<3<*8+8+0+80 +  0 < 4 PT ( w T T B_o76j nce zvyr_e zBl" 2 '  * T Bpo,,$ 0 ( N08^|pe~'`ce zvyr_e zl 28 T Bto,$ 0 . 1. P!k8^|pe~'`ce zvyr_e zl 2"  T B${o ,$  0 fF 1 [INk6P!k8^|pe~'`ce z: (R): H(n) = a1H(n - 1) + a2H(n - 2) + +akH(n - k) vQ-N 1 a1, a2, , ak:N8^pe 2 ak 0, n k0 2-  h J&l q  Tq ,$D  0 T Boq ~  & 2 [INR [^vyr_e z: 2< T B@o   (E): xk - a1x k - 1 - a2 x k - 2 - - a k-1 x - ak = 0>H 2                  ?H T 0޽h ? 3___PPT10+ &D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-6B'blinds(horizontal)*<3<*TD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-6B'blinds(horizontal)*<3<*TD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*TD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*TDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*TD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*T++0+T0 ++0+T0 ++0+T0 +  0 ` Xv( w Xl :  XZ<,$D  0 X Bo   (3) R v 2 : X BoP @ 1 (E) gk*NN N Tv[9hx1, x2, , xk, R(R) v /fH(n) = c1x1n + c2 x2n + + ck xknZ0 x2#x J X B\o :  vQ-N c1 c2 0 0ck /f8^pe [1uH(n)vRYagNnx[ N T 0A 2f  44$$l `   XV ,$D 0 X Bo`  z 2 (E)X[(We͑9hxpe 2 sS:(E)v9h/f x1, x2, x k-e, xp, xp, , xp$Z 2  +l X  <BCqDELF$o /[8A/#8Abqom<-V8@      i 3 =  X BoP  dqQ ge*N 2  X B4o P T< R(R)v/f H(n) = c1x1n + c2 x2n + + ck-e xk-en + c k-e+1xpn + c k-e+2 n xpn + + ck ne-1 xpn 2(#&8 %XH X 0޽h ? 3___PPT10+^D{' = @B D6' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* X%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* XD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* XD' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* X%(D' =-6B'blinds(horizontal)*<3<* X+   0 p A( w 8 `m  `m  B/o` Zt 3 (E) gN[qQmZ9h x 1,2 = r( cosq i sinq ) ,Rb; 2`   B0;o`m rb (R)v T(n) = c1rn cos nq + c2r nsin nq2 2 8    BEo ( O BlFibonacci^RvFn 2,   BKoR 9_  AF(n) =  2jr  Boi   BOo ]#F(n - 1) + F(n - 2) (n > 1)$ 2$  BMoZ i  k1 1 ( n = 1) 0 ( n = 0)2 22H  0޽h ? 3y___PPT10Y+D=' = @B +I  0 ph4`( ( w `  ` BDYo R (R): F(n) = F(n -1) + F(n - 2)* 2*& ` BD^o, & (E): x2 - x - 1 = 0@' 28  0`fs ` Hco 6t (E)v9h x1 = 1/2 + 5/2 , x2 = 1/2 - 5/2 x; 2  & *B ` TDo  B ` TDo8  1`+ ` Hto 8 V:N x1 x2 @bN F(n) = c1(1/2 + 5/2)n +c2 (1/2 - 5/2)nJN 20 +B ` TDo-  B ` TDoh8 P  3`8 p  ` Ho P   c1 + c2 = 0 c1( 1/2 + 5/2 ) + c2(1/2 - 5/2 ) = 1K 2    ~B ` NDo  = ~B ` NDo  _ xr ` Ho p 8    '`  rr !` Bo p  "` Bo@   C1 = 1/ 5R 2xB #` HDop   %` B`o   C2 = - 1/ 5 b 2~B &` NDo ; 8    4`  D (` Hdo    n \F(n) = 1/ 5 [ (1/2 + 5/2)n - (1/2 - 5/2)n ]8 2               3~B )` NDo -  ~B *` NDo  ~B +` NDo   @ 2` Nox > 1u F(0) = 0 TF(1) = 1 w, 2 4   H ` 0޽h ? 3y___PPT10Y+D=' = @B +  0 (P@( w   Bo  f,2 T( n - 1) + 2 T( n - 2 ) ( n > 2 )- 2-  BлoPP] ]# 3 ( n = 1 )$ 2$  BLop @} ^$ 8 ( n = 2 )% 2%jr  BoP0  B\oZg t O T( n ) = 2   B`o n4 (R): T( n ) = 2 T( n - 1) + 2 T( n - 2 ) 5 25  Bo@M y (E): x2 - 2x - 2 = 0@ 28 ! (!   HTo! ^ x1 = 1 + 3, x2 = 1 - 30 2  B   TDo!~B  NDo [ 8 @M  %@M j  Ho@M  ~ V:Nx1 x2 \T(n) = c1(1 + 3)n + c2( 1 - 3)n.@ 2 -B  TDoPPPB  TDo0HH8  a  & a P  Ho a   1uT(1) = 3 T T(2) = 8 _ c1 = 1/2 + 3/3, c2 = 1/2 - 3/3, i 2: B  0~B  NDoe p ~B  NDog ^g 8    '  p  Ho    EeT(n) = (1/2 + 3/3)(1 + 3)n + (1/2 - 3/3)( 1 - 3)ns 2     7     iB  TDo  F  B  TDo  v ~B ! NDou~B " NDoH  0޽h ? 3y___PPT10Y+D=' = @B +  0 B:( w 8 !`  !` ,  Ho  O BlSn = @ 2 ,  HXo` ` -  S K2D 2  H$op ?k = 0 2  Ho!. ;n 2  BX"o`m  1u Sn = 12 + 22 + + n2 (1)D 2 !9  BX/o  cS n-1 = 12 + 22 + +(n - 1)2 (2)E 2  7  B;o   1u1 - 2 _Sn - S n-1 = n2 (3)H 2L 1  B\GoP] f [3 cSn-1 - Sn-2 = (n - 1)2 (4)J 2 , 8  BOop}  2h 1u(3) - (4) _Sn - 2S n-1 + S n-2 = 2n - 15 2 " *8      P  BYo    S YO(u Nbvel mSI{SSYy_ _ S n - 4Sn-1 + 6Sn-2 - 4Sn-3 + Sn-4 = 0 (R)i 24 (6B  ZDo  t  Bfo   @ (E): x4-4x3+6x2-4x+1=0 ---------(x - 1) 4 = 0A 2a  Blo@M - x1 = x2 = x3 = x4 = 1. 22  Zwo7 A5$0 CH  0޽h ? 3y___PPT10Y+D=' = @B +S   0 zr ( w   Bpor R V:Nyr_e zv/fV͑9h @bN Sn = c11n +c2 n 1n + c3 n2 1n + c4 n3 1n = c1 + c2n + c3n2 + c4n3>l 2#O  Bo r  P 1u S0 = 0, S1 = 1, S2 = 5, S3 = 14, w c1 = 0 , c2 = 1/6, c3 = 1/2, c4 = 1/3.j 2    ,(+<  B o9 rF  L @bNSn = 1/6 n ( n + 1 ) (2 n + 1 )@' 2 H  0޽h ? 3y___PPT10Y+D=' = @B +K   0 rj p( w p p BloD 0 2 ^P!k8^|pe~'`ce zvyr_e zl 2"& p BoD b 1 [IN(R ):Nk6^P!k8^|pe~'`ce z: (R ): H(n) = a1H(n - 1)+a2H(n - 2)+ +akH(n - k)+f(n) vQ-N 1 a1, a2, , ak:N8^pe 2 ak 0, n k, f(n) 00 2.   x G p BoD  2 R v~g R v/fH(n) N[ gN*NyrH*(n) NR )v[^v P!ke z(R)v/fH (n)0 R gR vH(n) = H (n) + H*(n) { 2{  H p 0޽h ? 3y___PPT10Y+D=' = @B +#  0 t( w t t Bto  (3) (R )vyrb__ 2 F t B o3h,$  0  1 S_f(n) b_Ybnt( b0, t:^tepe e (R )vyr:N H*(n) = p1nt + p2nt-1+ + pt n + pt+1 vQ-Np1, p2, pt+1/f_[|pe0 2     4 " t B o ,$  0 | FO S_x = 1/f(R)v j ͑yr_9hj 1 e vQyr㉔^ 9e:N H*(n) = p1nt+j + p2nt-1+j+ + pt+1nj &f 2  h) t B% o  ,$  0 * 2 S_f(n) b_Y b rn( b0, r 0 e (R )vyr:N H*(n) = p rn vQ-Np/f_[|pe0X 2 t B4/ o ,$  0  FO S_ x = r /f(R ) [^v(R)v j ͑yr_9h( j 1)e (R )vyr㉔^9e:N H*(n) = p nj rn|a 2)$  H t 0޽h ? 36.___PPT10+hD' = = @B D' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*tD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*tD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*tD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*tD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*tD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*tD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*tD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*t++0+t0 ++0+t0 ++0+t0 ++0+t0 +`0  0    |9 ( w | | BC ou ,$ 0 G T(n) =  2r | Bo ,$@ 0n | BG o,$ 0 ` 2T( n - 1 ) + k (n > 1) (k:ckpe 1 21&, | BM oGT,$ 0 U k ( n = 1 ) 2F  | B,Q o,$ 0 D (R ) : T(n) = 2T(n - 1) + k# 2#,  | B`U oGT,$ 0 " (R) : T(n) = 2T(n - 1)# 2#"    | B,[ o ,$ 0 c) (E): x - 2 = 0 x = 2* 2*t  | BW o  ,$  0 : (R)v T(n) = c 2n@ 20  @  | B`f os  ,$  0 , V:N(R )-N f(n) = k 2, 4 | B0m o @ ,$   0 2 @bN  T*(n) = p  2 Z | Bp o1>,$   0 X >f6q T*(n - 1) = p - 2-#H | 0޽h ? 3_"W"___PPT107"+.ȎD'  = @B D' = @BA?%,( < +O%,( < +D{' =%(D#' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-6B'blinds(horizontal)*<3<*|DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-6B'blinds(horizontal)*<3<*|DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-6B'blinds(horizontal)*<3<*|DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-6B'blinds(horizontal)*<3<*|DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* |%(D' =-6B'blinds(horizontal)*<3<* |DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* |%(D' =-6B'blinds(horizontal)*<3<* |DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* |%(D' =-6B'blinds(horizontal)*<3<* |DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* |%(D' =-6B'blinds(horizontal)*<3<* |D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* |%(D' =-6B'blinds(horizontal)*<3<* |DN' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*|D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*|D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*|D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*|+0+0+|0 ++0+|0 ++0+|0 ++0+ |0 ++0+ |0 ++0+ |0 ++0+ |0 ++0+ |0 ++0+| ++0+|0 +   0  @( w &  Bđ or < bT*(n)0T*(n - 1)NeQ(R ) , 26 0  B$ or" @ gp = 2p + k \p = - k@! 2  BP oerr z& EeT*(n) = - k 2 `  B or d (R )vT(n) = T (n) + T*(n) = c 2n - k@3 2+&$:  BL oerr  d 1uT(1) = k, b[NeQ N_ g2 c - k = k c = k3 23"   B o r   \(R )vT(n) = k( 2n - 1) = O( 2n )X 20&HH  0޽h ? 3y___PPT10Y+D=' = @B +"  0 E =   ( w   B o "O T(n) = 0 2 jr  Bos0c  B$ o-P: '2n-3 - T( n -2 ) ( n > 4 )@( 2$  B o0 \" 1 ( n = 3 )# 2#  B o \" 2 ( n = 4 )# 2#v  B o},$  0 R (R ): T(n) = - T(n - 2 ) + 2n-3@* 2&%B  B< o,$  0 & (R): T(n) = - T(n - 2 )' 2'4 $  B o * ,$  0 ~" (E): x2 + 1 = 0@# 2   B om z ,$  0 >l (R) vT (n) = c1cos(np/2) + c2sin(np/2)7 2  & $  Bt o  ,$  0 X  vQ-Nr = 1 q = p/2 @- 24H  0޽h ? 31)___PPT10 +D'  = @B D' = @BA?%,( < +O%,( < +D' =%(Do' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*++0+0 ++0+0 ++0+0 ++0+0 ++0+0 +   0 l d   ( w  l M   M ,$D 0T  BH!oMZ J (R ) vyr/fT*(n) = p 2n@& 2$, L  B!om  b[NeQ(R ), gp 2n = - p 2 n-2 + 2 n-3 _p = 1/10\ 2! $ B ;    B!o=J `p \ T(n) = c1cos(np/2) + c2sin(np/2) + 2n/109 2    +   BL !o  <x 1uT(3) = 1 T T(4) = 2, wc1 = 2/5, c2 = -1/5b= 2' >      B)!o   ~ Ee\ T(n) = 2/5cos(np/2) - 1/5sin(np/2) + 2n/10  n > 2 fb 2 +&2 HH  0޽h ? 3IA___PPT10!+ۮD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* +^H  0 z ( J #8    2  H6!o " O QBlSn = @ 2 ,  Hl ,$  0 p6 (E): x - 1 = 0 x = 17 27m  Bu!o,$  0 ' (R): Sn - S n-1 = 0 ( 2b  B|!o  ,$  0 2 (R)vS n = c@ 2& >  B$!o  ,$  0 Z (R )vyr/fS*n = p1n3 + p2n2 + p3n. 20   Bh!o  ,$   0 Fn NeQ(R ), _p1 = 1/3, p2 = 1/2, p3 = 1/68 2  0 #4  Bx!o ,$   0 Z (R )vSn = p1n3 + p2n2 + p3n + c. 2&   B !oGT,$D   0 v 1uS0 = 0,wc = 0 Ee Sn = p1n3 + p2n2 + p3n < 2 <  H  0޽h ? 3/|/___PPT10\/+@D-' != @B D-' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*DD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*DDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*E%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*ED' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*EDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* I%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* ID' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* ID{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*<+P+0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 +c-  0 .&p( w v  B!o D S|pe/^~'`ce zvBl SR Sbc 0p#( 2 !  !  ,  BD!o`m,$  0  N0S ^~'` :N ~'`  2!!!! f  B!oV c ,$  0 0 NG(n) = H2(n),R g@ 2, l     t ,$D  0   BP!o   n4G(n) - 2G(n - 1) = 1 ( G(n) > 0, n > 0 )5 25   B!o   H G(0) = 4  2rr   Bo    B$!o9 F,$  0 H Nc_ _G(n) =5 2n - 1b% 2 >l  -  ,$D  0<  BD"o - @ \H(n) = 52n - 1f! 2 ~B  NDo  hl m m,$D  0r@ "  m  B@ "o"  E H(0) = 2 2   B,!o " O BlH(n)0]w 24A  B"o IH2(n) - 2H2(n - 1) = 1 ( H(n) > 0 , n > 0 ) bJ 2 =rr  BocH  0޽h ? 3___PPT10+4D' "= @B D' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*++0+0 ++0+ 0 ++0+0 +  0 T L  ( w p  B""o&<3 " N0S S|pe :N 8^|pe  2!!!!l G/ J2,$D 0*  B-"o0"/ H b (n = 1; b:^8^pe % 2%&@ ` q  `G@  B3"o`   j(n - 1) + S 1/n T(k - 1) + S 1/nT(n-k) (n > 1)@6 2 )   B89"od pq  =k=1 2   N="o Y f  < k=1    B@"o t  ;n 2   B E"o   ;n 2@ 0 op o   B8I"o 0  C T(n) =  2 rr  Bo0 op  N>MwP ",$D  0  N>M3 )",$D  0H  0޽h ? 35 - ___PPT10 +<D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*+   0 4,)1`( w   B0R"o  ~" tet09eQ Nc_ 28 x0 F  BW"o@0M F T(n) = (n - 1) + 2/n S T(k)@$ 2  B]"oKx  > n-1 2  BLb"o  =k=1 2J8 U 1U   H a"oX0e D nT(n) = n(n - 1) + 2 S T(k)@# 2   H`k"ol  > n-1 2   Ho"o  =k=1 2B  ZDo   Hs"o_Ul =(1) 228 Z  zO/&   Hdw"o$ J(n-1)T(n-1) = (n-1)(n - 2) + 2 S T(k)@& 2  Hl|"o. > n-2 2  H"om  =k=1 2B   `DoDbb  H"o =(2) 2  B"oZ* Zc 2  B"o   1u(1) - (2) _ nT(n) - (n - 1)T(n - 1) = 2(n - 1) + 2T(n - 1)R 2R, .8  z'  & z' *  BX"o  T sS T(n) = T(n - 1) + + 2+ ~B  NDo`7 7   B"oz '  =n+1 2  BD"o )  ;1 2~B  NDo0 p0   B<"o   ;n 2   B4"o (  ;1 2xB ! HDo % 0  " B"o    B2(n - 1) 2  # Bt"o  $  Bn(n + 1) 2 B $ ZDoP0 0  % B"o z  =(3) 28 [ pa 0[ paT ' B0"o p l NQ(n) = T(n), gQ(n - 1) = T(n - 1)7 27,~B * NDopPp + Bж"oT[a =n+1 2 , B8"oTc p ;1 2~B - NDo`p p . BP"o>OK ;n 2 / BT"o[ h ;1 2H  0޽h ? 3y___PPT10Y+D=' = @B +R,  0 y+q+BQp*( w 8 ` `@  H"o R NeQ(3)_Q(n) = Q(n - 1) + * 2*, B  TDo`  H"o3 Bn(n + 1) 2   H"o_ B2(n - 1) 2 8 6~F  I  H"o  8cQ(n - 1) = Q(n - 2) +  2h@  0   6~FB   TDo55   H"os#0 B(n - 1)n 2    H"oo - B2(n - 2) 2 A8 @   HL"oKX Y Q(n - 2) = Q(n - 3) +  2 ~B  NDo  H"oQ@ H(n - 2)(n - 1) 2  HP"o? B2(n - 3) 2   B"o,  r 0 28 ]U ]U  B"ot  j0 Q(2) = Q(1) + 1 21~B  NDo   B"oU]Uj f 2 1@ 2  BD$ohyx f 2 3@ 28 x x~B  NDo  B$o4x$ <+) 28  Q N  &&    BL $o   . Q(n) - Q(1) = @ 2 ! B$o   ;n 2 " B$o A N  =k=2 2~B # NDo 0   $ B$o! Q  Bk(k + 1) 2  % B$o0  B2(k - 1) 2 o F `    : {  N  Rw ;    < Bh$o  N0 2 = B#$ojRw =k=2 2 > B'$o   ;n 2 ? B,$o`  ;= 2xR @ Ho ~B A NDo \ @\  B B/$o B 1O  =k+1 2 C B2$o = J  ;4 2 D B|7$o   ;- 2xB E HDo`` `  F B ;$oc^ k  <k  2 G B?$ou@ 5M  ;2 2xb H HoP A  8  _ Q _ / H?$o Z  ;= 2T  [ J# h *~R 0 No e: B 1 TDoj !! 2 HtD$o  =n+1 2 3 HH$oU  ;4 2 4 HL$o |: ;- 2~b 8 No+V[ I BO$o ;1 2 K HhS$o >+ 2 2@ i _ Pi _ , HV$o N0 2 - H[$oiR_ =k=3 2 . H _$o ` ;n 2B L TDo00 M H|b$o1, ;k 2 N H,f$o# ;1 2H  0޽h ? 3y___PPT10Y+D=' = @B +  0 s( w f 8 ,  ` z@ X ,X  Bk$op f V:N 2N i _  X  B\o$o N0 2  Bs$oiR_ =k=3 2  B x$o ` ;n 2~B  NDo00  BH|$o1, ;k 2   Btz$o# ;1 2   BH$ov j 0 2P@  K X    B$o N0 2   B$o>K ;3 2  B$o$ ;n 2~B  NDo    B$o  ;1 2  B0$o ;x 2  Bܛ$oo | <dx 2  B$o  J= ln n - ln 3 28  VLn  B$o0= t 1uQ(n) = T(n), ST(1) = b, wQ(1) = 1/2b; 2;> ~B  NDo  B$oI =n+1 2  Bh$o ;1 2|  BX$o$   T(n) = (n + 1) Q(n) 2(n + 1) ln n + (b/2 - 1 - 2ln 3)(n +1) + 4@X 2'0  B $o   S = O(n ln n) 2H  0޽h ? 3y___PPT10Y+D=' = @B +   0 @P:(  Pr P S $o  $  P S H$ $ "p`PpH P 0޽h ? cc33___PPT10i.h>0(+D=' = @B +}   0 PT$(  Tr T S l$  $ r T S  $/  $ H T 0޽h ? cc33___PPT10i.i>X O+D=' = @B +  0 ?7(    H$?K ``NT{Hh"( 2& |  T$oX`+ d T{T(n) = 2b " nlog2n - 2b " n + 3b = O(nlog2n)^3/F `  2   <$' " 2. BlT(n)= " 2' ,~r  No?@`  B$op`< |aT(n/c) + bn (n > 1)" 2'    B$op@ Pb (n = 1)" 2' "   B&o` (a, c:cktepeb:ckpe 2 2' % 43F ` K    `   B& ?"`   ^T{S_ n = cr(r^tepe)e g T(n) = (bn) ki (k = a/c)`A  * Z N H    He K   <& ?" G ;i=0 2  <8& ?"H *  vlogc n: 2  <0& ?" , JS, 2  F aK  aK*  NH& ?" 8b (n = 1) (b:ckpe)  '   N$#& ?"K  T(n/2) + b n log2 n (n > 1)J! ' / '   N`(& ?" BT(n) =  '   N$ ?"a h1. (uclBl  ' r  H 8c?"0@H  0޽h ? ̙33y___PPT10Y+D=' = @B +   0    p (    B/& ?"?1 T(1) S_ a<c e, V:N ki 6e[eNN*N8^pe T(n) = O(n)>+ (N    <X9& ?" * (2) S_ a=c e T(n) = bn(r+1) = bn (logcn + 1) = O(n log n)@A 2, F   <0B& ?"  BJ (3) S_ a>c e, T(n) = bn " (kr+1 - 1) / (k-1) = bk / (k - 1) " ar - bn / (k - 1) = bk/(k - 1) " alogcn - bn/(k - 1) = O ( nlogca )$ 2" +.      $  F  P.   P.>  BV& ?" P.TLD___PPT9& Z(uyr_e zlBlT(n)0]w 2 T(n - 1) + n (n > 1) 1 (n = 1)B I ' I',< @`xr  HoW    B^& ?" p2  ^1 T(n) =0 '2  N8k& ?"#  2T{T(n) = 2n+1 - ( n + 2 )>   H  0޽h ? 3y___PPT10Y+D=' = @B +  0 %(  F $   $ rr  BojD  N|r& ?"$G J7T(n  1) - 12T(n  2) + 3n (n > 1)J& '/ '  N8y& ?"M P0 (n = 0)  '  N8}& ?"  P1 (n = 1)  '  N& ?"w \2 T(n)=0 'X  NȆ& ?"@+ FT{ T(n) = 10 " 4n - ( 3n + 10) " 3nP$ $$!  Bt&om)  4. ՋS_yr_e z(E)S+T gN͑9h x 1,2 = xp e P!ke z(R)S+T gT(n)= c1xpn + c2 n xpn\K0 2' / ' / ' / ' / / ' / ' / / ' n &&  B(& ?"  r P!k8^|pe~'`ce zY N H(n) = a1H(n-1) + a2H(n-2) + " " " " " " +akH(n-k) (R)U & $&   B& ?"j    [@b[^vyr_e z/f xk - a1xk-1 - a2xk-2 - " " " " " " - ak-1x - ak = 0 (E) W  .&F  '   Ft   <& ?" ' L [E N bNSfx = nxp/f(R)v sSS0N' 2  4   <& ?"  9n 2H  0޽h ? ̙33y___PPT10Y+D=' &= @B +  0 ,$ (  |  N& ?"P  [(E)$N TXNxn-k (x0) g xn - a1xn-1 -a2xn-2 - " " " " " " - a k-1xn-k+1 - ak xn-k = 0 (M)c   v1j  B|& ?"4   V:N(E) gN͑9hx1 = x2 = xp @bN(M)_S9eQb (x - xp)2 " f(x) = 0 (M)T  Z  !:  B' ?"1  [_(M)]Bl[ _0R nxn-1 - a1(n-1)xn-2 - a2(n-2)xn-3 - " " " " " " - ak-1(n-k+1)xn-k - ak(n-k)xn-k-1 (M ) `  $ x  <' ?"`  s(M ) I{N 2,  <& ?" h V S (M ) _[E N1\/f 2(x - xp) " f(x) + (x - xp) 2 " f  (x) =(x - xp)[2f(x) + (x - xp) " f  (x)] (N ) 2$b2j  < ' ?" 4 >f6q S_x = xpN g(N )I{N0R 2 FH  0޽h ? 3y___PPT10Y+D=' &= @B +}  0 04(  0  <,*' ?" ` _N1\/f bx = xpNeQ(M ) ^S_ g N_bz nxpn-1 - a1(n-1)xpn-2 - a2(n-2)xpn-3 - " " " " " " - ak-1(n-k+1)xpn-k - ak(n-k)xpn-k-1 = 0' 2 n5X  <  BM' ?" . N_$Nz TXNNxpxp 0 g nxpn - a1(n-1)xpn-1 - a2(n-2)xpn-2 - " " " " " " - ak-1(n-k+1)xpn-k+1- ak(n-k)xpn-k = 0  $ 5Z j    <b' ?" , (M ) I{N k0 2" D  <8h' ?"   2 dk_f x = nxp/f(R)vN*N0@ 2 4J  <O' ?"L   . f x = xp/f(R)vSN*N0@ 2  >  <\x' ?" 9 V ~ N yr_e z(E)S+T gN͑9h x 1,2 = xp e P!ke z(R)S+T gT(n) = c1xpn + c2 n xpn k0O 2H  0޽h ? 3y___PPT10Y+D=' &= @B +!xW=LSQ}PK)XZ5`(qq`c@Bg)q!`jG'f.DFutzν՗B!#s_>?}ٱ* B' )irWIhΰKEwM#/ss{CD^w_hq`Ck|KVu5k/iD׾"#g(i.%Ґ |4^BFNL OT(wCT/'[eMدURM*6kRIA+NhW>)f%'HӞ0qiF4DH٬c4f+6rIPw@,J,c%{"U>%;ސQe߭UKZdfR*B/W s,7e@;w / Gs D y?S@ߵʉ OBf*kyK[\sl2V[Lz9wNPyʉ-lP;De3/.E_h͂*!W:!(YDFB]P|0\ҭdX{Tee% ٠1 3a Aw_)=]%;*liXn>ȓ]Wp5Ø"$i3;5}b I- kD !]z%xWOSA>|բ?^8`1%ЖV/DHx^D`x:@P,ߓK;?+_yF1?GV_qaYPRpPM{QKcF:Гyq):ENłUԈ{4yAJE*qrţdlS58jgr󚫔9BRЊ$jE #].urYO5LesK4Z&$˴T7LS+Wlʙh,2eEX8̲'wSWBkxc}V,i bC1HK~ ]~NoW6Wɛܔ~U;ށ>JFbH;iNLP|:zFoM&IOv[Sq;p-dwMLD\C4a wjPNCqn{|R[<o}dv ` YA 'ӗ??4="{r з Pg>!~V;;gppj?e!osVva I+5!l{_O D\㫢j'[O`q"=`!8As#HS[&hkC~ x|R0ZB1̗ ie: a`̝|>kB(:)dS)ܻ] F; df3{m ?ƅ%O?h|QRv[.E)VLQUmj$AXP.UΏ!IrgQjalEwo_&ן: ȓgFxvI(,4W7'dwsb?]c3S)lǞu?z|t ]knŶzL\q??ujCobW2֖FNH&xU)$Bz !=]:0[؏`?}h3c#d8}%k NkqexAϲwg UKݖ/NeȒ3u H9|}̢%da˧-|ʦ^%*ﯧ/qU]@+1ŋ>",9FyL! znM6tg(ʧNU25ݭ,uR-\ [1p"uʞfRI˗LX +Z64I8vޮI1Ьt6:nCe۰k% "gLN e".isnRSɒ}!i fׄc?pD,xWMLAfj)EC?K x1QMxjh =I$^n<2LSa%-hS8F|qg,S ؜jGr㚳9Bъ%ZG =^$Ghՙv/Sohįz=ñD47ElDi!狖w !&ϙd,,&"^J+ wݚ7*FDw]#XzK(> +y-%_`]=О׾ܐ^s>2e$ ~֞.nzLP505 vy o 2Ў?q~,Nhdx wAw_IL=f!AS֣}dV"`ZN|Vk.xWMhSAv_׿4Q)şGSJm1ϦHןTͭXɓxRP/"*<'OͣB1qf߾M"(Nvggٝ}m(30P(6 ͊BXt]Q^a~vleaaz#W^ /<N*3< Xwܚr3HV%Rxt^60 k S)>돖h8[#~S _ׅ\įLV-ۥM¹7QO]aq5G;WhQ @V/&?!ţmXhdT)vC/>ʘ S8oל,VnѮ$RhFkK Zѡ3^ FӄDv:R6V! :B"O V4y͚Ӊ +9!}%Z_px˯ebתrrI{ұ%w_<PVYnȀw%@^H-di96;_:1AU0W^CK]쩬WVwmp.f -&);tsޘoYe@mK&F?~މ8]U.@#wd~F ^zͪyb&`zJ2 Lj1&"V ԕm2,EZl1wܓ>i=<+U_L p8Y=QCƍ|us cHЗO3ս}X俷V  Z|/|`;xXMhA~3V*% x0A=CE$=TiRkR@U/XłBId?v}ٜuyD_&\N+QS@]IP Qv1Jb 49j~}]!N,i1uB"z@ Diۄ8C+<+,2qoGbk0b¶] Om렸`ZuίUhŽ70#WQQّ6:Mޢ =P}LCN2*+U %2#mXoV o%jٿ%:$PF7x'ǂqȱW?'XugLHVtv2j&8*լj ˄ҎT"`V /:xV.`|dsb?X"v*<T>-̿}]=E+x0EUr*gSb/w2[5~n֫M}Eϱ3L`T7t |0  ur }D)WlIJU飯5 %J9jOw{?_S@R?aI)[!,A\pD$"rsTB&nBZ7J4q OYk MmiC`Jp&~ /ƗósE N1J)d[o%ðlze!*(A\XG(*<_Js\;0fUZ$G꟒(Ͼ3)śQ㳊Нk@\D)Ea:y5gF;w|\9 B3OI@uY5ٯfUf|U9'0-O 腴f,Жh׭B.׭JM n|օb>]mU2ۧ a}k@E0xH!$!1ݮ 9NlN $͂cұ-1;o uy{"*i*kd;a-I[G=ك}q%wa\fa,|8hCU=J \O{>vkEڊGE1ŜGwK6WR뫛xWOHQs",?Zf*n 7CfM\?3xSS]J(աCvVn5(7{o{E8 \sL7 8&)|Vc}/봉?$IB#SLTk^lڕ̠ID,0Y=׽ |8!E*_8Nu/\?BPEœr*i0GTa3liL>7t[s+te{Omd6V5n#p&ETɬyN1'GG@tI# `JhGKjs9d_x4N e}Apu}a*Nb!e]MLw 1IG㘱Sg2𝓜ƈ Sq_1ч?vy89O[_=[ΐ54Iǒ B{ڎJNnܡ[ދ2]hmk1vK'.7}dFWj30vm[1Z1`EYI׏zb򦵐 9>DwTso*xZcʁW)'݃&m}{/[ $E2E݇e%=DDը*YT$Kr}~d,CH8M0#F" .D+Zsnu 6xY]l\>wvۋ1 ,^R5oB|ݍ]l⵽Km&R&*JVTH(TҪo-}hU!CyZyBBmo޵׮7)M9s{s;?q׻]XlMue^C h3ؠk" ɥ%:Z.Iۨi̛>}oJ\[dyY3H`m~v6/D_|_K ٿIĤ y>#> =HuElέu-!/ϗ!O}ڀ 5t&8l@8I2q mzxLZk4}o]z{h#g? nns\&p?7 yAt#wMvz  ہn v>  dPn5@E@H{{}@oE=`_~\y+սy$c~YIuc|xޜo_Z.M~[rƼɬTJ #rȤ"5@^Wα3@3wR'pҖ#Ǒ Cdd=LFmڪ60(LylTA,ϏWФ??5kg*c>RPӳJal*kn=k(Ku[q+7h"d4]qTw̍٦p]'>;խE0t-$b=bvU3Rxd~#5uBO3N'YUp ]VS(Qsރ{R/E|X|y675K s5uOXK"w[@~+KMB޴﵆yJe}O/6,%mKҧJv~6c_<ʁ7؞5JsE7yZ:jrc/Q9c\.j.n^Z}!=JU5)w1Vݺ?@MAvMBNW˶>R,J֖M66Jre8m2>-&*O;]! 5wBQ"S`Ц,u*A֣D{Gh =<24 Pz3VD9W)N DF}Sv(],Mw8!bY˽Lz=Q\W]%AiYUTSN`e,/١dpG)hJ׳KtÖ_Jt~,4d*<[=;iJ]-ZGˎض~KROj~[b1iյVKnKV|Ms] º`;IF>:?`K×P>gKYyx+H&z 'ه_ AB,G)o7x_4\zdDPRQ%Q!J4gJjϠU=uI5>$1_i#RPBΛ|e>xx%a χf 9(_cAXŲ?_!/bӂKX 316y#k3QQ1Iyqԏ Z58諤rEE!a?_Gz%"x|u; \q.TUTk!'[ g1.CLayce:<|8ז%xd?zHWSkO2eYǼ|8K!jb Qz&ZaG~/Ɉ6&ҚN ^.'A1p󅄙Yyn-ɅsGܰPb.Ʌ%x`UzopWJSA@LF0>JPN*91]GJYVp\f0p4[\*^ ja PIUy /$p`Axw0irb1y Oh+'0T hp  ûлõƬHANBING ZHENG CDESIGNKSDWM93Microsoft PowerPoint@ u@dV%d.@`u%zGSg  )'    """)))UUUMMMBBB999|PP3f333f3333f3ffffff3f̙3ff333f333333333f33333333f33f3ff3f3f3f3333f33̙33333f333333f3333f3ffffff3f33ff3f3f3f3fff3ffffffffff3ffff̙fff3fffff3fff333f3f3ff3ff33f̙̙3̙ff̙̙̙3f̙3f333f3333f3ffffff3f̙3f3f3f333f3333f3ffffff3f̙3f3ffffffffff!___www4'A x(xKʦ """)))UUUMMMBBB999|PP3f3333f333ff3fffff3f3f̙f3333f3333333333f3333333f3f33ff3f3f3f3333f3333333f3̙33333f333ff3ffffff3f33f3ff3f3f3ffff3fffffffff3fffffff3f̙ffff3ff333f3ff33fff33f3ff̙3f3f3333f333ff3fffff̙̙3̙f̙̙̙3f̙3f3f3333f333ff3fffff3f3f̙3ffffffffff!___wwwsxsxsssssssssssssssssxsssüüØsssssssssssssssssssssssssssssssssssssüüÙssssxsyssüüüüüüüüüüÙxssxsssssssssssssssssssssssssssssssssxsxsssJJJmJsÙýÙýýüüüýüÙüÙüüssssssCC""JssssssüüüüsssxJJCCCJüüÙsxsssssssJ"C"C"ssssssssssssüüüüüüüsssssJC"JCsssssüüüüüüÙssxssssJ"CCJJsssssssssüüüüüüüüýssssxxJC"JCssxüüüüîsssxssrCC"CJsssssssssssüüüüüüüüüüssssssCC"C"ssssüüüüüüüüüssssJC"C"CssssssssssssüüüüüüüüüüüüüüüüÒÙsxssn"CCJJssssssüüüüüüüüüÙssssssC""JCmssssssssJsrsssPssssssssüüüüüüüüüüüüüüüüüüssssxsm"CCmmssssssssssssssssmsssüüüüüüüüüüüüüüüüsssssCCCJCmJsJsmsssssssssssssJsJsmsüýüüüüüüüüüüüüüüüüüüssssJ"JJsmsssJssssssssssssssssssssüüüüüüüüüüüsssxsssCJJsssJsJsJsssmsJsssssJsJmJsJssüüüÙüüüüüüüüüüüssssrmJsxssssssmsssssssssJsrsJsJsJüüüüüüüüüüüüÙsssxssCrsssssssssssssssJJJsJmJsJmüüüüüüüüüüüüüüxsssmJJsssssssJsrsJsJsssJsmmrüüüüüüüüüÙüxssxssJCJJssssssssCJJmJsssJmJsJmJsüüüüüüüüüüüsüÙsxsxsJJJssssmsssssJmJssssssssrsssüüüüüüüüüüüüÒsssmJ"JmssJDCJJJJJJmJssssssssüüüüüüüüüüüüüüüüüüsxssCCCmmsJCCCJJJJsJmJsüüüüüüüüüüÙsssysJCCCJJ"C"JCJJJJJJmJssssüüüüüüüüüüüüüsüsssssCCC"JCJCJDmJsJmJsmsssüüüüüüüüüÙüsssssJJ"CC"JJmJmJsJssssssssssssüüüüüüüüüüüüüüssxssCJCmJmJsmssssssssüüüüüüüüÙüxssxssJC"JJsssrsrsssxsssssssssssÙüüüüüüüüüüüüüsüssssJ"CJsssssssssssxsssüüüüüüüüüüüüüüssssJC"sssssssssxssxsJmssssüüüüüüüüüüüüüsüsssmCJJsssssssJssssJsüüüüüüüüÙüssssCDCJCJJssssssJsJmJsssssJssssüüüüüüüü¼üüüsxssmCJCCCJJmJsmsJJCJssssssssssüüüüüüüüsssssJJCC"C"CCC"C"C"CCmJsssssssssssüüüüüüüüüsxssJJ"C"CCJCC"CCJCJCssssssssüüssssJJCCC"CCC"CCJCCJssssrssssüüüsssssJmCCC"C"C"C"JJmJssssssssssxssCCC"CCCCJssssssssÒssssmCC"C"CCCCsssxssÙssssssxsm"!CC"msssssssssÙssssssrCC"C"CCsssssssssssssysmCC"ssssssssssÙsssxssCCCCmmsxsxsxsxssssxssxsxssCCCCmssxsssssssÙsssssssmJCC"JJssssssssssssssssCJCCCmsssssssssüssssssmJCC"C"CCsssxsxsxsssssssxsJCC"CCryssssxssssxssssssssJC""DCCCssssssssssÙÒsssxssxsm""CCJJJsssssssssxssssssJD"CCCsJJsssxsxsxssxssssxsssxJJ"C""CCCCsssJssxssxssxssüsssssssCJ""CCCCmstmnsxsssssssssxssssJmCJ"C"C"C"JCJssJJJsssssssxsxÙsssssJJCJCCCJCC"JCJCrssJmJssssssxsxssssJJ"CCCC"C"JCCJsmmCJJssssxsssÒssxssJmJmJD"CCDCJCCCJJsssmJCJJsssssÙssssrmJsJmCCCCC"C"CCJJsssJJ"JJssxssxssssssssJJ"C"JCC"mJmJJJsssJmCJmsssssssxsssssssJCDmJJ"C"JJmJJJmJJJJCJJssssÙsssssmCCCssmmCCCmJsJJJJJsJmCmJssssssssxss""CsJsssJJ"CCJJJ"JJsJJJmCJJsssÙssssssJmJnssrJJCJJsJJmmJCJJsJJmsssssssxssJmCJCJmsJJCJCJJJJsJJJsJJJsJsssÙsssssssJmJssssJssssmJsJJCsssCssszyssstKsssJJCJssssJssxJJJmJmJsJmmsssssÙtttssmJmmsssxssssssssssssyRtsmJJJsmssssxsssxsxsxsxssssssssxsÙýÙtssJmmsssssssmssssyssxssyÙÙssmJssssssmJCJ"DJsssssxsssssssÙÚssJssssssJJCJCC"JJsssssysýyyytsJsssmssxrJ"C"C""JJssxssssssssÙytyssssmssyssJJ"CCCCCJmssssssKytyttyttssJrJJCsssJJCCCCC"JPssxsssssÙttttÙJJ"CCJJsJJCCCC"C"CCsssxsxsssÙtytK$ty""CCJCC"CC"CCssssssssssszyyDKLÚÙsCD"JCC"C"CC"CC"CCsssssssssÚtytQ#KttyttKsCCCC""CCJCsssssssJstztztRKysJ"C"CCC"JJJJmmsssJCCmotLtttKyttRDC"C"J"JCJCJ"CttzyutyztzKC"C"CCCDCJCmCC"C"ttzRzRtytytyKK"CCCCCJCJCJCD"CtyyttÚÙsJDsDD"JCC"C"CC"CCmJJJJCCCtyttJtÙy"""C"JJmCC"""C"JCD""mtyttJJDýyJCCmsssJCCCC"C"C"CC"ttzttKJ"CDJ""JJsssssCC""""JtttsssJJCCCsstKCJsssssss"C"C"C"CCCssssJsJJCC""CC"JJsssrsJC"CC"CCssssssssrCC"C!CCsmssssssJ"CC"JJJ"C"C"CssssssmsrJ"C"CCJsJmssmsJJC"CJsJsJC"CmsssssssJJCJCJJsssJsssssssmsmsssssJmJmJsssmsssssJsssmsssJsJssssssssssssssJsJssssssxssytyyssrsttsssssssssssssssssssssyyyyystyttssssssJsüssssxsssKtÚÙttLÚtsssssssssssrsssKELyyttLLtKsssmsmsssssssss$tyÙsssssssssssssssJsssKttyttsssssssssmssÙsssssssssssststtKLtÙÙsssyssssssrssrsJsmsJsssrstyQtKKEtttsssPsrsJsJsssssssssssssyttRtttKLtytssssssmssssmsssssssssssKtKtRL$KKtttytssssmsJsJsÙssssssssssstKRLyttLttttLsssssrsmssmsssPsssssssss$LKsLtKsKttyssKnnsssmsJmJss™sssssssxsxsysLKysKKsssyKyssssssssJssssJsmsPsssssssKsssJssssssssssssssJsJsJssssssssssssssssssssssxssssssJsmsJsÙüÙJsJsJsJsJsJsrsssssssssssrsJsPsmsJsJsJmJrrÙÙsJsrsmssssssssssssssxssssssssssssJsmsJsJssJsJsJsmsssssssssJsssssssrsssmsJsJrJmJsJsJsssssssssssssssssssssssssssssJsJmssmJsJsJsJsmsJsrsJsJsJsJsmsrsJsJsJsJsJJJssJsJsJsmsmsssmsssJsmsJsmsssssmsssmsmsJsJssJsJsJsJsJsmsJsmsJsmsJsmsmsssJsmsJsJsJmrsmsssmssssssssssssssssssssssssssJsmsJ՜.+,0    $ =Ļʾ6-16B$< HTimes New RomanArial Wingdings _GB2312Symbol п ƿɻMicrosoft ʽ 3.0ݹ鼰ݹ㷨 Ҫݹʵֻ õƬ 4 õƬ 5 õƬ 6 õƬ 7 õƬ 8 ݹ ݹ麯 ݹ麯 ݹ麯 õƬ 13 õƬ 14 õƬ 15 õƬ 16 õƬ 17 õƬ 18 õƬ 19 õƬ 20 ݹ㷨 õƬ 22 õƬ 23 õƬ 24 õƬ 25 ݹСݹ㷨ʱ临Ӷȷ õƬ 28򵥵ݹʽ õƬ 30 õƬ 31 õƬ 32Master Method õƬ 34 õƬ 35 õƬ 36 õƬ 37 õƬ 38 õƬ 39 õƬ 40 õƬ 41 õƬ 42 õƬ 43 õƬ 44 õƬ 45 õƬ 46 õƬ 47 õƬ 48 õƬ 49 õƬ 50 õƬ 51 õƬ 52 õƬ 53ݹĶ õƬ 56 õƬ 57 õƬ 58 õƬ 59 õƬ 60  õ ʾĸģǶ OLE  õƬ<%_n3 AdministratorAdministrator  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=?@ABCDEVRoot EntrydO) FGPicturesCurrent UserGSummaryInformation(TPowerPoint Document(y3DocumentSummaryInformation8>