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Std i z lematu 1 - teza¡EEª Eð:¢ ð ´ ƒ ð0€t⿃¿Àÿð ð`@ð,$ñ  0 𦟠$W(n) ³ð éð n lg n ùð¡8 2 €€ª& ðH ð´ ƒ ð0ƒ“ŽŸ‹”Þ½h¿ÿ ?ðð´ð ûúâ@  ƒf™f3ΙdÍ33š2ì zˆÔŠÌº___PPT10‹¬+·SjDñ°'ñ ¹ÿÿÿÿ=ñ @Bñ Dñk'ñ ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +Dñn'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¾'ñ =ñ4@BñBñ Bñ°Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´ÿÿÿÿÿÿÿÿDñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ /%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´ƒ%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû*´ƒDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´ÿÿÿÿÿÿÿÿDñn'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¾'ñ =ñ4@BñBñ Bñ°Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´ÿÿÿÿÿÿÿÿDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´Œ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´ŒDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´ŒDñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ"/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* ´%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* ´+à+0+´ß ++0+´ß ++0+´ß ++0+ ´ß +î`Pï €ù K0 º&ð²& ð<B¸ ñð:&ð( ð´ëÿÿäÿìÿÿä ð¸ðl ð¸ C ð€,⃿ÿð p` ðà  ƒ ð žðJ¢ 𸠃 ð0€ˆãƒ¿ƒ¿Àÿð` à ð꟠¤Niech D bdzie drzewem binarnym, a p(x) - dBugo[ [cie|ki od korzenia do li[cia x.¡S 2Sª SðL¢ 𸠃 ð0€¡ ¿ƒ¿Àÿð€@ ÀÇð,$ñ  0 𸟠(Epl(D) = S xÎð D p(x)¡R 2 çÿˆçÿçÿªðT¢ 𸠃 ð0€0¦ ¿ƒ¿ÀÿðPzð,$ñ  0 ðÀŸ W[ród drzew lokalnie peBnych o f li[ciach Df warto[ epl(Df) jest najmniejsza, gdy li[cie znajduj si jedynie na dwóch ostatnich poziomach.¡BŽ 2+ çÿ çÿRª@* Rðð‚ ð¸ C ð”ÀÀÅÀÿWÿÿG™)€ÿÿƒÿ™3‹yÿŒd€Ž€€€¿ÿÀÀÀ?¿ÿDowód:ImpactðÀ p@° ð,$ñD  0ðBò ð¸ 3 ðæZÀÀÅÀÿwÿÿGù UÁN€ÿƒÌÿŒd¿ÿ€ôÿÿ¨)?¿ÿLemat4Arial Black$ €ÿÿÿk À! 2€ÿÿÿðÀ 8 ð,$ñD  0ðBðl ðÐ ð ÷ ð=¸ð Ðð ÷ð,$ñD  0ðfB ð¸B “ ð6…‡D¿Àÿˆð2 [ ðfB ð ¸ “ ð6…‡D¿Àÿˆð 2 [ [ ðf2 ð ¸ “ ð6…‡ƒ¿Àÿˆðâ 6 2 ðfB ð ¸B “ ð6…‡D¿ÀÿˆðÀ! ½0 ðfB ð ¸ “ ð6…‡D¿Àÿˆðç! 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=ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñ¦/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*"èÿÿÿÿÿÿÿÿ%ñ(ñDñ·'ñ ô=ñ-ñ6ñBñ#blinds(vertical)*ñ<3ñ<ñû*"èÿÿÿÿÿÿÿÿDñÙ'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ)'ñ =ñ4@BñBñ Bñ%°Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñ«/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*!èÿÿÿÿÿÿÿÿ%ñ(ñDñ¹'ñ ô=ñ-ñ6ñBñ%barn(outVertical)*ñ<3ñ<ñû*!èÿÿÿÿÿÿÿÿ++0+ èÍ ++0+ èÍ ++0+ èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+èÍ ++0+ èÍ ++0+"èÍ ++0+#èÍ +îQ%ï €ù K0 F ð> àð ìð® ð( ð ðìðr ðì S ð€œÃÍ¿ÿð p` ðà  Í ð žðþ¢ ðì ƒ ð0€äÄÍ¿ƒ¿Àÿð0ÐÐ* 𞟠XDany jest cig n-elementów do posortowania. ¡- 2-ª -ðê‚ ðì 3 ðŽÀÀÅÀÿWÿÿ€ÿÿƒÿ™3‹yÿŒd€Ž€€€¿ÿÀÀÀ?¿ÿAle...Impactð° ¶”ð,$ñDÿÿÿ  0ð6¢ ðì ƒ ð0€ÄÉÍ¿ƒ¿Àÿðð€jð,$ñÿÿÿ 0 𢟠\Elementy tego cigu nie s po prostu liczbami naturalnymi, lecz same maj wewntrzn struktur, np.. s to skoDczone cigi pewnych obiektów (np.. Liczb, cyfr, znaków itd..).¡¯ 2¯ª ¯ðô¢ ðì ƒ ð0€ ÏÍ¿ƒ¿Àÿðð P ð,$ñ ÿÿÿ 0 ð`Ÿ¨Metoda naiwnego rozrzucania¡ 2ª ðê¢ ðì ƒ ð0€0ÔÍ¿ƒ¿Àÿðp P ªð,$ñÿÿÿ  0 ðVŸ Rozrzuci elementy danego cigu do  koszyków ze wzgldu na kolejne pozycje w cigach skBadowych, tzn. tworzymy pewn liczb  koszyków , tak, |e i-ty koszyk odpowiada i-tej pozycji w cigach skBadowych. Nastpnie sortujemy ka|dy z koszyków osobno t sam metod. ¡  2 ª ðâ ð ì ã ðh€lÒÍ¿G´ñÿÿH0*€ÿÿ̃†A‡Á¿Àÿ Papeteriað`P À€ ð,$ñD ÿÿÿ 0 ðDŸ èTakie postpowanie jest kosztowne: Dla elementów, które s cigami liczb o d cyfrach, trzeba utworzy 10 d koszyków!¡,ui  ª uðÀâ ð ì ã ðh€„àÍ¿GDëÿÿH€ÿÿ̃†A‡Á¿Àÿ PapeteriaðÐ `Ðð,$ñD ÿÿÿ 0 ðôŸ ®Takie postpowanie nie zawsze daje poprawny wynik np. gdy cigi nie s równej dBugo[ci.¡XXª XðH ðì ƒ ð0ƒ“ŽŸ‹”Þ½h¿ÿ ?/ð ð ìð ìð ûúâ@  ƒf™f3ΙdÍ33š2ì zˆ›Š“º___PPT10‹s+&9é{Dñw'ñ ¹ÿÿÿÿ=ñ @Bñ Dñ2'ñ ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +DñR'ñ ·=ñ%ñ(ñÿÿÿÿDñú'ñ =ñ%ñ(ñDñ¢'ñ =ñ4@BñBñ Bñ°Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñ/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ìÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*ìÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*ìÿÿÿÿÿÿÿÿDñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ /%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ì%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû*ìDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ì %ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*ì Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*ì DñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* ìÿÿÿÿÿÿÿÿ%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* ìÿÿÿÿÿÿÿÿDñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* ìÿÿÿÿÿÿÿÿ%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* ìÿÿÿÿÿÿÿÿ+à+0+ìÍ ++0+ìÍ ++0+ ìÍ ++0+ ìÍ +î 3ï €ù K0  ðº ð ôðR ð( ð ðôðr ðô S ð€ˆóÍ¿ÿð p` ðà  Í ð žð>¢ ðô ƒ ð0€øôÍ¿ƒ¿ÀÿðPàŠð,$ñÿÿÿ  0 𪟠dDane : tablica n-liczb caBkowitych o d cyfrach.¡3 23ª 3ð,¢ ðô ƒ ð0€èùÍ¿ƒ¿Àÿð0 Àê ð,$ñÿÿÿ  0 𘟠RFor k := 1 to d do // rozrzu wszystkie liczby do  kubeBków o numerach //0,1, 2,...,9 ze wzgldu na k-t od koDca cyfr. //poBcz kubeBki w jeden cig. od¡ª 2ªª ªðî‚ ðô 3 ð’ÀÀÅÀÿWÿÿ€ÿÿƒÿ™3‹yÿŒd€Ž€€€¿ÿÀÀÀ?¿ÿAlgorytmImpactðà0\Ðð,$ñDÿÿÿ  0ðì‚ ðô 3 ðÀÀÅÀÿWÿÿ€ÿÿƒÿ™3‹yÿŒd€Ž€€€¿ÿÀÀÀ?¿ÿKoszt :Impactð 0ð ð,$ñDÿÿÿ  0ðæ¢ ðô ƒ ð0€|¿ƒ¿ÀÿðÐ ðpð ð,$ñDÿÿÿ 0 ðRŸ¨T(n) = O(d* n)¡ 2ª 𸢠ðô ³ ðV€ô¿€ÿÿ̃†A‡Á¿ÀÿPapeteriað0 P `j ð,$ñD ÿÿÿ 0 ðþŸ ¸Wszystkie elementy, obcite do k-1 ostatnich pozycji, tworz cig uporzdkowany niemalejco.¡] 2]ª ]ðŽðl ðÐ@v0  ð ôð@Ðv0 ð,$ñD ÿÿÿ 0ðZB ð ôB s ð*D¿ÀÑÿð@ÐÐ0 ð°‚ ð ô à ð€ÀÀÅÀ ÿWÿÿ3f™¿ÿÀÀÀÔ”?¿ÿNiezmiennikTimes New RomanðÐ@vŠðH ðô ƒ ð0ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ûúâ@  ƒf™f3ΙdÍ33š2ì zˆ×'ŠÏ'º___PPT10‹¯'+ãyàDñ³&'ñ ¹ÿÿÿÿ=ñ @Bñ Dñn&'ñ ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ô3%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*ô3Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*ô3Dñn'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¾'ñ =ñ4@BñBñ Bñ°Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ôÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*ôÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*ôÿÿÿÿÿÿÿÿDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ô†%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*ô†Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*ô†Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ô†§%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*ô†§Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*ô†§Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ô§ª%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*ô§ªDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*ô§ªDñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ#/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ôÿÿÿÿÿÿÿÿ%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû*ôÿÿÿÿÿÿÿÿDñÇ'ñ ·=ñ%ñ(ñÿÿÿÿDño'ñ =ñ%ñ(ñDñ'ñ =ñ4@BñBñ Bñ °Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ(/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* ôÿÿÿÿÿÿÿÿ%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* ôÿÿÿÿÿÿÿÿDñn'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¾'ñ =ñ4@BñBñ Bñ°Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ôÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*ôÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*ôÿÿÿÿÿÿÿÿDñ'ñ ·=ñ%ñ(ñÿÿÿÿDñª'ñ =ñ%ñ(ñDñR'ñ =ñA@BñBñ  Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ôÿÿÿÿÿÿÿÿ%ñ(ñDñ¹'ñ ô=ñ-ñ6ñBñ%slide(fromBottom)*ñ<3ñ<ñû*ôÿÿÿÿÿÿÿÿ+à+0+ô ++0+ô ++0+ô ++0+ô +înï €ù K0 |ðtðøð ð( ð ðøðr ðø S ð€à¿ÿð p` ðà   ð žð‚ ðø 3 ðÂÀÀBÅÀÿWÿÿ€ÿÿƒÿ™3‹yÿŒd€Ž€€€¿ÿÀÀÀ?¿ÿUwaga na implementacj kubeBków!Impactð0°ð,$ñD ÿÿÿ 0ðò ðø 3 ðôZÀÀÅÀÿwÿÿGù UÁN€ÿƒÌÿŒd¿ÿ€ôÿÿ¨)?¿ÿKubeBek= stosArial Black$ €ÿÿÿk À! 2€ÿÿÿð°àÜ€ ðî¢ ðø ƒ ð0€œ¿ƒ¿Àÿð0@0ð,$ñÿÿÿ  0 ðZŸ Dany cig :¡ 2 ª ðî¢ ðø ƒ ð0€” ¿ƒ¿Àÿð°00ð,$ñÿÿÿ  0 ðZŸ¨85 83 63 64 84 15¡ 2ª ðÞ¢ ðø ƒ ð0€Ì¿ƒ¿Àÿð°€P Ðð,$ñÿÿÿ  0 ðJŸ¨Stos 3¡ 2ª ð&¢ ð ø ƒ ð0€¨*¿ƒ¿ÀÿðÐpð ð,$ñ ÿÿÿ  0 ð’Ÿ NPo poBczeniu : 63 83 84 64 15 85¡( 2(ª (ð&¢ ð ø ƒ ð0€ .¿ƒ¿ÀÿðP `àpð,$ñ ÿÿÿ 0 ð’Ÿ NPo poBczeniu : 15 64 63 85 84 83¡( 2(ª (ðÞ¢ ð ø ƒ ð0€„'¿ƒ¿Àÿð°P Ðð,$ñÿÿÿ  0 ðJŸ¨Stos 4¡ 2ª ðÞ¢ ð ø ƒ ð0€L6¿ƒ¿Àÿð° ðÐð,$ñÿÿÿ  0 ðJŸ¨Stos 5¡ 2ª ðÞ¢ ð ø ƒ ð0€\:¿ƒ¿Àÿð P ð,$ñÿÿÿ   0 ðJŸ¨Stos 1¡ 2ª ðÞ¢ ðø ƒ ð0€l>¿ƒ¿Àÿð ð ð,$ñÿÿÿ   0 ðJŸ¨Stos 6¡ 2ª ðÞ¢ ðø ƒ ð0€|B¿ƒ¿Àÿð ð À ð,$ñÿÿÿ   0 ðJŸ¨Stos 8¡ 2ª ðߢ ðø ƒ ð0€HF¿ƒ¿Àÿð0à0 ðð,$ñDÿÿÿ 0 ðKŸ¨63 83¡ 2ª ðߢ ðø ƒ ð0€XJ¿ƒ¿Àÿð0à 0 ðð,$ñDÿÿÿ 0 ðKŸ¨84 64¡ 2ª ðߢ ðø ƒ ð0€hN¿ƒ¿Àÿð0€ Ððð,$ñDÿÿÿ  0 ðKŸ¨15 85¡ 2ª ðÜ¢ ðø ƒ ð0€xR¿ƒ¿Àÿð °  ð,$ñDÿÿÿ 0 ðHŸ¨15¡ 2ª ðߢ ðø ƒ ð0€ˆV¿ƒ¿ÀÿðP € Ð  ð,$ñDÿÿÿ 0 ðKŸ¨64 63¡ 2ª ð⢠ðø ƒ ð0€˜Z¿ƒ¿ÀÿðÀ P  @ ð,$ñDÿÿÿ 0 ðNŸ¨85 84 83¡ 2 ª ðú ðø à ðžÀÀ>ÅÀÿWÿÿ¿Àÿ†††?¿ÿTo nie jest dobre rozwizanieArial Blackðp\œ ð,$ñDÿÿÿ  0ðH ðø ƒ ð0ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ûúâ@  ƒf™f3ΙdÍ33š2ì zˆ-ZŠ%Zº___PPT10‹Z+oi»ÿDñiV'ñ ¹ÿÿÿÿ=ñ @Bñ Dñ$V'ñ ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +DñÇ'ñ ·=ñ%ñ(ñÿÿÿÿDño'ñ =ñ%ñ(ñDñ'ñ =ñ4@BñBñ Bñ °Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*øÿÿÿÿÿÿÿÿ%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû*øÿÿÿÿÿÿÿÿDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ø %ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*ø Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*ø Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ø%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*øDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*øDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ø%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*øDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*øDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* ø%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû* øDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû* øDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* ø%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû* øDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû* øDñ_'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¯'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñ(/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*øÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ0-#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*øÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*øÿÿÿÿÿÿÿÿDñ_'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¯'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñ./%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*øÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ0-#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*øÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*øÿÿÿÿÿÿÿÿDñ_'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¯'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñ4/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*øÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ0-#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*øÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*øÿÿÿÿÿÿÿÿDñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ:/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* ø(%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* ø(Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* ø%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû* øDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû* øDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ø%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*øDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*øDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ø%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*øDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*øDñ_'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¯'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñQ/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*øÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ0-#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*øÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*øÿÿÿÿÿÿÿÿDñ_'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¯'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñW/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*øÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ0-#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*øÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*øÿÿÿÿÿÿÿÿDñ_'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¯'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñ]/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*øÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ0-#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*øÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*øÿÿÿÿÿÿÿÿDñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñc/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* ø(%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* ø(DñR'ñ ·=ñ%ñ(ñÿÿÿÿDñú'ñ =ñ%ñ(ñDñ¢'ñ =ñ4@BñBñ Bñ°Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñh/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*øÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*øÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*øÿÿÿÿÿÿÿÿ+€+0+ø ++0+ø ++0+ø ++0+ ø ++0+ ø ++0+ ø ++0+ ø ++0+ ø ++0+ø ++0+ø ++0+ø ++0+ø ++0+ø ++0+ø ++0+ø ++0+ø +î^ï €ù K0 }ðu ðð ð( ð ððr ð S ð€ì¿ÿð p` ðà   ð žðd¢ ð ³ ðV€\¿€ÿÿ̃†A‡Á¿ÀÿPapeteriað   ð,$ñDÿÿÿ  0 𪟠bFor k := 1 to d do // rozrzu wszystkie liczby do  kubeBków o //numerach 0, //1, 2,...9 ze wzgldu na k-t //od koDca cyfr . //poBcz kubeBki w jeden cig. od¡² 2²ª ²ð¢ ð ƒ ð0€¨–¿ƒ¿ÀÿðP`±ð,$ñ ÿÿÿ 0 ðŠŸ >U|yjmy kolejek jako  kubeBków !¡ 2 ÿfþª ð¢ ð ƒ ð0€¨›¿ƒ¿Àÿð à€° ð,$ñÿÿÿ  0 ðˆŸ DDany cig : 85 83 63 64 84 15¡# 2#ª #ðî¢ ð  ƒ ð0€ü”¿ƒ¿Àÿðà  Ú ð,$ñÿÿÿ  0 ðZŸ¨Kolejka 3: 83 63¡ 2ª ðî¢ ð  ƒ ð0€ô¡¿ƒ¿Àÿð   š ð,$ñÿÿÿ  0 ðZŸ¨Kolejka 4: 64 84¡ 2ª ðî¢ ð  ƒ ð0€X¦¿ƒ¿Àÿð` ` Z ð,$ñÿÿÿ  0 ðZŸ¨Kolejka 5: 85 15¡ 2ª ðñ¢ ð  ƒ ð0€¼ª¿ƒ¿Àÿð°  ªð,$ñÿÿÿ  0 ð]Ÿ¨ 83 63 64 84 85 15¡ 2ª ð†B ð  s ð*D¿ÀÑÿð€ À  € ð,$ñD ÿÿÿ 0ðê¢ ð ƒ ð0€ø®¿ƒ¿Àÿð° ÐЪ ð,$ñÿÿÿ   0 ðVŸ¨Kolejka 1: 15¡ 2ª ðî¢ ð ƒ ð0€T³¿ƒ¿Àÿðp ÐÐj ð,$ñÿÿÿ   0 ðZŸ¨Kolejka 6: 63 64¡ 2ª ðñ¢ ð ƒ ð0€¸¿ƒ¿Àÿð0 Ð0* ð,$ñÿÿÿ   0 ð]Ÿ¨Kolejka 8: 83 84 85¡ 2ª ð†B ð s ð*D¿ÀÑÿðP ÐpP ð,$ñD ÿÿÿ  0ð¢ ð ³ ðV€¼¿€ÿÿ̃†A‡Á¿ÀÿPapeteriað€ Ðzð,$ñDÿÿÿ  0 ð]Ÿ¨ 15 63 64 83 84 85¡ 2ª ðFò ð 3 ðêZÀÀÅÀÿwÿÿGù UÁN€ÿƒÌÿŒd¿ÿ€ôÿÿ¨)?¿ÿPrzykBadArial Black$ €ÿÿÿk À! 2€ÿÿÿð 0\ ð,$ñDÿÿÿ 0ð`¢ ð s ð*€„À¿Ìÿÿ¿Àÿð °Cð,$ñDÿÿÿ  0 ðÒŸ L For k := 1 to d do // posortuj elementy ze wzgldu na kt od koDca pozycj stosujc jaki[ stabilny algorytm, np.algorytm CountingSort // od¡"§ 2¦ª@=R  ðH ð ƒ ð0ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ûúâ@  ƒf™f3ΙdÍ33š2ì zˆ!KŠKº___PPT10‹ùJ+¯ƒ•*Dñ=H'ñ ¹ÿÿÿÿ=ñ @Bñ DñøG'ñ ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*ÿÿÿÿÿÿÿÿDñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ /%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* %ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* DñR'ñ ·=ñ%ñ(ñÿÿÿÿDñú'ñ =ñ%ñ(ñDñ¢'ñ =ñ4@BñBñ Bñ°Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñ/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ0-#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*ÿÿÿÿÿÿÿÿDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*#%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*#Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*#Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* %ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû* Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû* Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* %ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû* Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû* Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* %ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû* Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû* DñÇ'ñ ·=ñ%ñ(ñÿÿÿÿDño'ñ =ñ%ñ(ñDñ'ñ =ñ4@BñBñ Bñ °Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ./%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* ÿÿÿÿÿÿÿÿDñ_'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¯'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñ3/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* %ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ0-#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû* Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû* Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*DñÇ'ñ ·=ñ%ñ(ñÿÿÿÿDño'ñ =ñ%ñ(ñDñ'ñ =ñ4@BñBñ Bñ °Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñK/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû*ÿÿÿÿÿÿÿÿDñY'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ©'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñP/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ è=ñ+ñÏ4ñ 8?ñRCñBñBñCñèBñ#ppt_wBñ*ñY3ñ>ñBñ ppt_w<ñû*ÿÿÿÿÿÿÿÿDñ'ñ è=ñ+ñÏ4ñ 8?ñRCñBñBñCñèBñ#ppt_hBñ*ñY3ñ>ñBñ ppt_h<ñû*ÿÿÿÿÿÿÿÿDñƒ'ñ è=ñ+ñK4ñ 8?ñÎCñBñBñ‰#ppt_x+(cos(-2*pi*(1-$))*-#ppt_x-sin(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CñèBñ€?Bñ*ñY3ñ>ñBñ ppt_x<ñû*ÿÿÿÿÿÿÿÿDñƒ'ñ è=ñ+ñK4ñ 8?ñÎCñBñBñ‰#ppt_y+(sin(-2*pi*(1-$))*-#ppt_x+cos(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CñèBñ€?Bñ*ñY3ñ>ñBñ ppt_y<ñû*ÿÿÿÿÿÿÿÿDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*ÿÿÿÿÿÿÿÿ+ +0+ ++0+ ++0+ ++0+  ++0+  ++0+  ++0+  ++0+ ++0+ ++0+ ++0+ ++0+ +î¨@ï €ù K0 Šð‚@ð ðð( ð ð ðr ð  S ð€¤ë¿ÿð p` ðà   ð žð„¢ ð  ƒ ð0€í¿ƒ¿Àÿð`€ ôð,$ñ  0 ððŸ Algorytm RadixSort zaimplementowany z kolejkami ma wBasno[ stabilno[ci.¡I 2Iª&  7ðò ð  3 ðôZÀÀÅÀÿwÿÿGù UÁN€ÿƒÌÿŒd¿ÿ€ôÿÿ¨)?¿ÿTwierdzenie Arial Black$ €ÿÿÿk À! 2€ÿÿÿð`Рð¢ ð  ƒ ð0€Äò¿ƒ¿ÀÿðàPp!ð,$ñ  0 ð„Ÿ >Je|eli elementy x, y s uporzdkowane ze wzgldu na k-1 ostatnich cyfr i wpadaj do tego samego  kubeBka to po k-tym przebiegu nadal s w tym samym porzdku.¡  2 ª  ð®¢ ð  ƒ ð0€ ô¿ƒ¿Àÿð P ´ð,$ñ  0 ðŸ ÔJe|eli wpadaj do ró|nych kubeBków, to po k-tym przebiegu s uporzdkowane ze wzgldu na k ostatnich cyfr.¡k 2kª kðŒ¢ ð  ƒ ð0€D¿ƒ¿Àÿð   Š ð,$ñ  0 ðøŸ @x = x k+1 10 k+1 + xk 10 k + x ¡n! 2 çÿ  çÿ ª& ðŒ¢ ð  ƒ ð0€ ¿ƒ¿Àÿðà   Ú ð,$ñ  0 ðøŸ @y = y k+1 10 k+1 + yk 10 k + y ¡n! 2 çÿ  çÿ ª& ð¢ ð  ƒ ð0€è¿ƒ¿Àÿð À°Jð,$ñ 0 ðzŸ (x < y , x ,y < 10 k¡" 2 ª ð´¢ ð  ƒ ð0€Ø¿ƒ¿Àÿð0 Ä ð,$ñ  0 ð Ÿ ”Albo xk=yk i wtedy x i y trafiaj do tej samej kolejki oraz x poprzedza y¡BK 2 çÿ çÿAª&Að¢ ð  ƒ ð0€`¿ƒ¿Àÿð° € ñ ð,$ñ  0 ðlŸ àAlbo xk<yk ale wtedy x trafi do kolejki o mniejszym numerze ni| y i w takiej kolejno[ci uka| si po poBczeniu¡Bq 2 çÿ çÿgª&gðê¢ ð  ƒ ð0€”&¿ƒ¿Àÿðð à„ð,$ñ  0 ðVŸ ÊAlbo xk>yk ale wtedy x trafi do kolejki o numerze wikszym ni| y i po poBczeniu y uka|e si przed x¡Bf 2 çÿ çÿ\ª&\ðî¢ ð  ³ ðV€€.¿€ÿÿ̃†A‡Á¿ÀÿPapeteria"ñ¿ ðå] Ñö ð,$ñD  0 ð&Ÿ Æ UWAGA Algorytm RadixSort mo|na te| stosowa do innych typów danych. ¡d 2dª&& 5ðH ð  ƒ ð0ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ûúâ@  ƒf™f3ΙdÍ33š2ì zˆ®,Š¦,º___PPT10‹†,+¿v<°Dñ:*'ñ ¹ÿÿÿÿ=ñ @Bñ Dñõ)'ñ ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* I%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû* IDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû* IDñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*  %ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*  Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*  Dñ{'ñ ·=ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* k%ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû* kDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû* kDñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* !%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* !DñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* !%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* !Dñ_'ñ ·=ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¯'ñ =ñA@BñBñ Bñ°Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñ!/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* %ñ(ñDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ0-#ppt_w/2BñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû* Dñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_yBñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû* DñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ'/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* K%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* KDñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ,/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* q%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* qDñÔ'ñ ·=ñ%ñ(ñÿÿÿÿDñ|'ñ =ñ%ñ(ñDñ$'ñ =ñA@BñBñ Bñ °Bñ0Bñ%ñ(ñEñÜ'ñ =ñ4 Bñ`BñPBñ`Bñ?<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñ1/%ñ,(ñ <ñ +Dñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* f%ñ(ñDñ§'ñ ô=ñ-ño6ñBñbox(out)*ñ<3ñ<ñû* fDñð'ñ ·=ñ%ñ(ñÿÿÿÿDñ˜'ñ =ñ%ñ(ñDñ@'ñ =ñA@BñBñ  Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* ÿÿÿÿÿÿÿÿ%ñ(ñDñ§'ñ ô=ñ-ño6ñBñdissolve*ñ<3ñ<ñû* ÿÿÿÿÿÿÿÿ+0+0+  ++0+  ++0+  ++0+  ++0+  ++0+  ++0+  ++0+  ++0+  ++0+  +î¤ï €ù K0 £ð›`ðð3ð( ð ððr ð S ð€¸eƒ¿ÿð p` ðà  ƒ ð žðr ð S ð€Œfƒ¿ÿðpà ðà ƒ ð žðâ ð ³ ðB€Hhƒ…‡G© ƒ¿Àÿ𻸠V ð@òóU 0òóÿU 0 ðMŸ¨pokaz¡ª ðH ð ƒ ð0ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ûúâ@  ƒf™f3ΙdÍ33š2ì zˆ‘Š‰º___PPT10‹ië. ¥Ã¸[+Dñ='ñ ¹ÿÿÿÿ=ñ @Bñ +ðfñ 0 &ð0ð¼ð¶ð( ð (PG  ð¼ðR ð¼ 3 ð¿ÿð°Ð ðà  ð$ ð¼ C ð€„s¿ÿð° @ Ððà   ðÄŸ¨@epl(D*) = epl(D) -2h +(h-1) -k +2(k+1)< 0 Czyli epl(D*) < epl(D)ªh!ðH ð¼ ƒ ð0ƒ“Þ½h”ŽŸ‹¿ÿ ?ð ÿÿÿ€€€Ì™33ÌÌÌÿ²²²ðøñ 0 ¸ð°`ðÈðHð( ð•1(•1 ðÈðR ðÈ 3 ð¿ÿð°Ð ðà  ð¶ ðÈ C ð€x|¿ÿð° @ Ððà   ðVŸ „sufit(lg f) = podloga(lg f) + 1 H nie mo|e by wiksze od sufit(lg f) bo w przypadku drzewa które ma liscie tylko na 2 poziomach mamy Gdyby h= sufit(lg f) +1 wtedy f= 2^(h-1)  y(nie-li[cie na poziomie h-1) + 2y > 2^(h-1) + 2^sufil(lg f) >f Inaczej, f > 2^(h-1), bo ma li[cie te| na poziomie h , a ka|dy wierzchoBek z poziomu h-1 daje albo jest li[ciem albo daje co najmniej jeden li[ na poziomie h. Std 2^h <2f czyli h< lg2f=1+lgf <= sufit(lg f). ª¶ "#$ ùðH ðÈ ƒ ð0ƒ“Þ½h”ŽŸ‹¿ÿ ?ð ÿÿÿ€€€Ì™33ÌÌÌÿ²²²ð ñ 0 àðØÀðäðpð( ð ðäðX ðä C ð¿ÿð°Ð ðà  ðØ ðä S ð€P‹¿ÿð° @ Ððà   ðrŸ Dlaczego w ostatniej ptli for zaczynamy od elementu z pozycji ntej? Chodzi o to (czasami jest to wa|na), aby kolejno[ elementów o jednakowej warto[ci (lub jednakowej warto[ci atrybutu ze wzgldu na który dokonujemy porównaD , byBa taka jak w danym na pocztku wektorze- wBasno[ taka nazywa si stabilno[ci). 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