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T(n)=2T(n/2)+c1 n e"2 c2 n<2 3. 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Öð3)n¡.@ 2��çÿ�†�Ž�çÿ†���çÿ�†�Ž�†�Ž�çÿ †�Ž�†�ª-ð„B ð  ã ðT�‚ƒ„…‡¿D¿ÀËŸoÿˆðPP°Pð„B ð  ã ðT�‚ƒ„…‡¿D¿ÀËŸoÿˆð0H�Hð¤ð8 ðÀ €a  ð& ðÀ €a ðP¢ ð  à ðH€ï�‚ƒ„¿�¿ÀËŸoÿˆðÀ €a  ðП Ð 1uÿT(1) = 3 ŒT T(2) = 8 —_ÿ c1 = 1/2 + Öð3/3, c2 = 1/2 - Öð3/3, ¡ši 2:��çÿ �†�Ž�çÿ†��†�ªB  0ð~B ð  Ó ðN�‚ƒ„‡¿D¿ÀËŸoÿˆð°e p ð~B ð ‚ Ó ðN�‚ƒ„‡¿D¿ÀËŸoÿˆðþg ^g ðÜð8 ð €  ð' ð € ðp¢ ð  à ðH€Ì�‚ƒ„¿�¿ÀËŸoÿˆð €  ððŸ ä EeÿT(n) = (1/2 + Öð3/3)(1 + Öð3)n + (1/2 - Öð3/3)( 1 - Öð3)n¡Îs 2�� †� � †� Ž� 7†� � †� Ž� � ªið„B ð  ã ðT�‚ƒ„…‡¿D¿ÀËŸoÿˆðæ  F  ð„B ð  ã ðT�‚ƒ„…‡¿D¿ÀËŸoÿˆðæ  v ð~B ð!  Ó ðN�‚ƒ„‡¿D¿ÀËŸoÿˆðuóóð~B ð"  Ó ðN�‚ƒ„‡¿D¿ÀËŸoÿˆðƒëëðH ð  ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿÿÿÿÿ™ÿÿÿ3–––ˆ�Šyº___PPT10‹Y+Dñ='ñ èÿÿÿÿ=ñ @Bñ +îï € 0 Bð: ð¤ñðÆð( ðžw ð¤ðð8 ð!` ê ð¤ð!` êð,¢ ð¤ à ðH€¨�‚ƒ„¿�¿ÀËŸoÿˆððÀý 𬟠 ‹O BlÿSn = ¡@ 2 ��çÿ�ª,ð¢ ð¤ à ðH€X�‚ƒ„¿�¿ÀËŸoÿˆð` ` - ðˆŸ  Sð K2¡D 2†�Ž��ªð¿¢ ð¤ à ðH€$�‚ƒ„¿�¿ÀËŸoÿˆðÝpê ð?Ÿ¨k = 0¡ 2�𻢠ð¤ à ðH€�‚ƒ„¿�¿ÀËŸoÿˆð¿!¯. ð;Ÿ¨n¡ 2�ðþ¢ 𤠳 ðB€X"�‚ƒ„¿�¿ÀËŸoÿð`€m ðŒŸ † ã‰ÿ1uÿ Sn = 12 + 22 + ·ð·ð·ð + n2 (1)¡ÈD 2 ��çÿ�����†���!�ª9ð¢ 𤠳 ðB€X/�‚ƒ„¿�¿ÀËŸoÿð°€½ ðŽŸ ˆ �¨cÿS n-1 = 12 + 22 + ·ð·ð·ð +(n - 1)2 (2)¡ÈE 2��çÿ�����†� ���ª 7ðô¢ ð ¤ ³ ðB€¨;�‚ƒ„¿�¿ÀËŸoÿð€  ð‚Ÿ Ž 1uÿ1 ÿ- ÿ2 ÿ —_ÿSn - S n-1 = n2 (3)¡„H 2��çÿ��çÿ���ªL 1ðØ¢ ð ¤ ³ ðB€\G�‚ƒ„¿�¿ÀËŸoÿðP€] ðfŸ ’ ù[ÿ3 ÿ�¨cÿSn-1 - Sn-2 = (n - 1)2 (4)¡„J 2��çÿ��çÿ ���ª, 8ð¤¢ ð ¤ ³ ðB€üO�‚ƒ„¿�¿ÀËŸoÿðp€}  ð2Ÿ h 1u(3) - (4) —_ÿSn - 2S n-1 + S n-2 = 2n - 1¡„5 2��çÿ��çÿ��çÿ �ª" ð*ð8 ð𠀑  ð¤ð𠀑 ðP¢ 𤠳 ðB€ÄY�‚ƒ„¿�¿ÀËŸoÿð𠀑  ðÖŸ Ð ÍS YO(u Nb—„v¹eÕl ÿˆm»SI{÷SóS¹�Yy˜_ ÿ—_ÿ S n - 4Sn-1 + 6Sn-2 - 4Sn-3 + Sn-4 = 0 (R)¡Èi 24��çÿ��çÿ��çÿ��çÿ��çÿ�ª (6ðŠB ð¤ ó ðZ�‚ƒ„…‡¿D¿ÀËŸoÎ×ÿ𬠌 ðt¢ 𤠳 ðB€øf�‚ƒ„¿�¿ÀËŸoÿðð €ý  ðŸ¨@ (E): x4-4x3+6x2-4x+1=0 ---------(x - 1) 4 = 0¡¦A 2���������ða¢ 𤠳 ðB€ìl�‚ƒ„¿�¿ÀËŸoÿð@€M ð- x1 = x2 = x3 = x4 = 1¡¦. 2��çÿ��çÿ��çÿ��çÿ�ðË2 ð¤ ó ðZ€ðw�‚ƒ„‡¿�ƒ¿ÀËŸoÿð‚Ÿ7‰ ðAŸ¨5¡$0 ÿ€CðH 𤠃 ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿÿÿÿÿ™ÿÿÿ3–––ˆ�Šyº___PPT10‹Y+Dñ='ñ èÿÿÿÿ=ñ @Bñ +îS ï € 0 zðr°ð¨ð ð( ðžw ð¨ðÄ¢ 𨠳 ðB€p‚�‚ƒ„¿�¿ÀËŸoÿð‰rò¾ ðRŸ Ö àV:Nyr�_¹e z„vã‰/fÛVÍ‘9h ÿ@båNÿ Sn = c11n +c2 n 1n + c3 n2 1n + c4 n3 1n = c1 + c2n + c3n2 + c4n3¡>l 2#��çÿ����çÿ����çÿ������çÿ������çÿ��çÿ��çÿ����çÿ���ªOð¢ 𨠳 ðB€ˆŸ�‚ƒ„¿�¿ÀËŸoÿð ròª  ðPŸ Ò 1uÿ S0 = 0, S1 = 1, S2 = 5, S3 = 14, åwÿ c1 = 0 , c2 = 1/6, c3 = 1/2, c4 = 1/3¡.j 2��çÿ��çÿ��çÿ ��çÿ��çÿ ��çÿ ��çÿ ��çÿ�ª,(+ð<¢ 𨠳 ðB€ ¬�‚ƒ„¿�¿ÀËŸoÿð9 ròF  ðÊŸ L @båNÿSn = 1/6 n ( n + 1 ) (2 n + 1 )¡@' 2��çÿ�ª ðH 𨠃 ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿÿÿÿÿ™ÿÿÿ3–––ˆ�Šyº___PPT10‹Y+Dñ='ñ èÿÿÿÿ=ñ @Bñ +îK ï € 0 rðjÀð pðð( ðžw ðpð¢ ðp ³ ðB€l´�‚ƒ„¿�¿ÀËŸoÿð‹DĘ 𔟠0 2 ^—PŸ!k8^û|pe¿~'`�¨c¹e z„vyr�_¹e zã‰Õl¡ 2�ª"ð&¢ ðp ³ ðB€äº�‚ƒ„¿�¿ÀËŸoÿðÛDĤ ð´Ÿ b ÿ1 ÿš[INÿ(R ):Nk6–^—PŸ!k8^û|pe¿~'`�¨c¹e z: (R ): H(n) = a1H(n - 1)+a2H(n - 2)+·ð ·ð ·ð +akH(n - k)+f(n) vQ-Nÿ 1 ÿa1, a2, ·ð ·ð ·ð , ak:N8^peÿ 2 ÿak ¹ð 0, n ³ð k, f(n) ¹ð 00¡¶² 2.��çÿ ��çÿ �†���çÿ��çÿ��çÿ�†���çÿ��çÿ�†��†� �†��ªx GðŽ¢ ðp ³ ðB€è¾�‚ƒ„¿�¿ÀËŸoÿðÛDĤ ðŸ ô ÿ2 ÿÿR ÿ„vã‰Ó~„gÿ ¾‹ÿÿR ÿ„v�ã‰/fH(n) ÿNƒ[ gN*Nyrã‰H*(n)ÿ €NÿR )øvù[”^„v PŸ!k¹e z(R)„v�ã‰/fH (n)0 R gÿR ÿ„vã‰ÿH(n) = H (n) + H*(n) ¡{ 2{�ªæ  ðH ðp ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿÿÿÿÿ™ÿÿÿ3–––ˆ�Šyº___PPT10‹Y+Dñ='ñ èÿÿÿÿ=ñ @Bñ +î#ï € 0 Œð„Ððtðð( ðžw ðtðò¢ ðt ³ ðB€tç�‚ƒ„¿�¿ÀËŸoÿðƒ€� ð€Ÿ  (3) (R )„vyrã‰b__¨‹º‹¡ 2�ª ðF¢ ðt ³ ðB€ �‚ƒ„¿�¿ÀËŸoÿð3€hð,$ñ  0 ð Ÿ ü 1 ÿS_f(n) b_‚Ybnt( b¹ð0, t:^—�tepe ÿöe ÿ(R )„vyrã‰:Nÿ H*(n) = p1nt + p2nt-1+ ·ð·ð·ð + pt n + pt+1 vQ-Nÿp1, p2, ·ð·ð·ð ÿ pt+1/f…_š[û|pe0¡à 2 ���†�†�ÿþŽ�ÿþçÿ†�ÿþŽ�ÿþ†�ÿþŽ�ÿþçÿ†�ÿþŽ�ÿþ †�ÿþŽ�ÿþçÿ†�ÿþŽ�ÿþçÿ†� ��çÿ��çÿ�†���çÿ�ª   4 ð"¢ ðt ³ ðB€¼ �‚ƒ„¿�¿ÀËŸoÿð〄 ð,$ñ  0 ð|Ÿ Ê FO ÿS_x = 1/f(R)„v j Í‘yr�_9hÿj ³ð 1 ÿöe ÿvQyr㉔^ 9e¾‹:Nÿ H*(n) = p1nt+j + p2nt-1+j+ ·ð·ð·ð + pt+1nj ¡&f 2�†� †�ÿþŽ�ÿþçÿ†�ÿþŽ�ÿþ†�ÿþŽ�ÿþçÿ†�ÿþŽ�ÿþ †�ÿþŽ�ÿþçÿ†�ÿþŽ�ÿþ†�ªh)ðТ ðt ³ ðB€% �‚ƒ„¿�¿ÀËŸoÿðã €„ ð,$ñ  0 ð*Ÿ ® 2 ÿS_f(n) b_‚Y b ×ð rn( b¹ð0, r ¹ð0 ÿöe ÿ(R )„vyrã‰:Nÿ H*(n) = p×ð rn vQ-Nÿp/f…_š[û|pe0¡ÀX 2�†����†�†�ÿþŽ�ÿþŽ�†�ª˜ðš¢ ðt ³ ðB€4/ �‚ƒ„¿�¿ÀËŸoÿð €´ð,$ñ  0 ðôŸ À FO ÿS_ x = r /f(R ) ù[”^„v(R)„v j Í‘yr�_9h( j ³ð 1)öe ÿ (R )„vyr㉔^9e¾‹:Nÿ H*(n) = p ×ð nj ×ð rn¡|a 2)�$†� †�ÿþŽ�ÿþ†�ÿþŽ�ÿþª” ðH ðt ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿÿÿÿÿ™ÿÿÿ3–––ˆ6Š.º___PPT10‹+Á¸h‡Dñ'ñ = ÿÿÿÿ=ñ @Bñ DñÍ'ñ –ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +Dñ{'ñ =ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*tÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*tÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*tÿÿÿÿÿÿÿÿDñ{'ñ =ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*tÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*tÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*tÿÿÿÿÿÿÿÿDñ{'ñ =ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*tÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*tÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*tÿÿÿÿÿÿÿÿDñ{'ñ =ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*tÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*tÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*tÿÿÿÿÿÿÿÿ+à+0+t0 ++0+t0 ++0+t0 ++0+t0 +î`0ï € 0 © ð¡ àð |ð9 ð( ðžw ð|ðí¢ ð| ³ ðB€ðC �‚ƒ„¿�¿ÀËŸoÿðu ‚ð,$ñ 0 ðGŸ¨ T(n) = ¡ 2�ðžr ð| ³ ðB�‚ƒ„‡¿�¿ÀËŸoÿð÷ °ð,$ñ@ 0ðn¢ ð| ³ ðB€€G �‚ƒ„¿�¿ÀËŸoÿðǰÔð,$ñ 0 ðÈŸ ` 2T( n - 1 ) + k (n > 1) (k:ckpe ÿ¡1 21�ª&,ðû¢ ð| ³ ðB€M �‚ƒ„¿�¿ÀËŸoÿðG€ðTð,$ñ 0 ðUŸ¨ k ( n = 1 )¡ 2�ðF¢ ð | ³ ðB€,Q �‚ƒ„¿�¿ÀËŸoÿð÷€ð,$ñ 0 ð Ÿ D ã‰ÿ(R ) : T(n) = 2T(n - 1) + k¡# 2#�ªð,¢ ð | ³ ðB€`U �‚ƒ„¿�¿ÀËŸoÿðG€Tð,$ñ 0 ð†Ÿ¨" (R) : T(n) = 2T(n - 1)¡# 2#�ª" ð ¢ ð | ³ ðB€,[ �‚ƒ„¿�¿ÀËŸoÿð�€ª ð,$ñ 0 ðcŸ¨) (E): x - 2 = 0 x = 2¡* 2*�ðt¢ ð | ³ ðB€W �‚ƒ„¿�¿ÀËŸoÿðÞ €ë ð,$ñ  0 ðΟ : (R)„v�ã‰ÿ T(n) = c 2n¡@ 2���ª0  ð@¢ ð | ³ ðB€`f �‚ƒ„¿�¿ÀËŸoÿðs €€ ð,$ñ  0 𚟠, àV:N(R )-N ÿf(n) = k¡ 2�ª, ð4¢ ð| ³ ðB€0m �‚ƒ„¿�¿ÀËŸoÿð± @¾ ð,$ñ   0 ðŽŸ 2 @båN ÿ ¾‹ÿ T*(n) = p ¡ 2�ª ðZ¢ ð| ³ ðB€„p �‚ƒ„¿�¿ÀËŸoÿð1€>ð,$ñ   0 ð´Ÿ X >f6q ÿ T*(n - 1) = p ¡- 2-�ª#ðH ð| ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿÿÿÿÿ™ÿÿÿ3–––ˆ_"ŠW"º___PPT10‹7"+.ÈŽDñë'ñ € ÿÿÿÿ=ñ @Bñ Dñ¦'ñ –ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +Dñ{'ñ =ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñT'ñ =ñA@Bñ�Bñ Bñ °Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*|ÿÿÿÿÿÿÿÿ%ñ(ñDñ»'ñ ô=ñ-ñƒ6ñBñ'blinds(horizontal)*ñ<3ñ<ñû*|ÿÿÿÿÿÿÿÿDñG'ñ =ñ4@Bñ�Bñ Bñ °Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*|ÿÿÿÿÿÿÿÿ%ñ(ñDñ»'ñ ô=ñ-ñƒ6ñBñ'blinds(horizontal)*ñ<3ñ<ñû*|ÿÿÿÿÿÿÿÿDñT'ñ =ñA@Bñ�Bñ Bñ °Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*|ÿÿÿÿÿÿÿÿ%ñ(ñDñ»'ñ ô=ñ-ñƒ6ñBñ'blinds(horizontal)*ñ<3ñ<ñû*|ÿÿÿÿÿÿÿÿDñT'ñ =ñA@Bñ�Bñ Bñ °Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*|ÿÿÿÿÿÿÿÿ%ñ(ñDñ»'ñ ô=ñ-ñƒ6ñBñ'blinds(horizontal)*ñ<3ñ<ñû*|ÿÿÿÿÿÿÿÿDñT'ñ =ñA@Bñ�Bñ Bñ °Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* |ÿÿÿÿÿÿÿÿ%ñ(ñDñ»'ñ ô=ñ-ñƒ6ñBñ'blinds(horizontal)*ñ<3ñ<ñû* |ÿÿÿÿÿÿÿÿDñT'ñ =ñA@Bñ�Bñ Bñ °Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* |ÿÿÿÿÿÿÿÿ%ñ(ñDñ»'ñ ô=ñ-ñƒ6ñBñ'blinds(horizontal)*ñ<3ñ<ñû* |ÿÿÿÿÿÿÿÿDñT'ñ =ñA@Bñ�Bñ Bñ °Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* |ÿÿÿÿÿÿÿÿ%ñ(ñDñ»'ñ ô=ñ-ñƒ6ñBñ'blinds(horizontal)*ñ<3ñ<ñû* |ÿÿÿÿÿÿÿÿDñT'ñ =ñA@Bñ�Bñ Bñ °Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* |ÿÿÿÿÿÿÿÿ%ñ(ñDñ»'ñ ô=ñ-ñƒ6ñBñ'blinds(horizontal)*ñ<3ñ<ñû* |ÿÿÿÿÿÿÿÿDñ'ñ =ñ%ñ(ñÿÿÿÿDñ¬'ñ =ñ%ñ(ñDñT'ñ =ñA@Bñ�Bñ Bñ °Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* |ÿÿÿÿÿÿÿÿ%ñ(ñDñ»'ñ ô=ñ-ñƒ6ñBñ'blinds(horizontal)*ñ<3ñ<ñû* |ÿÿÿÿÿÿÿÿDñN'ñ =ñ%ñ(ñÿÿÿÿDñö'ñ =ñ%ñ(ñDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*|ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*|ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*|ÿÿÿÿÿÿÿÿDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*|ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*|ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*|ÿÿÿÿÿÿÿÿ+0+0+|0 ++0+|0 ++0+|0 ++0+ |0 ++0+ |0 ++0+ |0 ++0+ |0 ++0+ |0 ++0+| ++0+|0 +î‰ ï € 0 °ð¨ðð €ð@ð( ðžw ð€ð&¢ ð€ ³ ðB€Ä‘ �‚ƒ„¿�¿ÀËŸoÿðÅròÒ ð´Ÿ < ŠbT*(n)0T*(n - 1)ãNeQ(R ) ,¡ 2�ª6 ð0¢ ð€ ³ ðB€$™ �‚ƒ„¿�¿ÀËŸoÿðrò" 𾟠@ gÿp = 2p + k \ðp = - k¡@! 2�†��ªðì¢ ð€ ³ ðB€P• �‚ƒ„¿�¿ÀËŸoÿðeròr ðzŸ & EeÿT*(n) = - k¡ 2�ª ð`¢ ð€ ³ ðB€„¢ �‚ƒ„¿�¿ÀËŸoÿðåròò ðd (R )„v�ã‰ÿT(n) = T (n) + T*(n) = c 2n - k¡@3 2+���ª&$ð:¢ ð € ³ ðB€L© �‚ƒ„¿�¿ÀËŸoÿðeròr  ðÈŸ d 1uT(1) = k, Šbƒ[ãNeQ N_ ÿ gÿ2 c - k = k c = k¡3 23�ª" ð¢ ð € ³ ðB€˜® �‚ƒ„¿�¿ÀËŸoÿðå rò†  ð’Ÿ ® \ð(R )„v�ã‰ÿT(n) = k( 2n - 1) = O( 2n )¡šX 2�†����0†�Ž�†�ª&HðH ð€ ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿÿÿÿÿ™ÿÿÿ3–––ˆ�Šyº___PPT10‹Y+Dñ='ñ èÿÿÿÿ=ñ @Bñ +îÎ"ï € 0 E ð= ð „ðÕ ð( ðžw ð„ð¢ ð„ ³ ðB€ü¼ �‚ƒ„¿�¿ÀËŸoÿðݶê ð’Ÿ "‹O T(n) = ¡0 2†��ª ðjr ð„ ³ ðB�‚ƒ„‡¿�¿ÀËŸoÿðs0ðcðõ¢ ð„ ³ ðB€$Á �‚ƒ„¿�¿ÀËŸoÿð-P€: ðƒŸ¨'2n-3 - T( n -2 ) ( n > 4 )¡@( 2��$�ð΢ ð„ ³ ðB€ÐÆ �‚ƒ„¿�¿ÀËŸoÿðÝð0ê ð\Ÿ¨" 1 ( n = 3 )¡# 2#�ð΢ ð„ ³ ðB€äË �‚ƒ„¿�¿ÀËŸoÿð�ð�š ð\Ÿ¨" 2 ( n = 4 )¡# 2#�ðv¢ ð„ ³ ðB€ðÏ �‚ƒ„¿�¿ÀËŸoÿð}€Šð,$ñ  0 ðП R ã‰ÿ(R ): T(n) = - T(n - 2 ) + 2n-3¡@* 2&���ª%ðB¢ ð„ ³ ðB€<Ö �‚ƒ„¿�¿ÀËŸoÿðÍ€Úð,$ñ  0 𜟨& (R): T(n) = - T(n - 2 )¡' 2'�ª4 ð$¢ ð„ ³ ðB€ Ü �‚ƒ„¿�¿ÀËŸoÿð €* ð,$ñ  0 ð~Ÿ¨" (E): x2 + 1 = 0¡@# 2�� �ðä¢ ð„ ³ ðB€Üá �‚ƒ„¿�¿ÀËŸoÿðm €z ð,$ñ  0 ð>Ÿ l (R) „v�ã‰ÿT (n) = c1cos(npð/2) + c2sin(npð/2)¡ˆ7 2��çÿ� †�Ž�çÿ †��ª& $ð–¢ ð„ ³ ðB€të �‚ƒ„¿�¿ÀËŸoÿð½ €Ê ð,$ñ  0 ððŸ X ÿ vQ-Nÿrð = 1 ÿ qð = pð/2 ÿ¡@- 2�†��ª4ðH ð„ ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿÿÿÿÿ™ÿÿÿ3–––ˆ1Š)º___PPT10‹ +¾‰DñÕ'ñ ö ÿÿÿÿ=ñ @Bñ Dñ�'ñ –ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +DñÇ'ñ =ñ%ñ(ñÿÿÿÿDño'ñ =ñ%ñ(ñDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*„ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*„ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*„ÿÿÿÿÿÿÿÿDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*„ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*„ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*„ÿÿÿÿÿÿÿÿDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*„ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*„ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*„ÿÿÿÿÿÿÿÿDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*„ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*„ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*„ÿÿÿÿÿÿÿÿDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*„ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*„ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*„ÿÿÿÿÿÿÿÿ++0+„0 ++0+„0 ++0+„0 ++0+„0 ++0+„0 +î ï € 0 l ðd ð °ðü ð( ðžw ð°ðÄ ðl ðM€®  ð °ðM€® ð,$ñD 0ðT¢ ð° ³ ðB€H!�‚ƒ„¿�¿ÀËŸoÿðM€Z ðÚŸ J ¾‹ÿ(R ) „vyrã‰/fÿT*(n) = p 2n¡@& 2$���ª, ðL¢ ð° ³ ðB€ !�‚ƒ„¿�¿ÀËŸoÿðm€ ðÒŸ ¶ Šbƒ[ãNeQ(R ), gÿp 2n = - p 2 n-2 + 2 n-3 —_ÿp = 1/10¡¶\ 2�!¡�� ���$� ��ªB ; ðÚ¢ ð ° ³ ðB€„!�‚ƒ„¿�¿ÀËŸoÿð=€J ð`Ÿ p \ð T(n) = c1cos(npð/2) + c2sin(npð/2) + 2n/10¡²9 2 � †�Ž�çÿ†�Ž�çÿ †�Ž�†��ª +ð¶¢ ð ° ³ ðB€L !�‚ƒ„¿�¿ÀËŸoÿð�€š  ð<Ÿ x 1uÿT(3) = 1 ŒT T(4) = 2, åwÿc1 = 2/5, c2 = -1/5¡b= 2'��çÿ ��çÿ�ª>   ðø¢ ð ° ³ ðB€¨)!�‚ƒ„¿�¿ÀËŸoÿð €®  ð~Ÿ  Eeÿ\ð T(n) = 2/5cos(npð/2) - 1/5sin(npð/2) + 2n/10 ÿ n > 2 ÿ¡fb 2 �+†�Ž�†�&�ª2 HðH ð° ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿÿÿÿÿ™ÿÿÿ3–––ˆIŠAº___PPT10‹!+Û®áüDñ'ñ èÿÿÿÿ=ñ @Bñ DñÀ'ñ –ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +Dñ÷'ñ =ñ%ñ(ñÿÿÿÿDñŸ'ñ =ñ%ñ(ñDñG'ñ =ñ4@Bñ�Bñ Bñ °Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* °ÿÿÿÿÿÿÿÿ%ñ(ñDñ»'ñ ô=ñ-ñƒ6ñBñ'blinds(horizontal)*ñ<3ñ<ñû* °ÿÿÿÿÿÿÿÿ+î^Hï € 0 ‚ðz ð´ñðð( ðœJ· ð´ð#ð8 ð€ í ð´ðÁÿ€ ®ð2¢ ð´ à ðH€6!�‚ƒ„¿�¿ÀËŸoÿˆðϰÜ ð²Ÿ " ‹O �QBlÿSn = ¡@ 2 ��çÿ�ª,ð¢ ð´ à ðH€l ð,$ñ  0 ðpŸ¨6 (E): x - 1 = 0 x = 1¡7 27�ðm¢ ð´ ³ ðB€u!�‚ƒ„¿�¿ÀËŸoÿðó€ð,$ñ  0 ðÇŸ¨' (R): Sn - S n-1 = 0 ¡„( 2��çÿ��çÿ���ðb¢ ð´ ³ ðB€˜|!�‚ƒ„¿�¿ÀËŸoÿð� €Ž ð,$ñ  0 𼟠2 (R)„v�ã‰ÿS n = c¡@ 2��çÿ�ª& ð>¢ ð´ ³ ðB€$ƒ!�‚ƒ„¿�¿ÀËŸoÿð € ð,$ñ  0 𘟠Z ¾‹ÿ(R )„vyrã‰/fÿS*n = p1n3 + p2n2 + p3n¡ê. 2��çÿ��çÿ����çÿ����çÿ�ª0 ðì¢ ð´ ³ ðB€h‘!�‚ƒ„¿�¿ÀËŸoÿð� €Ž ð,$ñ   0 ðFŸ n ãNeQ(R ), —_ÿp1 = 1/3, p2 = 1/2, p3 = 1/6¡„8 2��çÿ ��çÿ ��çÿ�ª0 #ð4¢ ð´ ³ ðB€x›!�‚ƒ„¿�¿ÀËŸoÿðÑ €Þð,$ñ   0 ðŽŸ Z (R )„v�ã‰ÿSn = p1n3 + p2n2 + p3n + c¡ê. 2��çÿ��çÿ����çÿ����çÿ�ª& ðˆ¢ ð´ ³ ðB€ °!�‚ƒ„¿�¿ÀËŸoÿðG€Tð,$ñD   0 ð⟠v 1uS0 = 0,åwÿc = 0 Eeÿ Sn = p1n3 + p2n2 + p3n¡ < 2 ��çÿ��çÿ��çÿ����çÿ����çÿ�ª<  ðH ð´ ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿÿÿÿÿ™ÿÿÿ3–––ˆ„/Š|/º___PPT10‹\/+­@ÈDñð-'ñ Ã!ÿÿÿÿ=ñ @Bñ Dñ«-'ñ –ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +Dñn'ñ =ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¾'ñ =ñ4@Bñ�Bñ Bñ°Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´D%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´DDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´DDñn'ñ =ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¾'ñ =ñ4@Bñ�Bñ Bñ°Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´E%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´EDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´EDñn'ñ =ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¾'ñ =ñ4@Bñ�Bñ Bñ°Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû* ´I%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû* ´IDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû* ´IDñ{'ñ =ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´ÿÿÿÿÿÿÿÿDñ{'ñ =ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´ÿÿÿÿÿÿÿÿDñ{'ñ =ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´ÿÿÿÿÿÿÿÿDñ{'ñ =ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´ÿÿÿÿÿÿÿÿDñ{'ñ =ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´ÿÿÿÿÿÿÿÿDñ{'ñ =ñ%ñ(ñÿÿÿÿDñ#'ñ =ñ%ñ(ñDñË'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´ÿÿÿÿÿÿÿÿDñn'ñ =ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¾'ñ =ñ4@Bñ�Bñ Bñ°Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*´<%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*´<Dñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*´<+P+0+´0 ++0+´0 ++0+´0 ++0+´0 ++0+´0 ++0+´0 +îc-ï € 0 .ð&pð˜ð¾ð( ðžw ð˜ðv¢ 𘠳 ðB€�Ï!�‚ƒ„¿�¿ÀËŸoÿðÄ€Ä ðŸ D ØSû|pe/^—¿~'`�¨c¹e z„vBl㉠ŸSRÿ ØSbc 0¡p#( 2�� !¡ � !¡ � ª,𞢠𘠳 ðB€DØ!�‚ƒ„¿�¿ÀËŸoÿð`€mð,$ñ  0 ðøŸ  N0ØS ^—¿~'` :N ¿~'` ¡ž 2�!¡�!¡�!¡�!¡�ª ðf¢ ð ˜ ³ ðB€Œâ!�‚ƒ„¿�¿ÀËŸoÿðV €c ð,$ñ  0 ðÀŸ 0 ã‰ÿäNÿG(n) = H2(n),R gÿ¡@ 2���ª, ð¨ðl ðƒ® ³  ð˜ð¾ t¤ ð,$ñD  0ðè¢ ð ˜ ³ ðB€Pé!�‚ƒ„¿�¿ÀËŸoÿð® ³»  ðnŸ¨4G(n) - 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1) + Sð 1/n T(k - 1) + Sð 1/nT(n-k) (n > 1)¡@6 2 �)†��ð·¢ ð ¼ ³ ðB€89"�‚ƒ„¿�¿ÀËŸoÿð�d pq  ð=Ÿ¨k=1¡ 2�ð¢ ð ¼ Ó ðN€="�‚ƒ„…‡¿�¿ÀËŸoÿð Y ©f  ð<Ÿ¨ k=1¡ �ðµ¢ ð ¼ ³ ðB€¸@"�‚ƒ„¿�¿ÀËŸoÿðÒ tß  ð;Ÿ¨n¡ 2�ðµ¢ ð ¼ ³ ðB€ E"�‚ƒ„¿�¿ÀËŸoÿð¾ Ý ê  ð;Ÿ¨n¡ 2�ð‡ð@ ð0 op ð¼ð¥oåð½¢ ð ¼ ³ ðB€8I"�‚ƒ„¿�¿ÀËŸoÿðÚ 0ç  ðCŸ¨ T(n) = ¡ 2 �ðrr ð¼ ³ ðB�‚ƒ„‡¿�¿ÀËŸoÿðÐ0 opðª ð¼ Ó ðN�‚ƒ„‡¿�ƒ¿ÀË>ßÿðMwP "ð,$ñD  0ðª ð¼ Ó ðN�‚ƒ„‡¿�ƒ¿ÀË>ßÿðM3 )"ð,$ñD  0ðH ð¼ ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿÿÿÿÿ™ÿÿÿ3–––ˆ5 Š- º___PPT10‹ +Ôû§<Dññ 'ñ ÿÿÿÿ=ñ @Bñ Dñ¬ 'ñ –ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +Dñ÷'ñ =ñ%ñ(ñÿÿÿÿDñŸ'ñ =ñ%ñ(ñDñG'ñ =ñ4@Bñ�Bñ Bñ °Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*¼ÿÿÿÿÿÿÿÿ%ñ(ñDñ»'ñ ô=ñ-ñƒ6ñBñ'blinds(horizontal)*ñ<3ñ<ñû*¼ÿÿÿÿÿÿÿÿDñn'ñ =ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¾'ñ =ñ4@Bñ�Bñ Bñ°Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*¼ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*¼ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*¼ÿÿÿÿÿÿÿÿDñn'ñ =ñ%ñ(ñÿÿÿÿDñ'ñ =ñ%ñ(ñDñ¾'ñ =ñ4@Bñ�Bñ Bñ°Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*¼ÿÿÿÿÿÿÿÿ%ñ(ñDñ'ñ ô=ñ+ñÙ4ñ 8?ñ\CñBñ#ppt_xBñCñèBñ#ppt_xBñ*ñY3ñ>ñBñ ppt_x<ñû*¼ÿÿÿÿÿÿÿÿDñ'ñ ô=ñ+ñá4ñ 8?ñdCñBñ1+#ppt_h/2BñCñèBñ#ppt_yBñ*ñY3ñ>ñBñ ppt_y<ñû*¼ÿÿÿÿÿÿÿÿ+î ï € 0 4ð,�ð)1À`ñð¤ð( ðžw ðÀðð¢ ðÀ ³ ðB€0R"�‚ƒ„¿�¿ÀËŸoÿð€  ð~Ÿ " tet09e™Q Nð��¨c_ÿ¡ 2�ªðãð8 ðx0 ðÀðôF‚ð¢ ðÀ ³ ðB€ W"�‚ƒ„¿�¿ÀËŸoÿð@0M 𢟠F T(n) = (n - 1) + 2/n Sð T(k)¡@$ 2�†��𸢠ðÀ ³ ðB€¼]"�‚ƒ„¿�¿ÀËŸoÿðKxû … ð>Ÿ¨ n-1¡ 2�ð·¢ ðÀ ³ ðB€Lb"�‚ƒ„¿�¿ÀËŸoÿðŠù  ð=Ÿ¨k=1¡ 2�ðJð8 ð�U ð1Àð�Uð ¢ ðÀ à ðH€ a"�‚ƒ„¿�¿ÀËŸoÿˆðX0e ð Ÿ D nT(n) = n(n - 1) + 2 Sð T(k)¡@# 2�†��ð¾¢ ð À à ðH€`k"�‚ƒ„¿�¿ÀËŸoÿˆðl� � ð>Ÿ¨ n-1¡ 2�ð½¢ ð À à ðH€ðo"�‚ƒ„¿�¿ÀËŸoÿˆðŠ  ð=Ÿ¨k=1¡ 2�ðŠB ðÀ ó ðZ�‚ƒ„‡¿D¿ÀËŸoÎ×ÿˆð ð½¢ ðÀ à ðH€s"�‚ƒ„¿�¿ÀËŸoÿˆð_Ul ð=Ÿ¨(1)¡ 2�ð2ð8 ðZð—¥  ðÀðzOŒ/ð&¢ ð À à ðH€dw"�‚ƒ„¿�¿ÀËŸoÿˆðôÌ$٠𦟠J(n-1)T(n-1) = (n-1)(n - 2) + 2 Sð T(k)¡@& 2�†��ð¾¢ ðÀ à ðH€l|"�‚ƒ„¿�¿ÀËŸoÿˆð.ðÞý ð>Ÿ¨ n-2¡ 2�ð½¢ ðÀ à ðH€Œ€"�‚ƒ„¿�¿ÀËŸoÿˆðm˜í¥  ð=Ÿ¨k=1¡ 2�ð�B ðÀ  ð`�‚ƒ„…‡¿D¿ÀËŸoÎ×ÿˆðDbbð½¢ ðÀ à ðH€„"�‚ƒ„¿�¿ÀËŸoÿˆð¿—Ì ð=Ÿ¨(2)¡ 2�ðÔ¢ ðÀ ³ ðB€´‡"�‚ƒ„¿�¿ÀËŸoÿðZÍ*Ú ðZŸ �¨cÿ¡ 2�ªð‚¢ ðÀ ³ ðB€¤‹"�‚ƒ„¿�¿ÀËŸoÿð€µ  🠢 1u(1) - (2) —_ÿ nT(n) - (n - 1)T(n - 1) = 2(n - 1) + 2T(n - 1)¡R 2R�ª, .ðÍð8 ð z'  ð&Àð z' ð*¢ ðÀ ³ ðB€X’"�‚ƒ„¿�¿ÀËŸoÿð  � ­  ð°Ÿ T sSÿ T(n) = T(n - 1) + ¡+ 2+�ª ð~B ðÀ Ó ðN�‚ƒ„…‡¿D¿ÀËŸoÿð`7 à7 ð·¢ ðÀ ³ ðB€˜–"�‚ƒ„¿�¿ÀËŸoÿðz ú'  ð=Ÿ¨n+1¡ 2�ðµ¢ ðÀ ³ ðB€Dš"�‚ƒ„¿�¿ÀËŸoÿðð °)  ð;Ÿ¨1¡ 2�ð~B ðÀ Ó ðN�‚ƒ„…‡¿D¿ÀËŸoÿð°0 p0 ðµ¢ ðÀ ³ ðB€<ž"�‚ƒ„¿�¿ÀËŸoÿðÜý œ  ð;Ÿ¨n¡ 2�ðµ¢ ð À ³ ðB€4¢"�‚ƒ„¿�¿ÀËŸoÿðÜ œ(  ð;Ÿ¨1¡ 2�ðxB ð!À à ðH�‚ƒ„‡¿D¿ÀËŸoÿð˜ % ð0 ð¼¢ ð"À ³ ðB€è "�‚ƒ„¿�¿ÀËŸoÿðÚ  Ú  ðBŸ¨2(n - 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