Download 2 3 Trees - Introduction to Algorithms - Lecture Notes and more Study notes Algorithms and Programming in PDF only on Docsity!
7 9@BA 5 =3-1/C
7 ED 3 -FG3HC>
IAKJMLONOPRQS T CIVU 3 W
X-Y Z[V\ ]^G[G`GaVbdce\ ^ebf]gY hVi jkelemenoi pk_h-i kHq=r sGk_j piteuHv w4xVy{zBZ|m~}v lo{Xfj n t bde~G]_]Vb s}Hb
M '6
7 3 F_3^ U^3 A C>5"^ A Ff(^ IA C3EF_3-&)?3)5-%C3^ IAC>3)1^ A &F^ A "%$;365%"FV$ U & IeU (^) : U " C%3 I 1 5 (^) :; C>143)
7 3 F_3^ U^3 A C>5^ IA IA< 1 43-&R5^ IA% "?1=$;3)1{14"^ U F_3)~C C>"1^ I ?C 7 3 6?3)1¡(^ IAC>3)1^ A &F^ A "%$;365¢&R5¢+E"?1.^ < IFG$1¡3^ A 7 &FeF£FG3-&)?365&)?3¤3)¥^ : &F£$3-¦%C § "?143¨1 (^) I "?1¡" (^) : 5 54Cg1 (^) :;< C: 1 43¤C;& (^) Aª©8 !¨W
X-Y Z[V\ ]^G[G`GaVbdce\ ^ebf]gY hVi jkelemenoi pk_h-i kHq=r sGk_j piteuHv w4xVy{zBZ|m~}v lo{Xfj n t bde~G]_]Vb s}
X-Y Z[V\ ]^G[G`GaVbdce\ ^ebf]gY hVi jkelemenoi pk_h-i kHq=r sGk_j piteuHv w4xVy{zBZ|m~}v lo{Xfj n t bde~G]_]Vb s}´
μ ·¶¸° º¹ »¨¼ )
7 &½+-,¡.,Cg1¡3)3¿¾^ IC$3-¦%CÁÀ^ <" A C&^ IA^5 L&R5¨&Â5^ :; 1 >&^ ¦'^ T & <" U ¦FG3HC>3^ IA &^1 /(ÂCg14363Ã"2$3-¦%CKÀÁÄ^ &R59ÅÆ+ÇÂF_3&)? 7 C3)1436{"?1¡3³&^ A (+-,/.,Cg14363K"$;3)¦CgÈÅÉF_"^ £LÊSÌËÍ-T ;&R Å SKËºÍ F_3&)?
7 WeWVW^5 ="'&^ A (Ì5^ :;< ÌC>143)3½¾^ ICÈÎ^ S F_3&)?365Â;&R5Â$3-¦%CÐÏ FG" (^) L|SM˺Í-T
D^3 -¦%C^ I^5 JKL F_"^ ³S T , < &A ¦3)14"?1^ U "?¦3)1>&ÑC^ I" A^5 #36Ò^ <I^3 A CFf(W
X-Y Z[V\ ]^G[G`GaVbdce\ ^ebf]gY hVi jkelemenoi pk_h-i kHq=r sGk_j piteuHv w4xVy{zBZ|m~}v lo{Xfj n t bde~G]_]Vb s}g^
ÓÔ¹'ÕR¹±Ö ¬ ¶× ¸'RÑ¹Ø Á
!#"ÚÙ A $K&¿5 :<)< 3 )5=5="?1{"?1¢ÛØ*
7 5 =C&^1 /C{14"^ U Cg3¨1¡""^ C 7 Ù A $C%3Ù1454C^ < IFG$±¾^ IC^ U &×Å^ Û LI ICM$"3)5^ A " C 3 H I 5 4C>55 (^) :;<6< 3 65=5>"?1 (^) :A $;3HÙ (^) A 3 )$½5 IA;< 3 ÚÛ I 5 ÜFV& 1 3 )1C& (^) A &FVF 3 F_3 U (^3) A C>5 (^) T
7 5 >3-&^1 <ÝCg3^ < IFG$ØÞ^5 5^ : Cg1¡3) !3 (^3) A 3 -1>&F;¦ (^) IF_"5>"?¦?(0&R5ß"?1 (^) ©8 !9Þ 5 -W2! (^) IVU (^3) JML F_" (^) ST W
X-Y Z[V\ ]^G[G`GaVbdce\ ^ebf]gY hVi jkelemenoi pk_h-i kHq=r sGk_j piteuHv w4xVy{zBZ|m~}v lo{Xfj n t bde~G]_]Vb s}
ÓÔ¹'ÕR¹à ¬ Ñ' Rá
!#" IA 5 =3-1/C¢& (^) A "%$;3Ãâ *
7 Ù A $μ&E5^ :;<6< 3 )5=5>"?1³ãÝ"2ÛäÑã#å^ â£æ^ LIØ$"3)5^ A " C3ç^ I^5 =CÙ^ A $μ& ¦143)$;3 (^) < 3 65=5>"?1& (^) A $M¦'3-1¡{"?1 U 5 4( UèU 3 6Cg1 I< "?¦3)1>&ÑC I"A (^5) T 7 &ÑC=C&^ <éâÌC>"KC3¦&^143 A Cê"ãë&^ A $ë%"?¦3¨ê&R5954C^ IFVF ÎÆ. (^) < IFG$;143 (^) A
7 I C%39"?¦'3¤Ê&^ IF_5^ LIW 3?WV-êÔ;&R5ì^ < IFV$;143^ A½A "¾^ T* í <^1 43-&ÑC>3Ý&^ A^3 6¾^ A "%$;3Ãêîß&^ A $é&ÑC=C&^ <é+^ < IFV$;143^ A "#ê C>" IC L 5 >" (^) A "¾êÁ&R5" (^) A Ff(ÂC/¾ " (^) < IFG$143 (^) A'T
í IA^5 =3)1¡C^ L^143 <):^1 ¡5^ I?3-F_(^ T ê î C>"¨ê^ Þ 5¢¦'&^1 ¡3^ ACï^ Iê^ I^5 &^ A "?1/, ¦& (^) A < 1 43-&ÑC>3 IC=5¦'& 1 ¡3 (^) A C Ù1¡5=C
D "365^ A " C^ I"Fe&ÑC=3¤C%3áðB3)¥^ : &F$;3)¦C%ñ^ <" A^5 4Cg1>&^ IA C Ä 5 =C (^) IFVF +-,/.,Cg14363ò
X-Y Z[V\ ]^G[G`GaVbdce\ ^ebf]gY hVi jkelemenoi pk_h-i kHq=r sGk_j piteuHv w4xVy{zBZ|m~}v lo{Xfj n t bde~G]_]Vb s}[
ó¬ R R|¹ ¬ ;® ¯±°ß²|
1 2 3 5 6 7 8 4
1 2 3 5 6 7 8 4
1 2 3 5 6 7 8 4
X-Y Z[V\ ]^G[G`GaVbdce\ ^ebf]gY hVi jkelemenoi pk_h-i kHq=r sGk_j piteuHv w4xVy{zBZ|m~}v lo{Xfj n t bde~G]_]Vb s}ô
