Diviser-pour-régner (Résumé du @BaEGIQe U du manuel) Table
Transcription
Diviser-pour-régner (Résumé du @BaEGIQe U du manuel) Table
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T (1) + 1 + 2 + . . . + (n − 2) + (n − 1) 0 + 1 + 2 + . . . + (n − 2) + (n − 1) = n−1 X i i=0 = n(n − 1) 2 nqxs stkuÁorvz{u6y+u6 workux b, Θ(n2 ) i 6ponqxsÍyuE+y+tkxo¦+u y+z{po¥t?x¶tku¬uz{z{~s¥6r urkxpstk{tvy¥y"z{ u6nqn+{wsyo{xeu6tk6uxei Ù?pµrv{¥u nq2}p?y z 6 nqt¤x¶y x.z{uyt tKy"?{|[rvus¡¿u~sip¸quo¨ xer¢z{¸quz{¸¶rv4¦qy~onq pGp?ez{tvu6u psy+z{xeu r?psqzu66ytuo6i rvr~ouuup? ¦q¥z{xsu¬¥zynqtkuxz{u6¥ xu6 x¶p?nqxs{rktkrkrv~s{y+¥xz{¥ y"zy+¾¬¦+u6zyr¬osuu6ps¹epsyrpopor r¢¡uxez{uK6i nqxz{¥ ~su [y nqx$otkpsrkxs[nz{u6tvtku 0{u6tepsuK6ut yÒu6 rktktvps z{¥ ~.yxotvu6 6, 5 . /, /, /. ]5 /, .Ì ^Y[Ìf.Ê4]ÒÌ c?Ô2Y[a^4ce]&Ç'b;Ê4^+Y¬^4Ì.`'Y[Ç] rkxsy xoz{³pst¤ {y+rvtknq¦qxsn¹z{rv{pssr¢¡qy+u¶x©{u tku¶snqr¢ÙÒ~sp&or¢¡n+Á~oy+xsÁtkysz{n 6¥~sp?z{u u Á2y+r¢Rºt¤yrk~suµ~su6 ¶´ Q, 4 ^a/lkmj/a-h""mn©x§ mn/h^|mj/a-hiqr+^a/l2kmj/a-h`v§ nqps¹´ p?ytkyswnqnqnqpsxsnq~otkxsur¢{0rk nqxy+ervexpsps{uu6rxotvuRy+psxr¢o rv¡qrken+psMuu6t¤¥6 ~snqMxrkrkyxs{~srvu6rk{ rky+u6tknquxu utv~¿u³x ps¹sxoºnqu rvtk[Ùyµnqxs~sp}nq{rkorvnq{rvxrv¡nqnx¬ up?¤ y+«tkn{z{E ~s~snqpG¥powoy+p?yx{wo0utvpozu4x¶y+pnqz'xKi &qtkuu Ù?~¥[6p? {rv®nqkx uy+Átkn+ez{psr tkuMuxÒ~su{psuÙKorkxs Θ(f z{ps(n)) {rvnqxsMouup?x¹{rknqz{xsnqxsp?¥6¡uuz otkpsoMo2y+2p?¤.y~sz¹u¶tkt2y ¥tk¥psrv{uuxe~¹ rvxs ¥6~sz{rkpoy+xs{uµrkn+~sxou .psi rv¡+y+xu{u6ot y nqxs ;6# 1 , , ³&$ 7 3 « & /. nmf/dnhm©m-d} :d``d2®dn/h®d-fmnbd}d-h}an`d}l-d``dchm-an`nbdcea2®e®d^mj/a-h ^a/lkmj/a-h"^al2bd-fm nd¶o*qxw¥mn/©xwl«g`^ yQ§ mn/h^|mj/a-hiqr+^a/l2kmj/a-h`v§ ni _ 2®d2nd} :d``d2®dn/h^|mja- h 2g"fd `g/hif-g} h e d g qsr:m«n/©`v ¦qsr±^a/l2km2j/a-h`vx§ ^a/lkmj/a-h""mn©x§ sn+nqpsr¢! zMÙ}x}~s~o¥6u³p?z{tksy¶rvz{uRnq{t ¥6yy+~sxr ynqxoeu³psou¹tvnqutvÙ?u6¬r¢{~s¥Eu¹uyp?.*Ù?r¢¡n+snq{r¢?{n+rkn+{¥r xK¬pon+nquRwsx{~s rkupG)u xs~sz{uzry{zrvr¢y"¡.u6yrvtk~sn+u z{u6x tkuz{ ¥.¥6eypoz{yrk{urv¬nqxs~su¹~s2y u¹z{nq¥6xp?¥6¦zz{yu6tkxsuµ|¤u³ºE6psy+r¢ps¡qy+u¹x{~oup /. , ³ • T (1) = Θ(1) |[{nqup?z otky6nqnqp?z0w.nrvxowoy+{urkxsnqrvx}z0tk~oy³u¬~s¥~su6p?r y+Ùxsu.qyzpo{rkr¢u¡? r?~sz{p¶rk¥{uu6 µu.xotkn+psps z'~stku¬p.{u6yz{orv{ rvnqxsnqxop?uz¬tkuux yspsur¢¡?tk r?z{~s¥p¶ps{u6z{rv[o • T (n) = 2T ( n2 ) + Θ(f (n)) + Θ(n) + Θ(1) /, -, 6, ! "#$%!&#'(#)"*#+!,$-%"." !,)(,!,-%/.0 # #12) & 1%!%35435"#-%67 #789:!,!$"2 1 !,(#;#2%!$#<=-%#-%(2 #2809 (#>#>%!.%-%#-%1? @BACD<=# !)7-E1!,-%61F&1!)' (!,#9"G-%&-%-%&G"1/-%# !$!,H!$E1!,-%6 %# /B(!,JI 3 T (n) = T ( n ) + T ( n − 1) + Θ(f (n)) + Θ(n) + Θ(1) 1 ? K 9"M/-%# !$"&G!,H!&&1-%6( ? K )- !,2#&# !,)2L: n ≤#RT(n ) T (n) ∈ O(n lg n) 2)1)9 2-%6&11!%!,G1!,# !,6,S!,## !,? N !,<O#)-,# # P-Q:-%1,T!,( !,2#− j (T zporvnqx e# p rvtux8p~ y+p?y+tkz{nu6z{³ epsn+u { f¿(n)rkt∈pΘ(n) nqy+p?zp?ez{psuuz t¤epsytku¦qtkn+uzz{r¢{{unqsxou0u6~sp?u¶¬nqp?¡zz{n+rrvtvzRuzy|24oy+Arktvi?~s6yuµpsx.t?z{y~o¥t u?pstktvyRu¹y+~sxp}¥6R~sz{r nqyror¢xo. u yO(n R s ~ µ u lg n) rkt' u6 Rnq6utkr¢pswor?tkz{uu6~sepsurk0~s¥{nqup?z{z tkrkuxsu.zRyzt y{rv{rvnq¥6xs~sxsr u6yxouÒux 6i y e s p u { k r q n x o p ' r µ u q n u + y v t + n { z R 6 u R s ~ u { 6 y ¡ q n ¢ r E z tk uR 6nqµ ½ nz{u6u"i x! 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