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    B Tng Hp - Mn Tr Tu Nhn To K2CN4 1

    Cu 1.(3)Trnh by s khc nhau gia thut ton v thut gii Heuristics. Hy nu 1 v ! v"

    thut gii HeuristicsCu 2.(7)a.Trnh by thut gii #obinson.b.$% !ng thut gii #obinson& ch'ng (inh bi ton sau)

    % * & +s *, +r s, & % u r& uc.Hy -y ng cy /0nh anh v t( ut theo %h23ng %h% vector /4c tr2ng c5a

    6uinan /7 -c /0nh (8t o9i *u /8c hay kh:ng /8c theo bng s; iu =? @8cA BgCt @? BhDn kh:ngE Fay @? BhDn kh:ngF Fhua =ng FG gai h:ngI Fay =ng cG gai @8cJ BgCt T( FG gai h:ng

    K Fhua =ng BhDn h:ngL BgCt T( BhDn h:ngH Fay T( cG gai @8c

    2 (c gii) trang 13)Cu 1(3 )Trnh by khi ni

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4

    3Cu 1 (3)

    a.Trnh by thut gii =23ng H9o.b.$% !ng thut ton =23ng h9o& ch'ng (inh bi ton sau)

    p 7 8 9( 7: 9r (: 8 p u r uCu 2 : (7)

    a.Trnh by thut gii A T .b. I_ng thut ton A T /7 gii bi ton TAFO sau)

    Tr9ng thi ban /`u Tr9ng thi k\t thc 4Cu 1: (4) FG R /8i bGng thi /Zu vng trn +2t /i,. Ei\t rdng )

    - @8i A / /Zu vi 8i E v /8i I.- @8i F / /Zu vi 8i I v /8i K- @8i I / /Zu vi 8i A v /8i K.- @8i E / /Zu vi 8i J v /8i K.

    A E F I J KA AE AF AI AJ AKE EF EI EJ EK

    F FI FJ FKI IJ IKJ JKK

    >fi /8i ch^ cG /2c thi /Zu 1 trn trong 1 tu`n.Fh^ cG Q /8i tha(gia 1 trn /Zu.Hy -\% 0ch thi /Zu sao cho s; tu`n in ra cc trn /Zu cn 9i t nhZt +I_ng thutton t: (u,Cu 2: (6) Fho bng *uan st )

    TT 6uang cnh Bhi2a ThZ% >9nh h:ngP #( (t TE Bh @2c BYng TE >9nh h:ngS >2a Fao >9nh h:ngR #( (t ThZ% >9nh @2cV >2a TE Bh h:ngU BYng TE Bh @2cl >2a ThZ% Bh h:ng

    am!!"#uong$gma%&'om- "2'n4&n-(!ar(&org 4rumK2CN4

    m J p

    6 I B

    m J6 p I B

    2

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4

    Mc /0nh /i"u ki! nho=m ng' 'haGu

    ) To Trung ?Snh Nam ChaGu .Y

    2 Nho; Thap Nam ChaGu .Y6 Nho; Trung ?Snh Nam ChaGu .Y4 To Cao Nam ChaGu .Zu Nho; Trung ?Snh N

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4

    am!!"#uong$gma%&'om- "2'n4&n-(!ar(&org 4rumK2CN4

    4

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4

    6BAI 1.:(3 IEM)R

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4T@Gn MaIu !o=' Ch@Hu 'ao CaGn na\ng +uIng "@m K@! 7ua;

    )& Rarah baIng Trung ?Snh Nh@D KhoGng Cha= nang2& +ana baIng Cao Trung ?Snh Co= KhoGng 'ha= nang6& .%@X NaGu VuIn Trung ?Snh Co= KhoGng 'ha= nang4& .nn@ baIng VuIn Trung ?Snh KhoGng Cha= nang& *m% Wo; Trung ?Snh Na\ng KhoGng Cha= nang

    3& @!@ NaGu Cao Na\ng KhoGng KhoGng 'ha= nang& cohn NaGu Trung ?Snh Na\ng KhoGng KhoGng 'ha= nang5& Ka!@ baIng VuIn Nh@D Co= KhoGng 'ha= nang

    am!!"#uong$gma%&'om- "2'n4&n-(!ar(&org 4rumK2CN4

    3

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4

    @" VBAI 1:(3 IEM)S dung thuat toan A !ho "a#$ toan tha% &a#'o$:Cho 6 'oD' .8B8C& ; 'oD' . ?an au 'o= n da (ap X@p

    !h@o !h

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4

    3 Nho; fanh No=nKhoGng

    mua

    Trung ?Snh Wo; TruD Mua

    am!!"#uong$gma%&'om- "2'n4&n-(!ar(&org 4rumK2CN4

    5

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4

    #BAI 1.:(3 IEM)Ru 7ua; 'u;a P@>' (

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4T@Gn MaIu !o=' Ch@Hu 'ao CaGn na\ng +uIng "@m K@! 7ua;

    )& Rarah baIng Trung ?Snh Nh@D KhoGng Cha= nang2& +ana baIng Cao Trung ?Snh Co= KhoGng 'ha= nang6& .%@X NaGu VuIn Trung ?Snh Co= KhoGng 'ha= nang

    4& .nn@ baIng VuIn Trung ?Snh KhoGng Cha= nang& *m% Wo; Trung ?Snh Na\ng KhoGng Cha= nang3& @!@ NaGu Cao Na\ng KhoGng KhoGng 'ha= nang& cohn NaGu Trung ?Snh Na\ng KhoGng KhoGng 'ha= nang5& Ka!@ baIng VuIn Nh@D Co= KhoGng 'ha= nang

    $ %BAI 1:(3 IEM)

    9):`haGn 'oGng8 %Q'h 'oGng !a='8 %Q'h !h auJ Co= mo>! 'uo>' ho> !ha;o "hoa hoD' P= 0 'hu; @

    "ha=' nhau8 moF 'hu; @ #@Fn ra !rong mo>! ?uoE& Ca=' 'hu; @ (au "hoGng

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4W@E Xa=' Qnh ng

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4

    B& $ ' *+,$ 1(c gii trang %)

    Cu 1.a.Trnh by s khc nhau gia thut ton v thut gii Heuristics.b.$% !ng nguyn th' t c5a k thut heuristics trnh by t2 t2Nng c5a bi ton

    chia B vt cG kh;i 2ng khc nhau thnh > nhG( /"u nhau. Lii bi ton chia U vtthnh P nhG(& cc vt cG trCng 2ng nh2 sau)

    n1 QU& nQ 1Q& nP PR& n 1R& nS QP& nR PQ& nV Q1& nU 1S.c.Trnh by t2 t2Nng v ( gi c5a thut gii eo /]i.

    -. Lii bi ton t( /2Xng/i t[ /i7( A /\n /i7( Etrong /] th0 cho N hnh 1theo thut gii eo /]i ;c/'ng.

    Cu 2.a.Trnh by thut gii #obinson.

    b.$% !ng thut gii #obinson& ch'ng (inh t% (

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4,ii / 1

    Cu 1. (3 im)a. khc nhau gia thut ton v thut gii Heuristics. +&S /i7(,Thut ton y hu h9n cc b2c& (fi b2c (: t chnh -c cc %hw% ton ho4c

    hnh /8ng c`n thc hi1& /4t nP vo nhG( >1 Tnh kh;i 2ng c5a cc nhG() >1)PR& >Q)& >P).

    m`n 4% Q) FhCn nhG( >Q& /4t nR vo nhG( >Q Tnh kh;i 2ng c5a cc nhG() >1)PR& >Q)PQ& >P).m`n 4% P) FhCn nhG( >P& /4t n1 vo nhG( >P Tnh kh;i 2ng c5a cc nhG() >1)PR& >Q)PQ& >P)QU.m`n 4% ) FhCn nhG( >P& /4t nS vo nhG( >P Tnh kh;i 2ng c5a cc nhG() >1)PR& >Q)PQ& >P)S1.Ti\% t!c 4% cho /\n h\t cc vt ta /2c k\t *u)BhG( >1 g]( cc vt nP& n& nQ cG kh;i 2ng) R

    BhG( >Q g]( cc vt nR& nV cG kh;i 2ng) SPBhG( >P g]( cc vt n1& nS& nU cG kh;i 2ng) RR

    am!!"#uong$gma%&'om- "2'n4&n-(!ar(&org 4rumK2CN4

    )6

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4

    c. T2 t2Nng& ( gi thut gii eo /]i +1&,)W T2 t2Nng +&S /i7(,)1. B\u tr9ng thi /`u c|ng tr9ng thi k\t thc th thot& th:ng bo t( /2c Xigii. Bg2c 9i /4t tr9ng thi hi

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4

    Cu 2 (2,0 im)a. jht bi7u thut gii #obinson. +&S /i7(,Thut gii #obinson hnh /8ng a trn %h23ng %h% ch'ng (inh bdng %hn

    ch'ng.b1) @2a vZn /" v" 9ng chun v %ht bi7u gii thi\t v k\t un c5a vZn /" 2i

    9ng sau)LT1& LTQ& ...&LTnm1& mQ&...&m(Trong /G cc LTiv m{/2c -y ng t[ cc bi\n (

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4==?+nhDn,+T+nhDn& /8c,& T+nhDn& kh:ng /8c,, +& ,.==?+gai,+T+gai& /8c,& T+gai& kh:ng /8c,, +P& 1,.

    Fc thu8c tnh v?& thu8c tnh (u cG 1 vector /3n v0& thu8c tnh v0 cG Q vector /3nv0 vy ta chCn thu8c tnh v0 th8c tnh %hn ho9ch& *u g9ch chn *u cG /8c +hnh a,.

    Fn 9i t% jFay cn n 8n *u /8c v kh:ng /8c& ti\% t!c %hn ho9ch thnh cct% con theo hai thu8c tnh (u v v?)

    Thu8c tnh (u) =>u+/?, +T+/?& /8c,& T+/?& kh:ng /8c,, +1& 11,.=>u+vng, +T+vng& /8c,& T+vng& kh:ng /8c,, +11&

    1,.=>u+t(, +T+t(& /8c,& T+t(& kh:ng /8c,, +11& 1,.

    Thu8c tnh v?) ==?+FG gai,+T+FG gai& /8c,& T+FG gai & kh:ng /8c,+QQ& Q,==?+BhDn,+T+BhDn& /8c,& T+nhDn & kh:ng /8c,+1& 11,

    Thu8c tnh v? cG Q vector /3n v0& vy ta chon thu8c tnh ny ( vector %hn ho9chti\% /2c cy /0nh anh nh2 +hnh b,.

    T[ cy /inh anh ta cG th7 suy ra h< ut nh2 sau)1. 6u cG v0 ngCt v *u cG v0 chua kh:ng /8czQ. 6u cG v0 cay v? nhDn kh:ng /8czP. 6u cG v0 cay v cG gai /8c.

    am!!"#uong$gma%&'om- "2'n4&n-(!ar(&org 4rumK2CN4

    )3

    v0

    C0

    FhuaBgCt

    A& J0 L

    cay

    E& 0 H

    Hnh 1

    v0

    C0

    FhuaBgCt

    A& J0 L cayv?

    0 H'

    BhDn FG gaiHnh Q

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4

    ,ii / 2(trang 2)Fu 1. +P /i7(,a. Trnh by khi ni

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4Q.P.P.. B\u Tkch2a -uZt hi

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4a. Thut gii =23ng H9o +&S /i7(,.b1) jht bi7u 9i gi thi\t v k\t un c5a vZn /" theo 9ng chun sau)

    LT1& LTQ& ...&LTnm1& mQ&...&m(Trong /G cc LTiv m{/2c -y ng t[ cc bi\n (8t ng /2c ch'ng (inh n\u t]n t9i chung (8t (

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4>8t vwc t3 =A+{, /2c gCi vector /3n v0 n\u nG ch^ cG uy nhZt (8t thnh %h`n

    cG gi tr0 1 v cc thnh %h`n khc cG gi tr0 .Thu8c tnh /2c chCn /7 %hn ho9ch thu8c tnh cG nhi"u vector /3n v0 nhZt.au khi %hn ho9ch -ong& ta -y ng cy /0nh anh. Fn c' vo cy /0nh anh&

    %ht sinh v ;i 2u t% ut.

    am!!"#uong$gma%&'om- "2'n4&n-(!ar(&org 4rumK2CN4

    21

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    B Tng Hp - Mn Tr Tu Nhn To K2CN4

    ut 5rganjh5 /0nh c5a %h5 /0nh +j, j

    +j6, +j 6,T23ng %hn +j6, +j6,Ie >organ +j 6, +j 6,

    +j 6, +j 6,Liao hon +j 6, +6 j,

    +j 6, +6 j,

    \t h% +j 6, # +j +6 #,,+j 6, # +j +6 #,,jhn %h;i j + 6 #, +j 6, +j #,

    j + 6 #, +j 6, +j #,j j jj j j

    j j 1j j

    am!!"#uong$gma%&'om- "2'n4&n-(!ar(&org 4rumK2CN4

    2)

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