haoi 08

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bi - Li gii 2008

Phm Nam Long

Phm Hi Minh

L n Khu

Ng Minh c

Nguyn Honh Tin

http://vnoi.info

Bin son: Ng Minh c

10/08/2008

v1.0

Hanoi-Amsterdam Olympiad in

Informatics
http://vnoi.info/http://vnoi.info/http://vnoi.info/

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Hanoi-Amsterdam Olympiad in Informatics

http://vnoi.info Trang 2

2008

Tng quan vngy thi thnht( 09082008 )

Bi thi Bi 1 Bi 2 Bi 3

Tn ba iGp tin M v tt

Gii phngmt bng

Gii hn thigian

0.5s/test 2s/test 3s/test

Tng sim 100 100 100

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2008

Gp tin

M bi: NOTE

Tc gi: Phm Nam LongLSM l c vn cao cp ca HAOI 2008 v c giao nhim v ra thi. Hn np bi ang n gn m LSMkhng c mt tng no. Th k Lola thc gic ngy m cng thm khon tin bi thng nu khnghon thnh cng tc ng hn lm LSM ht sc lo lng. Trong lc tuyt vng, LSM v tnh gp i lin tipt tin 100$ trc mt. Khi m t tin ra, trong tay LSM l t giy bc c cc vt gp ln xung. t nhin,mt tng le sng: nu c cch no xc nh c np gp th p tnh t tri sang phi ca t tin tinl ln hay xung, th y s l mt bi ton hay cho cc th sinh ca HAOI 2008. Hy gip LSM thot khitnh th kh khn ny nh!

T tin c hnh dng ch nht v lun c thc hin sao cho mp tri c gp ln mp phi. LSM thchin gp nh vy f ln. Tuy nhin trong thc t, ti mt lc no ng tin s khng th gp c do qudy, nhng chng ta b qua thc t ny v t tin vn c gp i chnh xc sau f ln.

D liu

Gm nhiu dng mi dng cha ng 2 snguyn ngn cch nhau bi du cch f v p tng ngl sln gp ttin v vtr np gp cn xc nh. (1 f 31. p tha mn khng vt qu slngnp gp c to ra sau f ln gp)

Dliu c kt thc bi 2 s0 v khng yu cu in ra kt qucho 2 sny.

Kt qu

Vi mi dng tng ng vi d liu vo, in ra mt k t duy nht mi dng: U cho np gp ln trn v Dcho np gp xung di.

V d

D liu2 1

2 2

2 3

0 0

Kt quU

D

D
http://s37.photobucket.com/albums/e81/beo_chay_so/?action=view&current=note.png

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2008

M v tt

M bi: KANDP

Tc gi: Phm Hi Minh/L n KhuTrn mt bi c vua kch thc v hn c mt con m v mt con tt. V tr ca qun m l (Mx, My), v trca qun tt l (Tx, Ty), trong x l ch s dng v y l ch s ct. Qun m c quyn i theo 8 hngnh bn c vua chun. Qun tt ch c i mt hng l i xung di (t v tr (x, y) n v tr (x-1, y)).Hai qun c s di chuyn theo lt, xen k nhau. Khi mt qun c vo v tr ca qun c khc ang ng thqun c va di chuyn s thng.

Bn bit v tr ban u ca hai qun c, qun c no i trc. Bn hy tnh xem qun m c kh nng thngkhng v nu thng th n s phi i t nht l bao nhiu nc.

D liu

Dng thnht ghi hai sMx, My. Dng thhai ghi hai sTx, Ty. Dng thba ghi 0/1 ng vi qun m i trc hoc qun tt i trc.

Kt qu

Dng thnht ghi YES/NO tng ng vi qun m c khnng thng hoc khng c khnngthng.

Nu dng thnht l YES th dng thhai ghi sbc t nht.

Gii hn

Mx, My, Tx, Ty l cc s nguyn c tr tuyt i nh hn hoc bng 1000. Trong 50% s test, Mx, My, Tx,Ty c tr tuyt i nh hn hoc bng 50.

V d

D liu0 0

0 3

0

Kt quYES

2

Gii thch

hnh v bn di, ch K th hin v tr qun m, ch P th hin v tr qun tt.

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2008

Li gii:

Nhn xt: do ta quan tm n vic m n tt nnbc i cui cng phi l ca m.

Xt trng hp tt i trc. Mi bc tt di chuyn theo vector (-1, 0) cn m di chuyn theo vector (x,y)trong x2+y2=5. Ta c th coi nh tt ng yn (di chuyn theo vector (0, 0)) cn m di chuyn theovector (x+1, y). Bng cch BFS tvtr ban u ca m, ta stm c sbc i ngn nht n vtr ttng.

Trong trng hp m i trc, ta cn duyt trc mt bc i bnh thng ca m(8 hng). Sau vimi bc i, BFS nh trn tm sbc ngn nht n vtr ca tt.

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2008Li gii:Pht biu li bi ton:Cho n im trn mt phng, im th i c trng s l s i

2+ 5 (vi cc sicho trc). Trng s ca mt ngthng l tng trng s ca cc im thuc ng thng . bi yu cu tm ng thng c trng s lnnht.

Nhn xt: ng thng c trngln nht luni qua t nht 2 im trongn im cho.Xt cc ng thng i qua im th i. Ta sp xp cc im j cn li theo phng i vi im i, bng cchs dng v so snh cc vector ch phng (x[j] - x[i], y[j] - y[i]). Sau khi sp xp, mi on vector ch

phng bng nhau cho ta mt ng thng i qua im i. Cng tt c trng s cc im trong on thuc trng s ca ng thngv so snh vi kt qu.

Thi gian thc hin: O(n2logn).

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2008

Tng quan vngy thi thhai( 10 08 2008 )

Bi thi Bi 4 Bi 5 Bi 6

Tn ba i HAOI6000Rp chiu

phimRc ucOlympic

Gii hn thigian

1s/test 1s/test 3s/test

Tng sim 100 100 100

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20081 M, N 1000

V d

D liu5 5

0 0 1 1 11 1 0 0 0

0 0 1 1 1

1 1 0 0 0

0 0 0 1 1

Kt qu10 2

Li gii

Xy dng thmi nh tng ng vi mt na vung. Hai nh c cnh ni khi hai na vung tngng knhau v khng c tng ngn cch.

V mi nh c bc khng qu 2 nn thchcha cc di hoc cc vng nh hnh v:

V chng ta xut pht tmt nh pha ra ngoi nn chi trn cc di m khng i vo vng.

Thut ton l duyt: khi ta ng mt nh, xem nh no kvi n m cha c i n th i ti (lun cduy nht mt nh nh vy); bao gii n mt nh nm ra pha Namth cp nhp kt quti u.

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2008

Rp chiu phim

M bi: CINEMA

Tc gi: L n KhuMegastar l rp chiu phim ln v hin i nht H Ni. Rp chiu ny c mt phng chiu gm M hnggh, mi hng c N gh. c c v xem phim, bn c th t v qua mng. Mi yu cu t v c tht mt lc nhiu v. Hin ti, sau khi nhn c cc yu cu t v, rp s sp xp b tr ch ngi cho ccyu cu sao cho cc ch ngi ca mi yu cu l mt vng lin thng. Mt gh khng nm hng u, hngcui, ct tri nht, ct phi nht s c 4 gh pha trc, pha sau, pha tri v pha phi c coi l k vin.

Cng vic sp xp ch ngi ny hin ti c lm hon ton bng tay. Bn hy vit chng trnh sp xpch ngi cho hp l nht.

D liu

Dng thnht ghi sM v N. Dng thhai ghi sK l syu cu t v. Dng thba ghi K sl slng v mi yu cu t.

Kt qu

Ghi ra M dng, mi dng N svi ngha gh dnh cho yu cu t v thi.

Nu mt ghl trng th in ra 0.

Gii hn

1 M, N 1000. Tng sv yu cu khng vt qu M * N. Trong 40% stest, M N 100.

V d

D liu5 4

3

4 5 9

Kt qu1 1 2 2

1 1 2 2

3 3 3 2

3 3 3 0

3 3 3 0

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2008Li giiBi ton ny c nhiu cch gii, tuy nhin c 1 cch lm n gin nh sau:

Xt ln lt cc yu cu, vi dng 1, ta sp xp ch ngi t tri sang phi, vi dng 2, ta spxp ch t phisang tri,v.v... Cch ny s m bo cc ch ngi trong mi yu cu lun thuc mt min lin thng.

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2008

Rc uc Olympic

M bi: TORCH

Tc gi: L n KhuOlympic Bc Kinh 2008 ang din ra v cng si ni v quyt lit. Ngay t lc ny, nhng nh t chc caOlympic London 2012 tnh n k hoch cho l rc uc ca Olympic ln ti. H d nh s i qua Nthnh ph. Mi thnh ph c ta (x, y) trn mt phng. K hoch ca l rc uc l ngn uc s btu t thnh ph 1, i ln lt gia cc thnh ph khc mi thnh ph ng 1 ln ri quay tr li thnh ph1. Bn hy tm mt hnh trnh tng ng i l nh nht.

D liu

Dng thnht ghi sN. N dng tip theo, mi dng ghi mt cp s(x, y) l ta ca cc thnh ph

Kt qu

Dng u tin ghi di ca hnh trnh c ng i ngn nht m bn tm c vi t nht 3 chssau du phy.

Dng thhai ghi N sbt u bng s1 v tip theo l ln lt cc thnh phtrn hnh trnh.

Gii hn

1 N 100 Ta cc thnh phc trtuyt i khng qu 105.

V d

D liu4

0 0

1 0

0 5

1 5

Kt qu 112.0000

1 2 4 3

Kt qu 220.1980

1 4 2 3

Kt qu 312.1980

1 2 3 4

Cch tnh im

Vi mi test, ban t chc c a ra mt p s ExpectedResult. Gi kt qu ca bn l Result.

Nu Result ExpectedResult bn sc 10 im.

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2008 Nu ExpectedResult < Result < 1.5 ExpectedResult bn sc 91.5(ResultExpectedResult) / 25 Ngoi ra, bn skhng c im.

Vi test v d trn, vi ExpectedResult = 12, output 1 s c 10 im, output 2 s c 0 im, output 3s c 7.997 im.

Li gii

y l mt bi ton thuc lp NP (khng c thut ton tt): tm chu trnh Hamilton trn th.

Trong trng hp cc nh ca thl cc im trn mt phng v trng scc cnh l khong cch, ta cmt cch lm cho kt qukh tt nh sau.

Dng phng php tm kim cc b (local search): ban u chn mt chu trnh no . Nu chu trnh cdng 1 ... u, v ... x, y ... 1 m uv ct xy th ta cp nht chu trnh mi l1 ... u, x ... v, y ... 1. Chu trnh miny chc chn tt hn chu trnh c.C lp li bc "nng cp" kt qunycho n khi khng nng cp

c na hoc vt qu gii hn thi gian cho php.

haoi 08

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