150 bai tap pascal
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150 bài toán tin của Thầy LÊ MINH HOÀNGTRANSCRIPT
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LIST 150+ BI TON TIN L MINH HONG001. TNH TON SONG SONG9
002. BNG S10
003. CARGO11
004. DY CON12
005. XU FIBINACCI13
006. VNG S NGUYN T14
007. I BN15
008. CA S VN BN16
009. VNG TRN CON17
010. B TR PHNG HP18
011. MUA V TU HO19
012. XIN CH K21
013. LC NM KIM CNG22
014. RI SI23
015. IP VIN24
016. KHONG CCH GIA HAI XU25
017. XP LI BNG S26
018. THM KHU TRIN LM27
019. D MN29
020. XP LI DY S30
021. CO DY BT PHN31
022. TUYN BAY32
023. M PHNG CC PHP TON33
024. DY CON CA DY NH PHN34
025. TNG CC CH S35
026. NG I NHIU IM NHT36
027. K HOCH THU NHN CNG37
028. DY CC HNH CH NHT38
029. SN CT39
030. CT VI40
031. CHIA KO41
032. BNG QUAN H42
033. ONG NC43
034. TR TIN44
035. HON V CH CI45
036. D TIC BN TRN46
037. TRO BI47
038. I XNG HO48
039. MNG MY TNH49
040. LT MI N50
041. S NH PHN LN NHT51
042. SN CC HNH CH NHT52
043. PHN HOCH TAM GIC53
044. CC THNH PHN LIN THNG MNH54
045. M GRAY55
046. D N XY CU56
047. BO TN NG VT HOANG D57
048. PH TNG58
049. TRUYN TIN TRN MNG59
050. HNH VUNG CC I60
051. ON XE QUA CU61
052. S LNG62
053. THM HIM LNG T63
054. TH T T IN64
055. DY LCH65
056. RT GN DY S66
057. BUN TIN67
058. DY NGOC68
059. THNG BM V PH NG69
060. S THP PHN70
061. DANH SCH VNG71
062. TNH DIN TCH72
063. THANG MY73
064. TRNG S XU74
065. PH MAY MN75
066. TN HIU GIAO THNG76
067. PHN NHM77
068. TUA DU LCH R NHT78
069. DU LCH NHIU TUA NHT79
070. PHN CNG80
071. NHN TIN81
072. CC S IN THOI82
073. GI TR LN NHT83
074. NT GIAO THNG TRNG IM84
075. TP KT85
076. MI KHCH D TIC86
077. KHI PHC NGOC87
078. DY XCH88
079. PHN CNG89
080. DY CUNG90
081. M CUNG91
082. DU LCH KIU C92
083. SA NG93
084. I THI94
085. MO KIU C95
086. THNH PH TRN SAO HO96
087. R BT XY NH97
088. T DUY KIU C98
089. 8-3, TNG HOA KIU C99
090. M HO BURROWS WHEELER100
091. BAO LI101
092. GIAI THA102
093. PH SNG103
094. DY NGHCH TH104
095. MUA HNG105
096. XU CON CHUNG DI NHT106
097. DY CON NGN NHT107
098. BIN I DY S108
099. GI TR NH NHT109
100. NI DY110
101. GHI A111
102. NG I THOT M CUNG112
103. CHU TRNH C BN113
104. CT CY S114
105. LCH SA CHA T115
106. KHP V CU116
107. HNG I VI U TIN117
108. HI CH118
109. SERIE A119
110. S HIU V GI TR120
111. PHP CO121
112. CHA NGOC122
113. M HO BURROWS WHEELER123
114. MNG RT GN124
115. DY NGOC125
116. LP RP MY TNH126
117. NG MT CHIU127
118. PH128
119. THP GCH129
120. THU THU130
121. PHN CNG131
122. XU CON132
123. LN SC SC133
124. V S134
125. GIAO LU135
126. GIAO LU136
127. I DIN137
128. HI CH138
129. LCH HC139
130. M LIN HON140
131. TUYN NHN CNG141
132. NG TRN142
133. ON 0143
134. HC BNG144
135. ON DNG145
136. TN HIU GIAO THNG146
137. PH147
138. DI CHUYN R-BT148
139. TRM NGH149
140. CHIA CN BNG151
141. LN XC XC152
142. CHUYN HNG153
143. GHT NHAU NM ...154
144. NI DY155
145. MY LAST INVENTION156
146. CY KHUNG NH NHT158
147. MNG MY TNH159
148. DY N IU TNG DI NHT160
149. LUNG CC I TRN MNG161
150. B GHP CC I162
151. B GHP Y TRNG S CC TIU163
152. TUYN NHN CNG164
153. DN N165
001. TNH TON SONG SONGBiu thc l mt dy k t gm cc bin k hiu bng ch ci thng ting Anh: a..z, cc php ton cng k hiu +, nhn k hiu * v cc du ngoc (,). c nh ngha nh sau:
i) Mi bin a,b,...,z l mt biu thc
ii) Nu X v Y l biu thc th (X+Y) v (X*Y) cng l biu thc .
iii) Nhng biu thc no khng xy dng c theo 2 nguyn tc trn khng l biu thc .
VD: Theo cch nh ngha trn th (a+(b+(c+d))) hoc ((a+b)+(c*d)) l cc biu thc .Cho bit thi gian tnh php + l P, thi gian tnh php * l Q, ngi ta nh ngha thi gian tnh ton mt biu thc nh sau: Nu biu thc ch gm 1 bin (a..z) th thi gian tnh ton l 0 Nu X v Y l 2 biu thc ; thi gian tnh X l TX thi gian tnh Y l TY th thi gian tnh
(X+Y) l max(TX,TY)+P thi gian tnh (X*Y) l max(TX,TY)+QT 1 biu thc ngi ta c th bin i v mt biu thc tng ng bng cc lut: Giao hon: (X+Y) (Y+X); (X*Y) (Y*X)
Kt hp: (X+(Y+Z)) ((X+Y)+Z); (X*(Y*Z)) ((X*Y)*Z)
Yu cu: Cho trc mt biu thc E di dng xu k t hy vit chng trnh:1. Tm thi gian tnh ton biu thc E
2. Hy bin i biu thc E thnh biu thc E' tng ng vi n sao cho thi gian tnh E' l t nht c th.
D liu vo c t trong file vn bn PO.INP nh sau: Dng th nht ghi 2 s P, Q cch nhau 1 du cch (P,Q100)
Tip theo l mt s dng, mi dng ghi 1 biu thc . Kt qu ra t trong file vn bn PO.OUT nh sau:
Vi mi biu thc E trong file PO.INP ghi ra file PO.OUT 3 dng Dng th nht: Ghi thi gian tnh ton E
Dng th hai: Ghi biu thc E'
Dng th ba: Ghi thi gian tnh ton E'
Ch : cho gn, mi biu thc trong input/output file c th vit m khng cn n cp du ngoc ngoi cng, d liu vo c coi l ng n v khng cn kim traV d:PO.INPPO.OUT
1 1a+(a+(a+(a+(a+(a+(a+a))))))(((a+(b+(c+d)))*e)*f) (((((a*b)*c)*d)+e)+(f*g))7((a+a)+(a+a))+((a+a)+(a+a))35(e*f)*((a+b)+(c+d))35((a*b)*(c*d))+(e+(f*g))3
002. BNG SCho mt bng hnh ch nht kch thc M x N vi M, N nguyn dng. M, N 50. Hnh ch nht ny c chia thnh M x N vung bng nhau vi kch thc n v bi cc ng song song vi cc cnh, trn vung [i, j] ghi s nguyn A[i, j] (2 A[i, j] 50).
T mng A ta lp mng B m B[i, j] c xy dng nh sau:
Biu din s A[i, j] thnh tng cc s nguyn t vi rng buc: trong biu din c nhiu nht ch mt s nguyn t xut hin hai ln. Trong cc cch biu din, chn ra biu din nhiu hng t nht th B[i, j] bng s s hng ca biu din ny k c bi (nu c).
V d:
Nu A[i, j] = 10 = 2 + 3 + 5 th B[i, j] = 3;
Nu A[i, j] = 12 = 2 + 2 + 3 + 5 th B[i, j] = 4;
Ch : Khng c biu din A[i, j] = 10 = 2 + 2 + 2 + 2 + 2 c B[i, j] = 5 v nh vy khng tho mn rng buc
a) D liu vo c cho bi Text file TABLE.INP trong :
Dng u ghi hai s M, N
M dng sau, dng th i ghi N phn t trn dng i ca bng A: A[i, 1], A[i, 2], ..., A[i, N] hai phn t lin tip cch nhau t nht mt du trng.
b) Kt qu ghi ra Text file TABLE.OUT
Gi tr bng B, mi dng ca bng ghi trn mt dng ca file, hai phn t lin tip cch nhau t nht mt du trng.
c) Hy tm hnh ch nht ln nht c to bi cc mang gi tr bng nhau ca bng B. Ghi tip ra file OUT.B1 mt dng gm 5 s l: din tch ln nht tm c, to trn tri v di phi ca hnh ch nht c din tch ln nht .
003. CARGOBn mt kho hng hnh ch nht kch thc mxn c chia thnh cc vung n v (m hng, n ct: cc hng nh s t trn xung di, cc ct nh s t tri qua phi). Trn cc ca bn c mt s k hiu:
Cc k hiu # nh du cc c mt kin hng xp sn,
Mt k hiu *: nh du ang c mt xe Ny Mt k hiu $: nh du cha kin hng cn xp Mt k hiu @: nh du v tr m cn phi xp kin hng B vo Cc k hiu du chm ".": Cho bit trngCn phi dung xe thy * tt thy kin hang $ ttn vj trI @ sao cho trong qua trlnh di chuytn cng nhw thy hang, khng chnn vao nhng kin hang t twic xtp san. (Xe thy c tht di chuytn sang nt trong 4 chung cnnh vthi tang tng). Ntu c nhiu phwng an thl ch ra nt phwng an sao cho xe thy phi di chuytn qua It bwthc nhit.Cc hng di chuyn c ch ra trong hnh di yNWESD liu: Vo t file vn bn CARGO.INP
Dng 1: Ghi hai s nguyn dng m, n cch nhau mt du cch (m, n 80) m dng tip theo, dng th i ghi n k hiu trn hng th i ca bn theo ng th t t tri qua phi. Cc k hiu c ghi lin nhau
Kt qu: Ghi ra file vn bn CARGO.OUT
Dng 1: Ghi s bc di chuyn xe Ny thc hin mc ch yu cu, nu khng c phng n kh thi th dng ny ghi s -1
Dng 2: Nu c phng n kh thi th dng ny ghi cc k t lin nhau th hin hng di chuyn ca xe Ny R (East, West, South, North). Cc ch ci thng (e,w,s,n) th hin bc di chuyn khng Ny hng, cc ch ci in hoa (E,W,S,N) th hin bc di chuyn c Ny hng.
V d:
CARGO.INPCARGO.OUT
8 8#########.....@......###........#.#####*.$......................23sswwwwwwNNNwnEseNwnEEEE
004. DY CONCho mt dy gm n ( n 1000) s nguyn dng A1, A2, ..., An v s nguyn dng k (k 50). Hy tm dy con gm nhiu phn t nht ca dy cho sao cho tng cc phn t ca dy con ny chia ht cho k.
D liu vao: file vn bn DAY.INP Dng u tin cha hai s n, k ghi cch nhau bi t nht 1 du trng.
Cc dng tip theo cha cc s A1, A2, ..., An c ghi theo ng th t cch nhau t nht mt du trng hoc xung dng (CR-LF).
Ktt qu: ghi ra file vn bn DAY.OUT Dng u tin ghi m l s phn t ca dy con tm c.
Cc dng tip theo ghi dy m ch s cc phn t ca dy cho c mt trong dy con tm c.
Cc ch s ghi cch nhau t nht mt du trng hoc mt du xung dng.
VI d:DAY.INPDAY.OUT
10 32 3 5 79 6 12 711 1591 3 2 4 56 7 10 8
005. XU FIBINACCIXt dy cc xu F1, F2, F3, ..., FN, ... trong : F1 = 'A'
F2 = 'B'
FK+1 = FK + FK-1 (K 2).
V d:F1 = 'A' F2 = 'B' F3 = 'BA'
F4 = 'BAB'F5 = 'BABBA'
F6 = 'BABBABAB'
F7 = 'BABBABABBABBA'
F8 = 'BABBABABBABBABABBABAB'
F9 = 'BABBABABBABBABABBABABBABBABABBABBA'
Cho xu S di khng qu 25, ch bao gm cc k t 'A' v 'B'. Hy xc nh s ln xut hin xu S trong xu FN, N 35. Ch : hai ln xut hin ca S trong FN khng nht thit phi l cc xu ri nhau hon ton.
D liu: vo t file vn bn FIBISTR.INP, bao gm nhiu dng, mi dng c dng N S. Gia N v
S c ng 1 du cch. D liu vo l chuNn, khng cn kim tra.
Kt qu: a ra file vn bn FIBISTR.OUT, mi dng d liu ng vi mt dng kt qu ra
V d:FIBISTR.INPFIBISTR.OUT3 A13 AB08 BABBAB4006. VNG S NGUYN TMt vng trn cha 2n vng trn nh (Xem hnh v). Cc vng trn nh c nh s t 1 n n theo chiu kim ng h. Cn in cc s t nhin t 1 n 2n mi s vo mt vng trn nh sao cho tng ca hai s trn hai vng trn nh lin tip l s nguyn t. S in vng trn nh 1 lun l s
1.164532D liu: Vo t file vn bn CIRCLE.INP cha s nguyn dng n (1 < n < 10)
Kt qu: Ghi ra file vn bn CIRCLE.OUT:
Dng u tin ghi s lng cc cch in s tm c (k).
Dng th i trong s k dng tip theo ghi cc s trong cc vng trn nh bt u t vng trn nh 1 c theo th t ca cc vng trn nh
V d:CIRCLE.INPCIRCLE.OUT
321 4 3 2 5 61 6 5 2 3 4
007. I BNTrc kia Tun v Mai l hai bn cng lp cn by gi hai bn hc khc trng nhau. C mi sng, ng 6 gi c hai u i t nh ti trng ca mnh theo con ng mt t thi gian nht (c th c nhiu con ng i mt thi gian bng nhau v u t nht). Nhng hm nay, hai bn mun gp nhau bn vic hp lp c nhn ngy 20-11.
Cho bit s giao thng ca thnh ph gm N nt giao thng c nh s t 1 n N v M tuyn ng ph (mi ng ph ni 2 nt giao thng). V tr nh ca Mai v Tun cng nh trng ca hai bn u nm cc nt giao thng. Cn xc nh xem Mai v Tun c cch no i tho mn yu cu nu trn, ng thi h li c th gp nhau nt giao thng no trn con ng ti trng hay khng ? (Ta ni Tun v Mai c th gp nhau ti mt nt giao thng no nu h n nt giao thng ny ti cng mt thi im). Nu c nhiu phng n th hy ch ra phng n Mai v Tun gp nhau sm nht.
D liu vao twic tt trong tp FRIEND.INP: Dng u tin cha 2 s nguyn dng N, M (1 N 100); Dng tip theo cha 4 s nguyn dng Ha, Sa, Hb, Sb ln lt l s hiu cc nt giao thng tng ng vi: Nh Tun, trng ca Tun, nh Mai, trng ca Mai.
Dng th i trong s M dng tip theo cha 3 s nguyn dng A, B, T. Trong A & B l hai u ca tuyn ng ph i. Cn T l thi gian (tnh bng giy 1000) cn thit Tun (hoc Mai) i t A n B cng nh t B n A.
Gi thit l s giao thng trong thnh ph m bo c th i t mt nt giao thng bt k n tt c cc nt cn li.
Ktt qu : Ghi ra tp vn bn FRIEND.OUT Dng 1: Ghi t YES hay NO tu theo c phng n gip cho hai bn gp nhau hay khng.Trong trng hp c phng n:
Dng 2: Ghi thi gian t nht Tun ti trng
Dng 3: Ghi cc nt giao thng theo th t Tun i qua Dng 4: Ghi thi gian t nht Mai ti trng Dng 5: Ghi cc nt giao thng theo th t Mai i qua
Dng 6: Ghi s hiu nt giao thng m hai bn gp nhau Dng 7: Thi gian sm nht tnh bng giy k t 6 gi sng m hai bn c th gp nhau.Cac s trn nt dng ca Input/Output file ghi cach nhau It nhit nt diu cach.V d : Vi s giao thng sau: (N=6,M=7, Ha=1, Sa=6, Hb=2, Sb=5)151020104515532156008. CA S VN BNXt vn bn T gm N k t (N 1000000, N khng cho trc) v vn bn P gm M k t (0 < M
100). Ca s di W l mt on vn bn gm W k t lin tip ca T (M < W 1000). Ni ca s W cha mu P nu tn ti mt cch xo mt s k t lin tip ca W nhn c P.
Hai ca s ca T gi l khc nhau nu chng bt u t nhng v tr khc nhau trong T. Hy xc
nh s ca s khc nhau trong vn bn T cha P.
D liu: File vn bn WINDOWP.INP Dng u cha hai s nguyn W, M Dng th hai cha M k t ca vn bn P; File WINDOWT.TXT cha vn bn TKt qu:a ra file WINDOW.OUT mt s nguyn xc nh s ca s tm c theo yu cu.
Lu : a s trng hp, file WINDOWT.TXT khng phi l Text file, c ngha l n cha cc k t trong khong #0..#255 (file of Char). Nh vy tnh c CR(#13) v LF(#10)
V d:WINDOWP.INPWINDOWT.TXTWINDOW.OUT4 2This is a sample text for the8 isfirst task on the contest009. VNG TRN CONCho hai dy s nguyn a1, a2, ..., am v b1, b2, ..., bn (2 m, n 100)
Cc s ny c xp quanh hai vng trn A v B: cc s ai quanh vng trn A v cc s bj quanhvng trn B. Vng trn C c gi vi cc s quanh n c1, c2, ..., cp c gi l vng trn con caA (hoc ca B) nu tn ti mt cch xo bt cc s ca A (hoc ca B) c vng trn C. Hy
tm vng trn C l vng trn con ca c A v B vi s phn t (p) ln nht c th.
Ch : Cac s trn 3 vng trn A, B, C twic xtp theo tng th t trong dy theo cung nt chiu kin tng h.D liu: Vo t file vn bn CIRCLE.INP
Dng u cha hai s nguyn m, n cch nhau t nht mt du cch.
m dng tip theo, dng th i ghi s ai n dng tip theo, dng th j ghi s bj
Kt qu: a ra file vn bn CIRCLE.OUT
Dng u ghi s nguyn p
p dng sau, dng th k ghi s ck.V d:122843376261845010. B TR PHNG HPC n cuc hp nh s t 1 n n ng k lm vic ti mt phng hi tho. Cuc hp i cn c bt u ngay sau thi im si v kt thc ti thi im fi. Hi c th b tr phng hi tho phc v c nhiu nht bao nhiu cuc hp, sao cho khong thi gian lm vic ca hai cuc hp bt k l khng giao nhau.
D liu vao t file vn bn ACTIVITY.INP Dng u tin cha s nguyn dng n ( n 10000)
Dng th i trong s n dng tip theo cha hai s nguyn dng si, fi (si < fi 32000) (i: 1 i
n).
Ktt qu: Ghi ra file ACTIVITY.OUT Dng u tin ghi s K l s cc cuc hp c chp nhn phc v
K dng tip theo lit k s hiu cc cuc hp c chp nhn theo th t t cuc hp u tin ti cuc hp cui cng , mi dng ghi s hiu mt cuc hp.
VI d:01234567891011122
351
4
ACTIVITY.INPACTIVITY.OUT537 932 451 311 63 7011. MUA V TU HOTuyn ng st t thnh ph A n thnh ph B i qua mt s nh ga. Tuyn ng c th biu din bi mt on thng, cc nh ga l cc im trn . Tuyn ng bt u t A v kt thc B, v th cc nh ga s c nh s bt u t A (c s hiu l 1) v B l nh ga cui cng.
Gi v i li gia hai nh ga ch ph thuc vo khong cch gia chng. Cch tnh gi v c cho trong bng sau y:
Khong cch gia hai nh ga (X)Gi v
0 < X L1C1
L1 < X L2C2
L2 < X L3C3
V i thng t nh ga ny n nh ga khc ch c th t mua nu khong cch gia chng khng vt qu L3. V th nhiu khi i t nh ga ny n nh ga khc ta phi t mua mt s v. Hn th na, nhn vin ng st yu cu hnh khch ch c gi ng mt v khi i trn tu v v s b hu khi hnh khch xung tu.
V d, trn tuyn ng st cho nh sau:
1234567AL1 = 3
BL2 = 6
L3 = 8 i t ga 2 n ga 6 khng th mua v i thng. C nhiu cch mua v i t ga 2 n ga 6: Chng hn t mua v t ga 2 n ga 3 mt chi ph C2 sau mua v t ga 3 n ga 6 mt chi ph C3, v chi ph tng cng khi i theo cch ny l C2 + C3. Hoc mua v t ga 2 n ga 4 mt chi ph C2, sau mua v t ga 4 n ga 5 mt chi ph C2 v mua v t ga 5 n ga 6 mt chi ph C1, nh vy chi ph tng cng l 2C2 + C1. Lu rng mc d khong cch gia ga 2 v ga 6 bng 12 = 2 L2 nhng khng c php mua 2 v vi gi C2 i thng t ga 2 n ga 6.
Yu cu: Tm cch t mua v i li gia hai nh ga cho trc vi chi ph mua v l nh nht.
D liu vao t file vn bn RTICKET.INP Dng u tin ghi cc s nguyn L1, L2, L3, C1, C2, C3 (1 L1 < L2 < L3 109; 1 C1 < C2 < C3 109) theo ng th t lit k trn. Dng th hai cha s lng nh ga N ( 2 N 10000).
Dng th ba ghi hai s nguyn s, f l cc ch s ca hai nh ga cn tm cch t mua v vi chi ph nh nht i li gia chng.
Dng th i trong s N - 1 dng tip theo ghi s nguyn l khong cch t nh ga A (ga 1) n nh ga th i + 1. Chi ph t nht t nh ga u tin A n nh ga cui cng B khng vt qu
109.
Ktt qu ghi ra file vn bn RTICKET.OUT chi phI nh nhit tln twic. VI d:RTICKET.INPRTICKET.OUT3 6 8 20 30 407072 6378131523012. XIN CH KGim c mt cng ty trch nhim hu hn mun xin ch k ca ng Kin trc s trng thnh ph ph duyt d n xy dng tr s lm vic ca cng ty. ng kin trc s trng ch k vo giy php khi b th k ca ng ta k duyt vo giy php. B th k lm vic ti tng th M ca to nh tr s lm vic gm M tng ca Vn phng Kin trc s trng thnh ph. Cc tng ca to nh c nh s t 1 n M, t thp n cao. Mi tng ca to nh c N phng c nh s t 1 n N t tri qua phi. Trong mi phng ch c mt nhn vin lm vic. Giy php ch c b th k k duyt khi c t nht mt nhn vin tng M k xc nhn. Ngoi b th k, mt nhn vin bt k ch k xc nhn vo giy php khi c t nht mt trong cc iu kin sau c tho mn: a) Nhn vin lm vic tng 1
b) Giy php c k xc nhn bi nhn vin lm vic cng s phng trong tng st di
c) Giy php c k xc nhn bi nhn vin lm vic cng s phng trong tng st trn d) Giy php c k xc nhn bi nhn vin lm vic phng bn cnh
Mi mt nhn vin (k c b th k) khi k xc nhn u i mt khon l ph. Hy ch ra cch xin c ch k ca Kin trc s trng i hi tng l ph phi tr l nh nht (gi thit rng ring ch k ca Kin trc s trng khng mt l ph).
D liu vao t file vn bn SIGN.INP Dng u tin cha ba s M, N, P (1 M 50; 1 N 100; 1 P N) y P l s phng b th k.
Dng th i trong s M dng tip theo cha N s nguyn dng theo th t l l ph phi tr cho cc nhn vin cc phng 1, 2, ..., N trn tng i. Cc s ny khng vt qu 109 v gi thit rng tng chi ph cn tr cng khng vt qu 109.
Ktt qu: Ghi ra file vn bn SIGN.OUTDng u tin ghi 2 s F, K theo th t l chi ph cn tr v s lng phng cn i qua.
K dng tip theo, mi dng ghi s tng v s phng ca mt phng theo th t cn i qua. (Cc s trn 1 dng ca input/output file cch nhau t nht 1 du trng)
VI d:SIGN.INPSIGN.OUT3449 610 101 101 3222 102 31 10 10 12 22 13 13 4013. LC NM KIM CNGLc l mt trang sc rt c cc c gi a chung. Chnh v vy m chng phi c ch to tht p v a dng. Xt vic ch to lc c m mt xch, mi mt c np mt vin kim cng. C n loi vin kim cng khc nhau, n 7; 2 m 27-n + 19.
Hai lc c gi l khc nhau nu ta khng th tm cch t sao cho cc mt tng ng c kim cng cng loi. Lu rng lc c hnh vng.
Vi m v n cho trc, hy xc nh xem c th tn ti bao nhiu loi lc khc nhau.
Cc loi kim cng c k hiu l A, B, C, ... Mt cu hnh lc c xc nh bi mt xu m k t A, B, C, ... v bt u bng k t nh nht.
Cho s th t l, hy xc nh cu hnh tng ng (Cc cu hnh c sp xp theo th t t in).
D liu: Vao t file BRASLET.INP c dnngm n l1l2...
Ktt qu: wa ra file BRASLET.OUTK - S lng lc khc nhau s1s2... (si xc nh cu hnh lc tng ng vi li)VI d:
BRASLET.INPBRASLET.OUT4 3212AAAB21CCCC
014. RI SIXt tr chi ri si vi mt ngi chi nh sau: Cho cy T v mt ng si gm K vin
mi bc ngi ta ly 1 vin si t ng si v t vo mt nt l tu chn
Nu nt p c r nt l v tt c v tt c cc nt l u c si th ngi ta gom tt c cc vin si l li, t 1 vin nt p, xo cc nt l ca n v hon tr r - 1 vin si cn li vo ng si.
Tr chi kt thc khi t c 1 vin si vo nt gc
Nhim v t ra l theo cu trc ca cy T, xc nh s vin si ti thiu ban u tr chi c th
kt thc bnh thng. Cy c n nt ( N 400), nt gc c nh s l 1.
D liu: vao t file vn bn STONE.INP Dng u: s n
Dng th i trong s n dng tip theo c dng: i m i1 i2 ... im. Trong m l s nt con ca nt i;
i1, i2, ..., im: Cc nt con ca nt i.Ktt qu: twa ra file STONE.OUT s lng vin si ti thiu cn thit
VI dSTONE.INPSTONE.OUT731 2 2 32 2 5 43 2 6 7015. IP VINa bn hot ng ca mt ip vin l mt khu ph m ch c cc ng ph ngang, dc to thnh mt li vung. Vi mc ch bo mt, thay v tn ng ph, ip vin nh s cc ph ngang t 0 n m v cc ph dc t 0 n n. mt s ng ba hoc ng t c cc trm kim sot. Anh ta ang ng nt giao ca hai ng (i1, j1) (j1 - ng ngang; i1 - ng dc) v cn ti im hn giao ca hai ng (i2, j2). trnh b theo di, ng i phi khng qua cc trm kim sot v c ti ch r th nht thit phi i hng i, thm ch c th sang ng v i ngc tr li. Vic i hng ch c thc hin ng ba hoc ng t. Hy xc nh ng i ngn nht ti im hn hoc cho bit khng c ng i p ng c yu cu nu.
D liu: vao t file SPY.INPDng u: m n i1 j1 i2 j2 ( 0 m, n 100)
Cc dng sau: mi dng 2 s i, j (to trm kim sot).
Ktt qu: twa ra file SPY.OUTDng u: di ng i ngn nht hoc thng bo NO nu khng c ng i.
Cc dng sau: mi dng 2 s i, j ch nt tip theo cn ti theo ng i tm c, bt u l i1 j1 v kt thc l i2 j2.
VI d:
SPY.INPSPY.OUT4 5 0 0 5 4130 10 00 41 02 21 12 31 04 02 05 22 15 33 1-13 24 24 33 34 34 45 4016. KHONG CCH GIA HAI XUCho hai xu k t S1 v S2, mi xu c di khng qu 100 k t. Cho php thc hin cc php bin i sau y i vi xu k t:
1. Thay th mt k t no bi k t khc
2. i ch hai k t lin nhau
3. Chn mt k t vo sau v tr no
4. Xo bt 1 k t
Ta gi khong cch gia hai xu S1 v S2 l s t nht cc php bin i nu trn cn p dng i vi xu S1 bin n thnh xu S2.
Yu cu: TInh khong cach gia 2 xu S1, S2 cho trwthc va ch ra th t cac php bitn ti.V d: Gi s S1 = 'Barney'; S2 = 'brawny'. Khong cch gia 2 xu l 4. Dy cc php bin i cn thc hin l:
1. Thay k t 1 ca S1 (B) bi b2. i ch k t th 2 (a) v th 3 (r) ca S1.
3. Chn k t w vo S1 sau k t th 3.
4. Xo k t th 5 ca S1.Dy cc php bin i c th m t nh sau:
'Barney' 'barney' 'braney' 'brawney' 'brawny'D liu: vao t file vn bn STREDIT.INP c ciu trc nhw sau: Dng u tin cha xu S1 Dng th hai cha xu S2Ktt qu: Ghi ra file vn bn STREDIT.OUT Dng u tin ghi s lng cc php bin i cn s dng K
Mi dng i trong s K dng tip theo m t php bin i c s dng ln th i gm cc tham s sau: cc tham s ghi trn 1 dng ghi cch nhau 1 du cch.
1, P, C (nu l php thay k t ti v tr P bng k t C)
2, I, I + 1 (nu l php i ch 2 k t th I v th I + 1)
3, P, C (nu l php chn k t C vo sau v tr P)
4, P (nu l php xo k t th P)VI d:
STREDIT.INPSTREDIT.OUTBarney brawny
41 1 b2 2 33 3 w4 5017. XP LI BNG SCho mt bng vung gm m hng v n ct. Cc c nh ch s theo (hng, ct) t (0, 0) n (m - 1, n - 1). Trn m x n ngi ta vit cc s t nhin t 0 n m x n - 1 theo mt th t tu . Cho php i ch hai s t trong hai th m giao chn. Cn tm cch i ch cc s sao cho thu c bng c tnh cht: S (i, j) l n x i + j.
D liu vao t file vn bn BOARD.INP: cc s ghi trn 1 dng cch nhau t nht 1 du trng.
Dng u ghi 2 s m, n (5 m, n 80)
m dng tip theo, dng th i ghi n s t nhin theo ng th t cc s ghi trn hng i ca bng.
Ktt qu twa ra file BOARD.OUT Dng th i cha 4 s X1, Y1, X2, Y2 cho bit ti bc th i cn i ch 2 s ti hai (X1, Y1) v (X2, Y2)
VI d: (n = n = 8)Bng ban uBng cn to00
11
22
33
44
55
66
77
Input/Output File:BOARD.INPBOARD.OUT8 810 12345678 9016 12 13 14 1511 17 18 19 20 21 22 2324 25 26 27 28 29 30 3132 33 34 35 36 37 38 3940 41 55 43 44 45 46 4748 49 50 51 52 53 54 4256 57 58 59 60 61 62 63
1 2 0 02 0 3 23 2 1 33 2 2 06 7 7 57 5 6 36 3 7 17 1 5 27 1 6 36 3 7 57 5 6 7018. THM KHU TRIN LMMt khu trin lm ngh thut c mxn phng c b tr trong mt hnh ch nht kch thc mxn (2m,n 20). Mi phng biu din bi mt v u c ca thng vi cc phng chung cnh vi n. Vi mi mt phng, ta nh ch s theo to (x, y) ca (1 hng xm; 1ct yn) v gn cho n mt ch ci in hoa ('A'..'Z') th hin loi ngh thut trng by ti phng . C th vo khu trin lm cc phng c to (x bt k, y = 1) v c th i ra cc phng c to (x bt k, y = n)
VI d vthi n=10 va n=11:1
2
3
4
5
6
7
8
9
10
Mt v th tng i thm trin lm c s thch c bit vi mt loi ngh thut. Yu cu ca ng ta "rt n gin" l khng nht thit phi i thm tt c cc phng cha loi ngh thut m ng ta thch nhng khng c i qua cc phng cha loi ngh thut khc.
VI d: t ti thn loni ngh thut B, Th twthng c tht ti:(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,6), (3,6), (4,6), (4,7), (4,8), (4,9), (4,10), (5,10), (6,10), (6,11).Nhwng khng phi lun tn tni twng ti nhw vy, vI d : ntu Th twthng nun ti thn loni ngh thut A thl khng tht tln twic nt twng ti (Bi ct 6 ca bng khng c nt ch A nao). c ng i ca v th tng i thm loi ngh thut A th nhng ngi qun l trin lm phi
tm cch i loi ngh thut ti hai phng no . Trong v d ny th c ng i chng ta c th i loi ngh thut B phng (5,6) cho loi ngh thut A phng (3,1) hoc phng (3,7), (3,8),
...
Trong nhng cch i , ngi ta thng quan tm n vic phi i sao cho tng s phng phi i l t nht c th c. Trong nhng cch i vi s cp phng phi i t nht hy ch ra cch i m con ng th tng phi i l ngn nht c th c. C th c nhiu nghim th ch cn ch ra mt nghim.
D liu vo t file vn bn TL.INP bao gm: Dng u tin ghi s m, n Dng th hai ghi mt ch ci in hoa th hin loi ngh thut th tng mun thm. m dng tip theo, dng th i l mt xu k t di n biu din cc loi ngh thut trong cc phng trn hng i theo ng th t t ct 1 n ct n.
Kt qu cho ra file vn bn TL.OUT bao gm: Dng u tin l s cp phng cn i (p). p dng tip theo mi dng gm 4 s a, b, c, d c ngha l ta cn i loi ngh thut ti phng(a,b) cho phng (c,d).
Dng tip theo ghi s phng trn con ng i ngn nht tm c (q).
q dng tip theo, mi dng ghi to x,y th hin cho con ng ngn nht theo ng th t
phng i qua.
Nu khng tn ti phng n i phng c ng i th ghi vo file TL.OUT mt dng: NO SOLUTION
VI d: Vthi khu tritn ln nhw trn:TL.INPTL.OUT
10 11
B BBBBBBFFFFF AAAAABDCCFF AFFFABAACFC BFEFABBBBBD FFDEABAAABA EEDEEEEEABB DDDEEEEEAAB DCCFFFCCABA DCCFFFCCAAA CCCCCCCCCCC0
16
1 11 21 3
1 41 5
1 62 63 6
4 64 7
4 84 94 10
5 106 10
6 11
TL.INPTL.OUT
10 11
ABBBBBBFFFFF AAAAABDCCFF AFFFABAACFC BFEFABBBBBD FFDEABAAABA EEDEEEEEABB DDDEEEEEAAB DCCFFFCCABA DCCFFFCCAAA CCCCCCCCCCC1
5 6 3 118
2 12 2
2 32 42 5
3 54 5
5 55 65 7
5 85 9
6 97 98 9
9 99 10
9 11
019. D MNCho mt bi mn kch thc mxn vung, trn mt c th c cha mt qu mn hoc khng,
biu din bn mn , ngi ta c hai cch:
Cch 1: dng bn nh du: s dng mt li vung kch thc mxn, trn ti (i, j) ghi s 1 nu c mn, ghi s 0 nu khng c mn
Cch 2: dng bn mt : s dng mt li vung kch thc mxn, trn ti (i, j) ghi mt s trong khong t 0 n 8 cho bit tng s mn trong cc ln cn vi (i, j) ( ln cn vi (i, j) l c chung vi (i, j) t nht 1 nh).
Gi thit rng hai bn c ghi chnh xc theo tnh trng mn trn hin trng.
VI d: Bn t tanh diu va bn t nt t twng ng: (n = n = 10)Bn nh du
1010101000
0100010011
0010100001
0111100110
0111000101
0001010100
1110011011
1001010101
0010111110
1000010000
V nguyn tc, lc ci bi mn phi v c bn nh du v bn mt , tuy nhin sau mt thi
gian di, khi ngi ta mun g mn ra khi bi th vn ht sc kh khn bi bn nh du b tht lc !!. Cng vic ca cac lp trlnh vin la: T bn t nt t, hy tai tno lni bn t tanh diu ca bi nln.D liu: Vo t file vn bn MINE.INP, cc s trn 1 dng cch nhau t nht 1 du cch Dng 1: Ghi 2 s nguyn dng m, n (2 m, n 80)
m dng tip theo, dng th i ghi n s trn hng i ca bn mt theo ng th t t tri qua phi.
Kt qu: Ghi ra file vn bn MINE.OUT, cc s trn 1 dng ghi cch nhau t nht 1 du cch Dng 1: Ghi tng s lng mn trong bi
m dng tip theo, dng th i ghi n s trn hng i ca bn nh du theo ng th t t tri qua phi.
V d:MINE.INPMINE.OUT10 150 3 2 3 3 3 5 3 4 4 5 4 4 4 31 4 3 5 5 4 5 4 7 7 7 5 6 6 51 4 3 5 4 3 5 4 4 4 4 3 4 5 51 4 2 4 4 5 4 2 4 4 3 2 3 5 41 3 2 5 4 4 2 2 3 2 3 3 2 5 22 3 2 3 3 5 3 2 4 4 3 4 2 4 12 3 2 4 3 3 2 3 4 6 6 5 3 3 12 6 4 5 2 4 1 3 3 5 5 5 6 4 34 6 5 7 3 5 3 5 5 6 5 4 4 4 32 4 4 4 2 3 1 2 2 2 3 3 3 4 2
801 0 1 1 1 1 0 1 1 1 1 1 1 1 10 0 1 0 0 1 1 1 0 1 1 1 0 1 10 0 1 0 0 1 0 0 1 1 1 0 0 1 11 0 1 1 1 0 0 1 0 0 0 0 0 1 11 0 0 0 1 1 1 0 0 1 0 0 1 0 10 0 0 0 1 0 0 0 0 1 1 0 1 0 00 1 1 0 0 1 0 0 1 1 0 0 1 0 01 0 1 0 1 0 1 0 1 1 1 1 0 1 00 1 1 0 1 0 0 0 0 0 1 1 1 1 11 1 1 1 1 0 1 1 1 1 0 0 0 0 1020. XP LI DY SCho dy A = (a1, a2, ..., an) l dy cc s nguyn dng i mt khc nhau.
Hy lit k tt c cc cch hon v phn t ca dy A tho mn: gia hai gi tr M v N bt k trong
hon v , khng tn ti gi tr P no : 2P = M + N.
V d: Vi dy A l (11, 22, 33, 44) thHon v (11, 44, 33, 22) l tho mn iu kin trnHon v (11, 44, 22, 33) khng tho mn v c gi tr P = 22 nm gia hai gi tr M = 11 v N = 33 m: 22 * 2 = 11 + 33.D liu: Vo t file vn bn SORT.INP. Cc s trn 1 dng cch nhau t nht 1 du trng
Dng 1: Ghi s n (2 n 11)
Dng 2: Ghi gi tr n phn t ca dy A (1 ai 100).
Kt qu: Ghi ra file vn bn SORT.OUT. Cc s trn 1 dng cch nhau t nht 1 du trng
Dng cui cng ghi s lng hon v tm c (K)
K dng trc dng cui cng, mi dng ghi 1 hon v tm c
021. CO DY BT PHNCho mt bng A kch thc 8x8; Cc dng v cc ct c nh s t 0 n 7. Trn mi ca bng cha mt s nguyn trong khong t 0 n 7.
Cho dy X = (x1, x2, ..., xn), c cc phn t xi N; 0 xi 7. (2 n 200).
Vi i: 1 i < n. Php co R(i) thc hin trn dy X: Xo hai phn t xi v xi+1 v thay vo gi tr nm trn hng xi, ct xi+1 ca bng A, sau dy X c nh ch s li t tri quaphi bt u t 1.V d:01234567V d: Vi bng A nh trn v dy X = (0, 1, 2, 3, 1, 2) nu ta thc hin php co R(3) th ta s c dy (0, 1, 1, 1, 2). Nu thc hin tip R(4) th ta s c dy (0, 1, 1, 3). Thc hin tip R(2) th s c dy (0, 2, 3). Thc hin tip R(1) th s cn (2, 3) v thc hin R(1) mt ln na s c (1).Yu cu: cho trwthc nt gia trj V (0 V 7), hy tln nt th t thc hin n - 1 php co trn dyX tt gia trj cn lni cui cung la V. Ntu c nhiu phwng an thl ch cn cho bitt nt.D liu vo t file vn bn OCT.INP
8 dng u tin, dng th i ghi 8 s trn hng th i - 1 ca bng A theo ng th t t tri qua phi
Dng th 9 ghi s n
Dng th 10 ghi n s: x1, x2, ..., xn theo ng th t.
Dng th 11 ghi gi tr V.
Kt qu ghi ra file vn bn OCT.INP, ch gm 1 dng, trn :
Ghi s 0 nu khng tn ti phng n s dng n - 1 php co cho gi tr V. Hoc ghi (theo
ng th t thc hin) n - 1 v tr ca cc php co trn dy X cho gi tr V. Ch : Cc s trn 1 dng ca Input/Output File ghi cch nhau t nht 1 du cch.
V d:OCT.INPOCT.OUT13 13 10 10 10 9 7 7 6 5 3 3 2 1022. TUYN BAYC N thnh ph v M ng hng khng hai chiu gia mt s cp thnh ph no , cc ng bay c qun l bi 16 hng hng khng. Cc thnh ph c nh s t 1 ti N (N 100) v cc hng c nh s t 1 ti 16.
c bit chi ph bay trc tip gia hai thnh ph i, j bt k (nu nh c ng bay ) l C. Nu ang i my bay ca mt hng n sn bay no ri chuyn sang my bay ca hng khc th s phi mt thm mt khon ph ph A.
Yu cu: Cho trwthc hai thanh ph S va F, hy tln hanh trlnh bay t thanh ph S ttn thanh phF vthi chi phI It nhit. Vthi gi thitt rng lun lun tn tni cach bay t S tthi F.D liu: Vo t file vn bn AIRLINES.INP. Trong : Dng 1 ghi su s nguyn dng N, M, C, A, S, F. (1 A, C 100)
M dng tip theo, mi dng c dng u v k1 k2 ... cho bit rng gia thnh ph u v thnh ph v c ng bay v k1, k2, ... l s hiu cc hng s hu ng bay
Kt qu: Ghi ra file vn bn AIRLINES.OUT. Trong : Dng 1: Ghi chi ph ti thiu phi tr
Cc dng tip theo, mi dng ghi mt b ba i, j, k. Th hin ti bc s bay t thnh ph i n thnh ph j bi my bay ca hng k. Th t cc dng phi theo ng th t bay trong hnh trnh.
Cac s trn nt dng ca Input/Output file ghi cach nhau It nhit nt diu cach.V d: Vi mng li ng khng nh di y: cn i t thnh ph 1 n thnh ph 5. Chi ph ng bay trc tip gia hai thnh ph bt k C = 3, ph ph chuyn tuyn A = 2. Cc s ghi bn cnh cc ng bay trc tip l tn cc hng s hu ng bay .
111 & 2
123421
5
1 & 3111678910
123111 & 31 & 31112131415
023. M PHNG CC PHP TONCho hai s nguyn dng a v b (1 b a < 101000), hy tnh a + b, a - b, a * b, a div b, a mod b.
D liu: Vo t file vn bn OPT.INP
Dng 1: Cha s a
Dng 2: Cha s bKt qu: Ghi ra file vn bn OPT.OUT
Dng 1: Ghi gi tr a + b
Dng 2: Ghi gi tr a - b
Dng 3: Ghi gi tr a * b Dng 4: Ghi gi tr a div b Dng 5: Ghi gi tr a mod bV d:OPT.INPOPT.OUT
56501066280016
024. DY CON CA DY NH PHNXt dy B0, B1, B2, ..., Bn l cc dy cc xu nh phn, c xy dng nh sau: B0 = '1'
Vi i: (i 1) th Bi l ghp ca Bi-1 vi (Bi-1). Trong (S) l xu c to thnh t xu S
bng cch o tt c cc s 1 thnh 0 v s 0 thnh 1
B0=1
B1=10
B2=1001
B3=10010110
B4=1001011001101001
B5=10010110011010010110100110010110
B6=...1001011001101001011010011001011001101001100101101001011001101001
Yu cu: Cho trc s nguyn dng n 30 v mt s k 2n. hy cho bit k t th k ca Bn l k t 0 hay 1.
025. TNG CC CH SCho trc hai s nguyn dng n v k (n 20, k 30).
Yu cu 1: Hy cho bit c bao nhiu s c n ch s m tng cc ch s ng bng k
Yu cu 2: Cho s nguyn dng p, hi nu em cc s tm c sp xp theo th t tng dn th s th p l s no. (p khng ln hn s lng cc s tm c)
D liu: Vo t file vn bn DIGITSUM.INP gm 1 dng cha ba s n, k, p theo ng th t cch nhau 1 du cch.
Kt qu: Ghi ra file vn bn DIGITSUM.OUT gm 2 dng
Dng 1: Ghi s lng cc s tm c trong yu cu 1
Dng 2: Ghi s th p trong yu cu 2 tm c
V d:DIGITSUM.INPDIGITSUM.OUT3 8 1045107026. NG I NHIU IM NHTCho mt bng A kch thc m x n (1 m, n 100), trn ghi cc s nguyn aij (aij 100). Mt ngi xut pht ti no ca ct 1, cn sang ct n (ti no cng c).
Quy tc i: T (i, j) ch c quyn sang mt trong 3 (i, j + 1); (i - 1, j + 1); (i + 1, j + 1). Xem hnh v:
12679
76567
12342
47876
Yu cu: Hy tln vj trI xuit phat va nt hanh trlnh ti t ct 1 sang ct n sao cho tng cac sghi trn twng ti la lthn nhit.D liu: Vo t file vn bn MAX.INP. Trong :
Dng 1: Ghi hai s m, n l s hng v s ct ca bng.
m dng tip theo, dng th i ghi n s trn hng i ca bng theo ng th t t tri qua phi.
Kt qu: Ghi ra file vn bn MAX.OUT. Trong :
Dng 1: Ghi s im ti a c c
n dng tip theo, dng th i ghi ch s hng ca th i trong hnh trnh.
Cac s trn 1 dng trong Input/ Output file cach nhau It nhit 1 diu cachVI d:
123456712345MAX.INPMAX.OUT5 7419 -2 6 2 1 3 410 -1 6 7 1 3 328 -2 8 2 5 3 231 -1 6 2 1 6 127 -2 6 2 1 3 7345027. K HOCH THU NHN CNGGim c iu hnh ca mt Cng ty tin hc cn xc nh s lng nhn cng cn s dng trong mi thng thc hin mt d n pht trin tin hc. ng gim c nm c s lng nhn cng ti thiu cn cho mi thng. Mi ln thu hoc sa thi mt nhn cng lun mt thm mt khon chi ph. Mi khi mt th no c thu, anh ta lun nhn c tin lng ngay c khi khng lm vic. Gim c nm c chi ph thu mt nhn cng mi, chi ph sa thi mt nhn cng, lng thng ca mt nhn cng. Vn t ra cho gim c l phi xc nh s lng nhn cng cn thu hay sa thi trong mi thng cho chi ph thc hin d n l ti thiu.
D liu: Vo t file vn bn PROJECT.INP. Dng u tin ghi thi gian thc hin d n n (n v tnh: thng, n 12)
Dng th hai cha ba s nguyn dng theo th t l chi ph thu mt nhn cng mi, lng thng ca mt nhn cng, chi ph sa thi mt nhn cng.
Dng cui cng ghi n s nguyn dng d1, d2, ..., dn, trong di l s lng nhn cng cn s
dng trong thng i.
Kt qu: Ghi ra file vn bn PROJECT.OUT Dng u tin ghi chi ph ti thiu tm c
Mi dng th i trong s n dng tip theo ghi s si. c hiu l:
Nu si > 0 th n l s lng nhn cng cn thu thm thng i.
Nu si < 0 th si l s lng nhn cng cn sa thi thng i
Nu si = 0 th khng c bin ng nhn s trong thng i ca d n
V d:PROJECT.INPPROJECT.OUT345 610 9 11
1991001028. DY CC HNH CH NHTGi s ABCD l mt hnh ch nht trn mt phng to c cc nh: A (0, 0); B(0, 1); C(K, 1) v D(K, 0).
Ta xem hnh ny l hnh c s hiu 1.
Hnh c s hiu 2 xy dng trn cnh Bc ca hnh 1 v cnh kia gp K ln. Hnh c s hiu 3 xy dng trn cnh ty ca hnh ch nht hp cc hnh 1 v 2 v cnh kia gp K ln. Hnh c s hiu 4 xy dng trn cnh nam ca hp cc hnh 1,2,3 v cnh kia gp K ln. Hnh c s hiu 5 xy dng trn cnh ng ca hp cc hnh 1,2,3,4 v cnh kia gp K ln. Tng t quy lut vi cc hnh mang th t 6,7...
Bi ton t ra l cho trc 3 s thc K,X,Y, hy cho bit s hiu nh nht ca hnh ch nht cha
im c to (X,Y)
D liu: Vo t bi file vn bn REC.INP gm 1 s dng.
Mi dng gm 3 s K,X,Y vi ngha nu trn.
Kt qu: Ghi ra file vn bn REC.OUT nh sau:
Vi mi dng ca file d liu ghi trn 1 dng s hiu ca im cho:
Ch : K, X, Y c th c ti 100 ch s.
V d:REC.INPREC.OUT3 0 112 7 -254 1 172NWES029. SN CTTrn mt nn phng c chia thnh cc li vung n v gm mxn (m, n 100), ngi ta t chng kht ln nhau cc khi lp phng n v thnh nhng ct. Khi di cng ca ct chim trn mt ca li. Chiu cao ca mi ct c tnh bng s khi lp phng n v to thnh ct . Sau khi xp xong ton b cc ct, ngi ta tin hnh sn cc mt nhn thy c ca cc ct. Yu cu: Bitt chiu cao ca ni ct, hy tInh s tn vj din tIch cn sn.D liu vo t trong file vn bn PAINT.INP. Trong :
Dng u tin ghi hai s nguyn dng m, n l kch thc ca li nn (m hng, n ct)
m dng tip theo, dng th i ghi n s nguyn khng m, s nguyn th j biu th chiu cao ca ct dng ti (i, j) ca li. Cc s cch nhau t nht mt du cch.
Kt qu ra t trong file vn bn PAINT.OUT, ghi s din tch cn sn. V d:Vi hnh v bn, cc ct c xy trn nn kch thc 2x3. Cc file d liu vo v kt qu ra s l:
PAINT.INPPAINT.OUT42030. CT VIMt c s may mc chuyn sn xut khn vung mi kch c, nguyn liu l cc tm vi. Vi mt tm vi hnh ch nht chiu di m n v v chiu rng n n v (m, n nguyn dng khng qu 100), ngi ta c hai cch ct, ct ngang v ct dc.
c im ca mi thao tc ct l: mi ln ct bt buc phi ct ri mt mnh vi hnh ch nht thnh hai mnh khc cng hnh ch nht v kch thc hai mnh ct ri cng phi l s nguyn.
Yu cu: Cho trwthc tin vi kIch thwthc n x n. Hy tln cach ct tin vi t thanh nhng nnh vung ( khng twic tt lni nt nnh nao khng vung) sao cho s nnh vung ct ra la It nhit.D liu: Vo t file vn bn CUT.INP gm 1 dng cha hai s m, n cch nhau 1 du cch
Kt qu: Ghi ra file vn bn CUT.OUT. Trong :
Dng 1: Ghi s K l s mnh vung ti thiu c th ct ra c
K dng tip theo, mi dng ghi 3 s X, Y, d. y (X, Y) l to vung gc tri trn ca mt hnh vung ct ra c v d l di cnh hnh vung . Quy c to ca gc tri trn hnh ch nht ban u l (1, 1). To ca gc phi di hnh ch nht ban u l (m, n). Ba s X, Y, d ghi cch nhau t nht 1 du cch.
V d:
123456
1
2
3
4
CUT.INPCUT.OUT4 631 1 41 5 23 5 2031. CHIA KOCho n gi ko nh s t 1 n n, gi ko th i c Ai vin ko. Gi thit 2 n 200 v 1 Ai 200 vi i: 1 i n.
Yu cu: Chia n gi ko cho lm hai nhm sao cho hiu s ko ca hai nhm chnh lch nhau t nht, nu c nhiu cch chia th ch cn ch ra mt cch.
D liu: Vo t file vn bn CANDY.INP. Trong : Dng u tin ghi s n n dng tip theo, dng th i ghi s AiKt qu: Ghi ra file vn bn CANDY.OUT. Trong : Dng u tin ghi hai s m1 v c1 cch nhau t nht mt du cch, m1 l s gi nhm I, c1 l s
ko nhm I.
m1 dng tip theo, mi dng ghi ch s mt gi ko c chn vo nhm I
Dng m1+2 ghi hai s m2 v c2 cch nhau t nht mt du cch, m2 l s gi nhm II, c2 l sko nhm II.
m2 dng tip theo, mi dng ghi ch s mt gi ko c chn vo nhm II
V d:CANDY.INPCANDY.OUT
61004956983 1111453 111236
032. BNG QUAN HCho bng vung A, kch thc nxn, cc phn t l s nguyn {-2, -1, 0, 1, 2, 3}. Gi thit 2 n 200.
Bng A gi l tng thch vi dy T = (t1, t2, ..., tn), hay dy T tng thch vi bng A nu: Aij = 0 ti = tj
Aij = 1 ti < tj
Aij = -1 ti > tj
Aij = 2 ti tj
Aij = -2 ti tj
Aij = 3 ti tj
(Vi mi i, j: 1 i, j n)
V d: Dy T = (1, 4, 5, 4, 5, 9) tng thch vi bng:
A123456
1
2
3
4
5
6
Dy T = (10, 20, 30, 20, 30, 40) cng tng thch vi bng
Yu cu, cho trwthc bng quan h A, hy tln dy s nguyn dwng T = (t1, t2, ..., tn) twng thIch vthi bng A na nax(T) la b nhit c tht. Bitt rng lun tn tni nt dy nhw vyD liu: Vo t file vn bn REL.INP:
Dng 1: Cha s n
n dng tip theo, dng th i ghi n s trn dng i ca bng A theo ng th t t Ai1 n AinKt qu: Ghi ra file vn bn REL.OUT:
Ch gm 1 dng ghi n s ca dy T tm c theo ng th t t t1 n tn. Cac s trn nt dng ca Input/ Output File cach nhau It nhit 1 diu cach V d:REL.INPREL.OUT6011122
1 2 3 2 3 4-201022-2 -10301-2 -23011-1 -20 -101-1 -2 -1 -1 -10033. ONG NCNn phng ca mt cng trng xy dng c chia thnh li vung n v kch thc mxn . Trn mi (i, j) ca li, ngi ta dng mt ct b tng hnh hp c y l (i, j) v chiu cao l Hij n v. Sau khi dng xong, th tri ma to v lu. Gi thit rng nc khng thNm thu qua cc ct b tng cng nh khng r r qua cc ng ghp gia chng.
Yu cu: Xac tjnh lwing nwthc tng gia cac ctCh k thut: m, n, Hij l cc s nguyn dng. 1 m, n 100. 1 Hij 1000
D liu: Vo t file vn bn WATER.INP c ghi di khun dng sau:Dng 1:m nDng 2:H11 H12 ... H1nDng 3:H21 H22 ... H2n......Dng m + 1:Hm1 Hm2 ... HmnCc s trn 1 dng cc nhau t nht 1 du cch
Kt qu: Ghi ra file vn bn WATER.OUT cha s n v khi nc ng
V d:WATER.INPWATER.OUT
5 59 9 9 9 99 2 2 2 99 2 1 2 99 2 2 2 99 9 9 9 964
WATER.INPWATER.OUT
10 109 9 9 9 9 9 9 9 9 99 1 1 1 1 9 1 1 1 99 1 1 1 1 1 1 1 1 99 1 1 1 1 9 1 1 1 99 9 9 9 9 9 9 1 9 99 1 1 1 1 9 1 1 1 99 1 1 1 1 9 1 1 1 99 1 1 1 1 9 1 1 1 99 1 1 1 1 9 1 1 1 99 9 9 9 9 9 9 1 9 9128
034. TR TINNc Silverland s dng h thng 20 loi tin xu, trong cc xu c mnh gi l mt s chnh phng t 12 n 202:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400. Vi h thng ny, tr 10 xu ta c 4 cch:
1. Tr 10 ng 1 xu
2. Tr 6 ng 1 xu v 1 ng 4 xu
3. Tr 2 ng 1 xu v 2 ng 4 xu
4. Tr 1 ng 1 xu v 1 ng 9 xu
Nhin v ca bnn la xac tjnh xen c bao nhiu cach tr nt s tin cho trwthc Silverland va cho bitt nt cach tr phi dung It tng xu nhit.D liu vo t file vn bn COIN.INPGhi s tin nguyn dng khng ln hn 666 xu.
Kt qu: a ra file vn bn COIN.OUT Dng 1: Ghi s cch tr s tin ghi trong file d liu Dng 2: Ghi s ng xu ti thiu phi tr
Cc dng tip theo, mi dng ghi hai s a, b cch nhau t nht mt du cch: cho bit s c ang xu loi mnh gi b2 trong phng n ti u (dng t ng xu nht)
V d:COIN.INPCOIN.OUT
10421 31 1
035. HON V CH CICho mt xu S ch gm cc ch ci in hoa, 1 di 9.
Hy lp chwng trlnh tr li hai cu hi sau: C bao nhiu cch hon v cc ch ci ca xu S Lit k cc hon v theo th t t in.D liu: Vo t file vn bn PERMUTE.INP gm 1 dng cha xu S
Kt qu: Ghi ra file vn bn PERMUTE.OUT.
Dng 1: Ghi s lng hon v tm c (K)
K dng tip theo, mi dng ghi mt xu hon v ca xu S (phi lit k theo ng th t t in)
PERMUTE.INPPERMUTE.OUT ABAB6AABBABABABBA BAAB BABA BBAA036. D TIC BN TRNC n nh khoa hc nh s 1, 2, ..., n v 26 lnh vc khoa hc k hiu A, B, C, ..., Z. Thng tin v ngi th i c cho bi mt xu k t Si gm cc ch ci in hoa th hin nhng lnh vc khoa hc m ngi bit.
V d: S2 = 'ABCXYZ' cho bit nh khoa hc th 2 c hiu bit v cc lnh vc A, B, C, X, Y, Z.Mt ln c n nh khoa hc n d mt ba tic. Ch nhn ca ba tic nh xp n nh khoa hc ngi quanh mt bn trn, nhng mt vn khin ch nhn rt kh x l cc nh khoa hc ca chng ta c hiu bit x hi tng i km, nn nu nh phi ngi cnh mt ai khng hiu bit g v cc lnh vc ca mnh th rt kh ni chuyn.
Vy hy gip ch nhn xp n nh khoa hc ngi quanh bn trn sao cho hai ngi bt k ngi cnh nhau phi c t nht mt lnh vc hiu bit chung, cc nh khoa hc ca chng ta khng nhng n ngon m cn c th tr chuyn rm r.
D liu: Vo t file vn bn PARTY.INP. Trong :
Dng 1: Ghi s n
n dng tip theo, dng th i ghi xu k t SiKt qu: Ghi ra file vn bn PARTY.OUT gm n dng.
Dng th i ghi nh khoa hc ngi ti v tr i ca bn (Cc v tr trn bn trn c nh s t 1
n n theo chiu kim ng h)
Lu : n 20 Nu c nhiu cch xp th ch cn ch ra mt cch
Nu khng c cch xp th ghi vo file PARTY.OUT mt dng: NO SOLUTIONV d:PARTY.INPPARTY.OUT
6AV DIQR DVCQACDR136245
037. TRO BIC 2n l bi, trn ghi ln lt cc s t 1 n 2n (mi l bi ghi mt s v khng c hai l bi no trng s). Ban u cc l bi c xp chng nhau theo th t t l bi ghi s 1 n l bi ghi s 2n t di ln trn.
Sau t ngwi ta titn hanh trao cac la bai theo cach: Nu th t cc l bi t di ln ang l:(1, 2, 3 ..., n, n + 1, n + 2, n + 3, ..., 2n) S tro thnh th t mi:
(n + 1, 1, n + 2, 2, n + 3, 3, ..., 2n, n).Bng cch i vai tr cc l bi cho nhau, ta c th hnh dung ra c cch tro trong cc ln tip theo.
V d: n = 3Trng thi ban u:(1, 2, 3, 4, 5, 6)Sau ln tro th nht:(4, 1, 5, 2, 6, 3) (Xem hnh v) Sau ln tro th hai:(2, 4, 6, 1, 3, 5)Sau ln tro th ba:(1, 2, 3, 4, 5, 6)65 34 623 51241Cch tro bi ny rt hay c s dng, tng rng n s to ra mt hon v hon ton "v t" i vi cc qun bi nhng thc ra khng phi nh vy, sau mt s hu hn ln tro, tp bi li tr v trng thi ban u nh cha tro.
V d nh b bi c 52 qun (n = 26) th ch qua 52 ln tro l u vn hon y, hay b bi c104 qun (n = 52) th ch qua c 12 ln tro l s tr v trng thi ban u.Nhin v ca bnn la khi bitt twic s n la nt na s qun bai, hy tInh xen sau It nhit bao nhiu ln trao thl tp bai s tr v trnng thai ban tu.D liu: Vo t file vn bn CARD.INP ch gm 1 dng ghi s nguyn dng n ( n 10000)
Kt qu: Ghi ra file vn bn CARD.OUT cng ch gm 1 dng ghi mt s nguyn dng, l s ln tro ti thiu tp bi tr li trng thi ban u.
V d:CARD.INPCARD.OUT
999333
jnh ngha:
038. I XNG HO Mt xu k t X gi l cha xu k t Y nu nh c th xo bt mt s k t trong xu X c xu Y: V d: Xu '1a2b3c45d' cha xu '12345'.
Mt xu k t gi l i xng nu n khng thay i khi ta vit cc k t trong xu theo th tngc li: V d: 'abcABADABAcba', 'MADAM' l cc xu i xng
Cho trwthc nt xu k t S c t dai khng qua 128. Hy tln xu k t T tho nn c 3 tiu kin:1. i xng2. Cha xu S3. C It k t nhit (c t dai ngn nhit)Lu rng vi mt xu S, nu c nhiu xu T tho mn ng thi 3 iu kin trn th ch cn cho bit mt. Chng hn vi S = 'a_101_b' th chn T = 'ab_101_ba' hay T = 'ba_101_ab' u ng.D liu: Vo t file vn bn STR.INP ch gm 1 dng cha xu k t S
Kt qu: Ghi ra file vn bn STR.OUT cng ch gm 1 dng ghi xu k t T
V d: Mt vi file d liu vo v file kt qu tng ng:
STR.INPSTR.OUT
MADAMMADAM
STR.INPSTR.OUT
00_11_22_33_222_1_000000_11_222_33_222_11_000
STR.INPSTR.OUT
abcdefg_hh_gfe_1_d_2_c_3_baab_3_c_2_d_1_efg_hh_gfe_1_d_2_c_3_ba
039. MNG MY TNHTrn mt nn phng vi h to Decattes vung gc t n my tnh v m cp mng ni chng. Cc my tnh c nh s 1, 2, ..., n v cc cp mng c nh s 1, 2, ..., m. V tr ca my tnh th i c cho bi to (Xi, Yi), cp mng th j c cho ni gia hai my tnh (pj, qj). Hai my tnh bt k c th chuyn thng tin cho nhau bng mt trong hai cch: Truyn trc tip qua cp ni chng (nu c) hoc truyn qua mt s my trung gian.
Yu cu: Ngwi ta nun ni thn cac dy cap nnng sau cho hai nay bit k trong c h thng n nay tInh tu c tht chuytn thng tin cho nhau. Hy ch ra cach ni thn cac dy cap nnng sao cho tng t dai cac dy cap ni thn la It nhit, gi thitt rng cac dy cap nnng twic ni theo twng thng gia hai nay.D liu: Vo t file vn bn NET.INP theo khun dng sau:DngNi dung
1n m
2x1 y1
3x2 y2
......
n + 1xn yn
n + 2p1 q1
n + 3p2 q2
......
n + m + 1pm qm
Kt qu: Ghi ra file vn bn NET.OUT. Trong : Dng 1: Ghi s nguyn dng K v s thc L. K l s dy cp mng phi ni thm v L l tng di cc dy cp mng ni thm (L ly chnh xc ti 6 ch s sau du chm thp phn).
K dng tip theo, mi dng ghi s hiu hai my tnh, cho bit s t thm dy cp mng ni hai my tnh
Lu :1. Cc s trn mt dng ca Input/ Output file cch nhau t nht mt du cch
2. 1 n 1000; 0 m 10000 v to ca cc my tnh l s nguyn c gi tr tuyt i khng qu 1000.
V d:7 8 94 5 61 2 3040. LT MI NCho n qun -mi-n xp dng ng theo hng ngang v c nh s t 1 n n. Qun -mi-n th i c s ghi trn l ai v s ghi di l bi. Xem hnh v:
123456
114406
631161
Bit rng 1 n 100 v 0 ai, bi 6 vi i: 1 i n.
Cho php lt ngc cc qun -mi-n. Khi mt qun -mi-n th i b lt, n s c s ghi trn
l bi v s ghi di l ai.
Vin t tt ra la hy tln cach lt cac qun t-ni-n sao cho chnh lch gia tng cac s ghi hang trn va tng cac s ghi hang dwthi la ti thitu. Ntu c nhiu phwng an lt tt nhw nhau, thl ch ra phwng an phi lt It qun nhit.D liu: Vo t file vn bn DOMINO.INP. Trong :
Dng 1 ghi s n
Dng 2 ghi n s a1, a2, ..., an theo ng th t.
Dng 3 ghi n s b1, b2, ..., bn theo ng th t.Kt qu: Ghi ra file vn bn DOMINO.OUT. Trong :
Dng 1: Ghi s qun -mi-n b lt (C)
Dng 2: Ghi ch s ca C qun -mi-n b lt Dng 3: Ghi chnh lch gia tng cc s hng trn v tng cc s hng di sau khi lt.Cac s trn nt hang ca Input/ Output File cach nhau It nhit nt diu cach.V d:DOMINO.INPDOMINO.OUT621 1 4 4 0 66 56 3 1 1 6 10041. S NH PHN LN NHTXu nh phn l xu k t ch gm cc ch s 0 v 1. Ngi ta ni xu nh phn X l xu con ca xu nh phn Y nu c th xa bt mt s k t trong xu Y c xu X.
V d: Xu '0101' l xu con ca xu '000111000111'.
Lu rng nu nh xu X = xu Y th xu X cng c coi l xu con ca xu Y.
Nu coi xu nh phn l biu din nh phn ca mt s nguyn th s nguyn gi l tr s ca xu nh phn.
Yu cu: Cho trwthc hai xu nhj phn A va B, hy tln nt xu nhj phn C la xu con ca c Ava B na trj s ca C la lthn nhit c tht twic.D liu: Nhp t file vn bn BSTR.INP gm 2 dng:
Dng 1: Ghi xu nh phn A
Dng 2: Ghi xu nh phn BKt qu: To file vn bn BSTR.OUT gm 1 dng ghi xu nh phn C tm c.
V d:BSTR.INPBSTR.OUT
0000000010100010101010000000000000101011000010101
042. SN CC HNH CH NHTMt bng hnh ch nht phng c chia thnh cc min hnh ch nht khng giao nhau v c cnh song song vi cnh ca bng. Ngi ta mun sn cc min ch nht ny, mi min s c sn bng mt mu nh sn.
V khi sn c hin tng sn chy xung pha di nn mt min ch nht pha di ch c php sn khi m cc min trn, c nh hng ti n c sn.
y
6
56 (xanh)
4
37 (xanh)
5 ()
4 ()3 (xanh)
Theo hnh bn th min 2 ch c sn sau khi min 52v min 7 sn xong. Ni mt cch chnh xc: Min
A bt buc phi sn sau min B nu c hai iu kin1sau tha mn:
2 (xanh)
1 ()1. Hnh chiu ca min A v min B trn trc honh c t nht hai im chung
2. Tung tm min B ln hn tung tm min A
0123456x sn tt c cc min, ngi ta s dng mt h thng chi sn mu sc, hai chi sn khc nhau c mu khc nhau. Hy tln th t sn cac nin ch nht sao cho s ln phi thay chi la It nhit.D liu: Vo t file vn bn PAINT.INP. Trong :
Dng u tin ghi s min ch nht trong bng (n)
n dng tip theo, Dng th i ghi thng tin v min th i gm 5 s nguyn X1 Y1 X2 Y2 C theo ng th t . (X1, Y1) l ta nh tri di, (X2, Y2) l ta nh phi trn, C l m mu cn t cho min.
Kt qu: Ghi ra file vn bn PAINT.OUT. Trong
Dng 1: Ghi s ln thay chi t nht (tnh c ln u tin khi bt u sn)
Dng 2: Ghi s hiu cc min ch nht theo ng th t s t.Cc s trn mt dng ca Input/ Output file ghi cch nhau t nht mt du cch. Gii hn: 1 n 20; 1 m mu 15; 0 cc ta 100;
V d: Vi hnh v trong bi, s 2 l m mu v s 1 l m mu xanh.
PAINT.INPPAINT.OUT74 0 6 320 0 4 214 3 6 512 5 6 622 2 4 520 4 2 610 2 2 41
34 5 3 6 7 2 1043. PHN HOCH TAM GICXt mt a gic li vi n cnh, cc nh c nh s theo th t t 1 ti n. Mt b n - 3 ng cho i mt khng ct nhau s chia a gic cho thnh n - 2 tam gic. Ta gi b gm n - 3 ng cho l mt php tam gic phn ca a gic li ban u.
Trng s ca mt php tam gic phn l tng di cc ng cho c s dng trong php phn hoch.
Yu cu:Cho trwthc nt ta giac li, hy tln nt php tan giac phn nh nhit (c trng s nh nhit)D liu: Vo t file vn bn POLYGON.INP. Trong :
Dng 1: Ghi s nh n ca a gic cho
n dng tip theo, dng th i gm 2 s thc Xi, Yi theo th t l honh v tung canh th i. (Cc nh c lit k theo ng th t gi tn a gic)
Kt qu: Ghi ra file vn bn POLYGON.OUT. Trong :
Dng 1: Ghi trng s ca php tam gic phn nh nht
n - 3 dng tip theo, mi dng ghi hai s nguyn dng i, j cho bit c s dng ng cho ni nh i vi nh j trong php phn hoch tm c
Cc s trn mt dng ca Input/Output file c ghi cch nhau t nht mt du cch.
Gii hn:1. n nguyn dng, 4 n 1002. Cc to nh l s thc: Xi, Yi 1063. Trng s ca php tam gic phn nh nht c ghi di dng s thc lm trn ly 6 ch s sau du chm thp phn.
V d:y0 x044. CC THNH PHN LIN THNG MNHCho th c hng G = (V, E) gm n nh v m cung.
Mt th con G' ca G c gi l mt thnh phn lin thng mnh nu hai iu kin sau tho
mn:
1. Hoc G' ch gm 1 nh, hoc vi hai nh i, j bt k ca G' lun tn ti ng i t nh i ti nh j.
2. Vic thm vo G' mt nh bt k s lm hng tnh cht 1
Yu cu: Cho bitt s thanh phn lin thng nnnh ca t thj t cho va lit k tit c cac thanh phn lin thng nnnh.D liu: Vo t file vn bn GRAPH.INP, trong :
Dng 1: Ghi hai s n, m
m dng tip theo, mi dng ghi hai s nguyn dng x, y th hin c cung ni t nh x ti nh y
Kt qu: Ghi ra file vn bn GRAPH.OUT, trong :
Dng 1: Ghi s thnh phn lin thng mnh (K)
K dng tip theo, dng th i, ghi cc nh thuc thnh phn lin thng mnh th i tm cCac s trn nt dng ca Input/ Output file twic ghi cach nhau It nhit nt diu cachGii hn: 1 n 1000; 1 m 3000V d:1243
045. M GRAYMt hnh trn c chia lm 2n hnh qut ng tm, cc hnh qut c nh s t 1 ti 2n theo chiu kim ng h. Hy ch ra mt cch xp tt c s t 0 ti 2n - 1 vo cc hnh qut, mi s vo mt hnh qut sao cho bt c hai s no hai hnh qut cnh nhau u ch khc nhau ng 1 bt trong biu din nh phn ca n.
V d: Vi n = 4:64
1412108
20
31
119151375D liu: Nhp t bn phm s nguyn dng n. Gii hn (1 n 20).
Kt qu: Ghi ra File (of LongInt) GRAYCODE.OUT gm 2n s nguyn kiu LongInt theo ng th t t s ghi trn hnh qut 1 ti s ghi trn hnh qut 2n.
046. D N XY CUTrong mt khu cng vin nc c n hn o nh v mt s cu ni gia chng. Gi thit rng cc cu c ni theo ng thng.
Hai cu hi t ra l:
1. C tn ti mt ng i qua tt c cc o mi o ng mt ln hay khng ?
2. Nu khng tn ti ng i nh vy, hy ch ra cc xy thm cc cy cu thc hin c
iu sao cho tng di nhng cy cu xy thm l t nht.
D liu: Vo t file vn bn WPARK.INP
Dng 1: Ghi s o n ( 16) v s cu c m
n dng tip theo, dng th i gm 2 s thc x[i] y[i] l to ca hn o i. m dng tip theo, dng th j ghi s hiu hai o tng ng vi chic cu th j.Kt qu: Ghi ra file vn bn WPARK.OUT
Dng 1: ghi s k l s cu cn xy thm v s thc T (ly ti 6 ch s sau du chm thp phn)
l tng di cc cy cu xy thm
k dng tip theo, mi dng ghi s hiu hai o tng ng vi mt cy cu xy thm
Dng k + 2 ghi s hiu cc o trn ng i tm c (sau khi xy thm cu)Cc s trn mt dng ca Input/ Output file c ghi cch nhau t nht mt du cch.
V d:y12
3456
789100x047. BO TN NG VT HOANG DMt khu bo tn ng vt c n a im v cc ng i hai chiu ni cc a im , a im th
i c nhit l ti, gia hai a im bt k c nhiu nht l mt ng i ni chng.
Ngi ta mun di chuyn mt loi ng vt qu him t a im A ti a im B, tuy nhin nu
chnh lch v nhit gia hai a im lin tip trn ng i l qu cao th loi ng vt ny rt c th b cht.
Yu cu: Hy ch ra nt hanh trlnh na t lch nhit t lthn nhit gia hai tja titn lin titp bit k trn twng ti la cc titu.D liu: Vo t file vn bn MOVE.INP
Dng 1: Cha ba s n, A, B (2 n 200; A B)
Dng 2: Cha n s t nhin t1, t2, ..., tn (i: 0 ti 20000)
Cc dng tip theo, mi dng cha hai s nguyn dng u, v cho bit gia hai a im u v v c ng i ni chng.
Kt qu: Ghi ra file vn bn MOVE.OUT
Dng 1: Ghi lch nhit ln nht gia hai a im lin tip bt k trn ng i tm c, nu khng tn ti ng i th dng ny ghi s -1.
Trong trng hp tm c ng i th dng 2 ghi hnh trnh tm c, bt u t a im A, tip theo l nhng a im i qua, kt thc l a im B. Cc a im phi c lit k theo ng th t i qua trn hnh trnh
Cac s trn nt dng ca Input/ Output file twic ghi cach nhau It nhit nt diu cach.V d:2224
25
3020 14
7 26
362927048. PH TNGC mt to lu i hnh ch nht vi hai cnh l m, n nguyn dng khng ln hn 50. Lu i c chia thnh cc vung n v. Cc dng vung c nh s t 1 ti m t trn xung di, trn mi dng, cc c nh s theo th t t 1 ti n t tri qua phi. Quanh mi c th c t 0 ti 4 bc tng, tuy nhin tnh trng c tng ti cc k cnh l khng mu thun nhau.
th hin tnh trng tng quanh mt , ta gn cho mi mt s nguyn, m trong biu din nh
phn ca s nguyn :
Bt 0 (Bt n v) bng 1 hay 0 tu theo c tng hay khng c tng hng Ty
Bt 1 bng 1 hay 0 tu theo c tng hay khng c tng hng Bc Bt 2 bng 1 hay 0 tu theo c tng hay khng c tng hng ng Bt 3 bng 1 hay 0 tu theo c tng hay khng c tng hng NamQuanh lu i c tng bao bc.
V d trong hnh v di, ta c mt lu i 4 x 7.
Tnh trng tng ca (2, 2) c th hin bi s 9 = 1001
Tnh trng tng ca (3, 5) c th hin bi s 13 = 11011234567N129WE313
S4
Lu i c chia thnh cc phng, cc phng phn cch nhau bi cc bc tng. Hy lp chng trnh tr li cc cu hi sau:
1. Cho bit lu i c bao nhiu phng
2. Cho bit s ca phng rng nht
3. Hy tm cch ph i mt v ch mt bc tng c mt phng rng nht c th
D liu: Vo t file vn bn DWALL.INP
Dng 1: Ghi hai s m, n
m dng tip theo, dng th i ghi n s nguyn, s th j th hin tnh trng tng quanh (i, j)Kt qu: Ghi ra file vn bn DWALL.OUT
Dng 1: Ghi s phng
Dng 2: Ghi s ca phng rng nht Dng 3: Ghi hai s P, Q v k t c {W, N, E, S} vi ngha ph tng hng c ca (P, Q)
Dng 4: Ghi s ca phng rng nht thu c sau khi ph tngCc s trn mt dng ca Input/Output file c ghi cch nhau t nht mt du cchV d:
DWALL.INPDWALL.OUT4 711 06 11 06 03 10 0607 09 06 13 05 14 0501 10 12 07 13 07 0513 11 10 08 10 12 13
593 2 S16049. TRUYN TIN TRN MNGTrong mt mng gm N my tnh nh s t 1 n N. S ni mng c cho bi m knh ni trc tip gia mt s cp my trong mng. Bit chi ph truyn mt n v thng tin theo mi knh ni ca mng.
Ngi ta cn chuyn mt bc thng ip t my S n my D (S D). m bo an ton, ngi ta mun chuyn bc thng ip ny theo hai ng truyn tin khc nhau (tc l khng c knh no ca mng c s dng trong c hai ng truyn tin). Chi ph ca mt ng truyn tin c hiu l tng chi ph trn cc knh ca n. Chi ph truyn thng ip bng tng chi ph ca hai ng truyn.
Yu cu: Gi s bc thng tip c t dai la 1 tn vj thng tin, hy tln cach truyn thng tip ts ttn t sao cho chi phI truyn thng tip la nh nhitD liu: Nhp t file vn bn MESSAGE.INP vi cu trc nh sau:
Dng u tin ghi bn s n, m, S, D (n100);
Mi dng th i trong s m dng tip theo ghi thng tin v knh ni th i ca mng gm ba s ai, bi, ci, trong ai, bi l ch s ca hai my tng ng vi knh ny v ci (nguyn dng 200) l chi ph truyn mt n v thng tin t my ai n my bi (v ngc li) theo knh ny (i=1,2,...,m).
Kt qu: Ghi ra file vn bn MESSAGE.OUT theo cu trc sau:
Dng u tin ghi chi ph truyn thng ip theo cch truyn tin tm c.
Dng th hai ghi ng truyn tin th nht di dng dy c th t cc my, bt u t my Sv kt thc my D.
Dng th ba ghi ng truyn tin th hai di dng dy c th t cc my bt u t my S v kt thc my D.
Nu khng tn ti cch truyn th ch cn ghi vo file MESSAGE.OUT mt dng: NO SOLUTION
Cc s trn mt dng ca Input/ Output file ghi cch nhau t nht mt du cch. V d:
835831234545
MESSAGE.INPMESSAGE.OUT5 7 1 51 2 31 4 82 3 52 4 43 5 54 3 84 5 3
241 2 3 51 4 5050. HNH VUNG CC ICho mt bng kch thc mxn, c chia thnh li vung n v m dng n ct. Trn cc ca bng ghi s 0 hoc 1. Cc dng ca bng c nh s 1, 2... m theo th t t trn xung di v cc ct ca bng c nh s 1, 2..., n theo th t t tri qua phi.
Hy tln nt hlnh vung gn cac ca bng tho nn cac tiu kin sau:1. Hlnh vung la tng nhit: tc la cac thuc hlnh vung t phi ghi cac s ging nhau (0 hoc 1)2. Cnnh hlnh vung song song vthi cnnh bng.3. KIch thwthc hlnh vung la lthn nhit c tht.D liu: Vo t file vn bn SQUARE.INP
Dng 1: Ghi hai s m, n
m dng tip theo, dng th i ghi n s m s th j l s ghi trn (i, j) ca bngKt qu: Ghi ra file vn bn SQUARE.OUT
Dng 1: Ghi kch thc cnh hnh vung tm c
Dng 2: Ghi 4 s nguyn r1, c1, r2, c2. y (r1, c1) l ch s hng v ch s ct ca thuc gc trn bn tri, (r2, c2) l ch s hng v ch s ct ca thuc gc di bn phi hnh vung tm c.
Cac s trn nt dng ca Input/ Output file ghi cach nhau It nhit nt diu cach.V d:SQUARE.INPSQUARE.OUT11 13
73 3 9 9051. ON XE QUA CUCho mt on xe gm n chic i trn mt ng mt chiu v on xe c b tr theo th t t
1 n n. Mi mt xe trong on c vn tc l vi v trng lng wi.
Khi i qua mt chic cu c trng ti gii hn l P th on xe phi chia thnh cc nhm sao cho tng trng lng ca mi nhm khng qu P (Lu rng khng c o th t on xe). Cc nhm phi i tun t c ngha l nhm th i ch c khi hnh khi m ton b xe ca nhm th i -
1 qua cu. Gi thit rng P > wi vi i: 1 i n.
R rng khi thi gian mt nhm xe qua cu ph thuc vo xe chm nht trong nhm nu coi nh chiu di cng nh khong cch ca cc xe l khng ng k.
Hy tln cach chia toan xe thanh cac nhn sao cho thi gian na toan xe sang twic cu la nhnhit c tht twic.D liu: Vo t file vn bn CARGROUP.INP Dng u l 3 s nguyn dng n, P v L (n, P, L 1000) th hin cho s xe, trng lng gii hn ca cu v di ca cu.
Dng th i trong n dng k tip gm 2 s nguyn dng wi v vi (wi, vi 100)Kt qu: Ghi ra file vn bn CARGROUP.OUT Dng u ghi mt s thc l tng thi gian nh nht xe qua cu, cho php lm trn ly 2 chs sau du chm thp phn.
Dng k tip gm cc s x1, x2, .., xk th hin: nhm 1 gm cc xe t 1 n xe th x1, nhm 2 gm cc xe th x1+1 n xe th x2..., nhm k t xe th x[k - 1] ti x[k]
Cac s trn nt dng ca Input / Output file ghi cach nhau It nhit nt diu cach.V d:
P = 100
25202010507030255070 (km / h)
100 km
4050507012949382719
4h5h10h4h2h
CARGROUP.INPCARGROUP.OUT10 100 10040 2550 2050 2070 1012 5009 7049 3038 2527 5019 70
25.001 3 6 8 10052. S LNGCho s nguyn dng n (n 2 000 000 000). Hy xc nh xem trong phm vi t 1 ti n c bao nhiu s m trong dng biu din nh phn ca n c ng K ch s 0 c ngha.
V d: n = 18, k = 3 c 3 s:1. 8 = 10002. 17 = 100013. 18 = 10010D liu: Vo t file vn bn NUMBER.INP, gm mt dng cha hai s nguyn N v K cch nhau mt du cch.
Kt qu: a ra file NUMBER.OUT, ghi s lng cc s tm c
V d:NUMBER.INPNUMBER.OUT18 33053. THM HIM LNG TMt nh kho c nghin cu nhng di sn vn ho c i mt thnh ph b chn vi di lng
t. thm him thnh ph , nh kho c ca chng ta buc phi o cc ng ngm.
Bt u ti v tr xut pht, ng ta o theo mt trong 4 hng ng (E), Ty (W), Nam (S), Bc (N), mi ln o mt n v di. Sau c th o tip theo hng hoc i hng theo mt trong 4 hng trn. Gi s rng ng knh ca ng ngm o c l khng ng k.
trnh b lc, ng ta ghi li vo file vn bn MAP.INP trong my tnh xch tay ca mnh mt trong 4 k t E, W, S, N tng ng vi mt trong bn hng m ng ta s o ti mi ln.
V d vi im xut pht v quy trnh o hm di y, s cc ng ngm s l:FinishStart
Sau khi t kho sat xong, nha kho c nun quay tr lni titn xuit phat bng twng hn t tao. Hy da vao thng tin trong nay tInh xach tay ca nha kho c tt ch cho ng ta twng ti ngn nhit quay tr lni.D liu: Vo t file vn bn MAP.INP ca nh kho c gm 1 dng khng qu 5000 k t {E, W, N, S}
Kt qu: Ghi ra file vn bn MAP.OUT gm 1 dng cha cc k t ch hng i dn v ni xut pht.
V d:
MAP.INPMAP.OUT EEEENNNWWWSSSSSSSEEEEENNNNNWWSWWWW054. TH T T INMt bng danh nc gn cac t t twic sp xtp theo nt trt t t titn nao tiy (khng nhit thitt la t titn thng thwng). Yu cu t bng danh nc, hy khi phc lni trt t t titn t dung. D liu vo c cho bi file vn bn NOTE.INP. Dng u l s lng t, cc dng tip, (theo th t) mi dng l mt t trong bng danh mc. Gi thit rng mi t u khng qu
20 k t c ly trong bng ch ci nh ting Anh (t 'a' n 'z'). S lng t trong bng danh mc khng qu 10000.
Kt qu a ra file vn bn NOTE.OUT gm mt dng l xu gm cc ch ci xut hin trong bng danh mc. Cc ch ci trong xu vit lin nhau v theo th t ph hp vi trt t t in dng.
V d:NOTE.INPNOTE.OUT10 svxngqqnsnvqv snngg qsqsqvgsqq qqnsqnvq nsxnxnvsqsvvs nqgnn xsgvsgggqvsqqsxgv xxgxxggsvnxsnxsnqq
gsvqnxCho hai dy s nguyn:
A = (a1, a2, ..., an)B = (b1, b2, ..., bn)
055. DY LCH(n 100; -10000 ai, bj 10000 vi i, j : 1 i, j n )
Hy tln nt hoan vj = (1, 2, ..., n) ca dy s (1, 2, ..., n)t cc titu hoa bitu thc:F() := 1 - a1 + b1 - a2 + b2 - a3 + ... + bn-1 - an + bn - 1D liu: Vo t file vn bn SLANTING.INP
Dng 1: Ghi s nn dng tip theo, Dng th i ghi 2 s nguyn ai v bi cch nhau t nht 1 du cch
Kt qu: Ghi ra file vn bn SLANTING.OUT
Dng 1: Ghi gi tr cc tiu F() tm c
n Dng tip theo, dng th i ghi gi tr iV d:056. RT GN DY SCho dy gm n s nguyn dng a = (a1, a2, ..., an). Trn dy s ny ta c th thc hin php rt gn ti v tr i:
R(i): thay hai s hnng lin titp ai va ai+1 bng hiu ca chng ai - ai+1.Sau n - 1 ln rt gn, vi dy a, ta thu c duy nht mt s nguyn.
V d: Thc hin ln lt cc php rt gn 2, 3, 2 v 1 i vi dy s (12, 10, 4, 3, 5) ta s thu c kt qu nh sau:
1. Ban u: (12, 10, 4, 3, 5)
2. Rt gn R(2):(12, 6, 3, 5)
3. Rt gn R(3):(12, 6, -2)
4. Rt gn R(2):(12, 8)
5. Rt gn R(1):(4)
Yu cu cho dy s a = (a1, a2, ..., an) v s T, hy tm th t thc hin N - 1 php rt gn i vi dy cho thu c T.
D liu: Vo t file vn bn SUBTRACT.INP
Dng u tin cha hai s n v T cc nhau mt du cch (1 n 100; -10000 T 10000) Dng th i trong s n dng tip theo ghi s ai. (1 ai 100).
Kt qu: Ghi ra file vn bn SUBTRACT.OUT
Gm n - 1 dng, dng th i ghi v tr thc hin php rt gn th i. Gi thit rng cc d liu u c t nht mt li gii
V d:SUBTRACT.INPSUBTRACT.OUT4 531012152057. BUN TINMt ngi lm vic mt ngn hng ngoi t theo di t gi hi oi pht hin ra l: Nu khn kho, th t mt lng ngoi t ban u, nh chuyn i sang cc loi ngoi t khc, anh ta c th thu c li nhun ng k.
V d: Nu anh ta c 1 USD v t gi hi oi gia cc ngoi t nh sau: 1 USD= 0.7 bng Anh 1 bng Anh = 9.5 Franc Php 1 Franc Php= 0.16 USDKhi vi 1 USD anh ta c th mua c 0.7 * 9.5 * 0.16 = 1.064 USD nh vic chuyn i tin qua bng Anh, ri t bng Anh sang Franc Php, v cui cng li quay v USD. Nh mi USD em li cho anh ta li nhun l 0.064USD.Gi s trong nh bng qun l n loi ngoi t nh s 1, 2, ..., n. Bit bng t gi hi oi R[i, j] (1 i, j n). (Tc l 1 n v ngoi hi i mua c R[i, j] n v ngoi hi j). Cn xc nh xem c cch
i tin em li li nhun hay khng ?
D liu: Vo t file vn bn MONEY.INP
Dng u tin cha s n (n 100)
Dng th i trong s n dng tip theo cha n s thc dng R[i, 1], R[i, 2], ..., R[i, n].
Kt qu: Ghi ra file vn bn MONEY.OUT
Dng u tin ghi YES hoc NO tng ng vi vic c hoc khng c cch i tin sinh li nhun Nu dng u tin l YES th dng th hai ghi hai s u v s. Trong u l loi tin xut pht, cn s l li nhun thu c nh cch i 1 n v tin u. Dng th ba ghi trnh t cn tin hnh i tin thu li c li nhun bt u t loi tin xut pht
Cac s trn nt dng ca Input/Output File twic ghi cach nhau It nhit nt diu cachLii nhun (ntu c) trong Output File c tht ch cn lan trn gi lni 6 ch s sau diu chin thp phn.V d:MONEY.INPMONEY.OUT51.001.100.830.810.850.831.000.861.090.810.890.841.000.831.020.840.831.011.000.841.090.840.870.901.00
YES1 0.0071601 2 4058. DY NGOCMt dy du ngoc hp l l mt dy cc k t "(" v ")" c nh ngha nh sau:
i.Dy rng l mt dy du ngoc hp l su 0
ii.Nu A l dy du ngoc hp l su k th (A) l dy du ngoc hp l su k + 1
iii.Nu A v B l hai dy du ngoc hp l vi su ln lt l p v q th AB l dy du ngoc hp l su l max(p, q)
di ca mt dy ngoc l tng s k t "(" v ")"
VI d: C 5 dy diu ngoc hip l t dai 8 va t su 3:((()())) ((())()) ((()))() (()(())) ()((()))Bai toan tt ra la khi cho bitt trwthc hai s nguyn dwng n va k. Hy cho bitt c bao nhiu dy ngoc hip l c t dai la n va t su la k. Ntu c khng qua 100 dy thl hy lit k htt cac dy, ntu c nhiu hn 100 dy thl hy ch ra 100 dy ngoc phn bit.D liu: Vo t file vn bn NGOAC.INP gm 1 dng ghi hai s nguyn dng n v k cch nhau
mt du cch (n 64, k 32).
Kt qu: Ghi ra file vn bn NGOAC.OUT
Dng 1: Ghi s C l s lng dy ngoc hp l c di l n v su l k.
Nu C 100, th C dng tip theo mi dng ghi mt dy ngoc tm c. Nu C > 100, th 100 dng tip theo mi dng ghi mt dy ngoc. Cc dy ngoc c lit k i mt khc nhau.
V d:NGOAC.INPNGOAC.OUT
8 35((()())) ((())()) ((()))() (()(())) ()((()))
059. THNG BM V PH NGBm thng ph ng trong mt cuc nh cc v buc ph ng phi i ru. Ph ng bn by ra mt dy n chai cha y ru, v ni vi Bm rng c th ung bao nhiu tu , nhng chn chai no th phi ung ht v khng c ung ba chai lin nhau bi l iu xui xo.
Bnn hy ch cho Bn cach ung twic nhiu rwiu nhit.D liu: Vo t file vn bn BOTTLES.INP
Dng 1: Ghi s nguyn dng n (n 10000)
Cc dng tip ghi cc s nguyn dng ( 10000) l dung tch ca cc chai ru ph ng by ra, theo th t lit k t chai th nht ti chai th n, cc s c ghi cch nhau bi du cch hoc du xung dng.
Kt qu: Ghi ra file vn bn BOTTLES.OUT
Dng 1: Ghi s chai c chn v lng ru ti a c th ung cch nhau mt du cch.
Cc dng tip theo, mi dng ghi ch s ca mt chai chn ra cV d:BOTTLES.INPBOTTLES.OUT66 10 10 1310 10
4 402356060. S THP PHNKt qu ca php chia: a/b vi a v b l hai s nguyn (b 0) c th biu din di dng mt s
thp phn hu hn hoc s thp phn v hn tun hon.
V d:6/25= 0.241/3= 0.(3)-17/140= -0.12(142857)Vin t tt ra la khi bitt hai s nguyn a, b (-109 a 109; -107 b 107; b 0). Hy tln bitu din thp phn ca php chia a/b.D liu: Vo t file vn bn DECIMAL.INP
Input file gm nhiu dng, mi dng ghi mt b d liu l cp s nguyn a, b cch nhau mt du cch.
Kt qu: Ghi ra file vn bn DECIMAL.OUT
Output file c s dng bng s dng ca input file, chng trnh phi ghi kt qu tng ng vi b
d liu th i trong input file vo dng th i ca output file.
Ch : Trong trng hp a/b l s nguyn th ch ghi kt qu phn nguyn, khng c phn thp phn v du chm thp phn.
Trng hp a/b l s thp phn hu hn, khng c ghi tha s 0 cui. Trng hp a/b l s thp phn v hn tun hon, phn thp phn ng trc chu k phi l ngn ti tiu.
V d:DECIMAL.INPDECIMAL.OUTDECIMAL.OUT di y tuy gi tr ng nhngl sai khun dng
100 106 251 399 101431 3500100.240.(3)0.(9801)0.123(142857)10.000.2400.33(3)0.98(0198)0.123142(857142)
061. DANH SCH VNG lm vic vi mt danh sch gm N s nguyn cn phi c hai thao tc.
Thao tc Top chuyn phn t u tin ca danh sch xung v tr cui cng ca danh sch.
Thao tc Bottom chuyn phn t cui cng ca danh sch ln v tr u tin ca danh sch.Mt php bin i danh sch cho l vic thc hin K ln thao tc Top, ri sau n L ln thao tc Bottom.
Do s ln thc hin php bin i trn l rt ln nn i hi phi c nhng th tc thc hin hiu qu thc hin lin tip X php bin i a danh sch v trng thi cui cng.
Yu cu: Vit chng trnh cho php vi mt danh sch v ba s K, L, X cho trc, xc nh trng thi ca danh sch sau X ln thc hin php bin i.
D liu: Vo t file vn bn CLIST.INP
Dng u tin cha ba s nguyn dng N, K, L (1 N, K, L 10000).
Dng th hai cha N s nguyn, mi s c gi tr tuyt i khng qu 10000, c sp xp theo th t tng ng vi trng thi khi u ca danh sch.
Dng th ba cha s nguyn X (0 X 2.109).Kt qu: Ghi ra file vn bn CLIST.OUT
Ghi ra trn mt dng ca file vn bn CLIST.OUT cc phn t ca danh sch sau X php bin i. Cc phn t phi c ghi ng th t t phn t u tin n phn t cui cng.
Cc s trn mt dng ca Input/Output File ghi cch nhau t nht mt du cch.
V d:CLIST.INPCLIST.OUT5 2 13 5 2 4 79
7 3 5 2 4062. TNH DIN TCHCho mt li vung kch thc MxN. Mi cha mt s 0 hoc 1. Cc s 1 trn li to thnh mt ng kn (tc l dy cc m hai lin tip c chung cnh hoc nh v cui cng ca dy c chung cnh hoc nh vi u tin) bc c mt vng ca li m ta s gi l mt hnh. Din tch ca hnh l s cha s 0 nm trong .
Yu cu: Vitt chwng trlnh tInh din tIch ca hlnh trong nt lwthi vung cho trwthc. Gi thitt la din tIch ca nt hlnh khac 0.D liu: Vo t file vn bn SZERO.INP:
Dng u tin cha hai s nguyn dng M, N (5 M, N 100)
M dng tip theo m t bng cho trc, mi dng cha dy gm N s 0 hoc 1 c ghi lin nhau
Kt qu: Ghi ra trn mt dng ca file vn bn SZERO.OUT din tch ca hnh trn li cho.
V d:SZERO.INPSZERO.OUT
6 80100000010100000100100001000100001010000001000007
063. THANG MYTrong to nh ca mt trung tm thng mi gm 101 tng (cc tng c nh s t 0 n 100)
khch hng c th s dng hai loi thang my:
Thang my loi I: cho php di chuyn n bt k tng no vi thi gian di chuyn qua mt tng l E1 giy.
Thang my loi II (siu tc) ch dng li cc tng c ch s chia ht cho 10, thc hin vic di chuyn qua 10 tng vi thi gian l E2 giy.
Bt k thang my ang u, thi gian ch i thang my I v II ( chuyn thang my hoc vo thang my) l W1 v W2 giy tng ng. Ngoi ra ti mi tng, khch hng cn c th di chuyn t tng ny ln tng trn hoc xung tng di theo cu thang c nh vi thi gian l S giy.
Yu cu: Xc nh thi gian nh nht T cn thit mt khch hng c th di chuyn t tng X
n tng Y. Gi thit l 1 E1, E2, W1, W2, S 1000.
D liu: Vo t file vn bn LMOVE.INP
Dng u tin cha hai s E1, W1.
Dng th hai cha hai s E2, W2. Dng th ba cha s S
Dng th t cha hai s X, Y.Kt qu: Ghi ra file vn bn LMOVE.OUT thi gian T tm c
Cc s trn mt dng ca input file c ghi cch nhau t nht mt du cch.V d:
LMOVE.INPLMOVE.OUT2 25964 151085 43Cch di chuyn ti u vi d liu trn nh sau:
ang tng 85, ch thang loi I:
25 giy Tt xung tng 80:2giy x 5 = 10 giy Ch thang loi II:
15 giy
Tt xung tng 40:4giy x 4 = 16 giy
Di chuyn theo cu thang ln tng 43: 10giy x 3 =30 giy
Tng cng:96 giy
064. TRNG S XUXt tp ch ci A = {I, W, N}. Mt t l mt dy lin tip khng qu 6 k t ca A. Cho mt danh sch L gm m t phn bit.
Mi t trong danh sch c gn mt trng s dng 60000.
Nhng t khng c trong danh sch mang trng s 0.Xt mt xu S ch gm cc k t trong A. Trng s ca xu S c tnh bng tng trng s cc t trong S. (Cc t trong S c lit k di dng cc on k t lin tip ca S tnh c vic giao nhau v cha nhau)
Yu cu: Cho trwthc danh sach L va t dai n 100. Hy tln xu S = S1S2...Sn c trng s nhnhit. Ntu c nhiu xu S tu c trng s nh nhit thl ch cn ch ra nt xu.D liu: Vo t file vn bn STR.INP
Dng 1: Ghi hai s n, m cch nhau mt du cch.
m cp dng tip theo, cp dng th i gm 2 dng: Dng th nht ghi t th i trong danh sch L Dng th hai ghi trng s ca t Kt qu: Ghi ra file vn bn STR.OUT gm 2 dng:
Dng 1: Ghi trng s ca t S tm c
Dng 2: Ghi xu k t S
V d:STR.INPSTR.OUT
8 10I13W6N12II6NI6IIN13WWW7WNN23NWW18NWN062WWIWWIWW
065. PH MAY MNNgi dn thnh ph Byteland c rt nhiu iu king k trong cuc sng. Theo quan im ca h, cc s 2, 6, 13 v nhiu s khc khng mang li iu may mn. Trong khi , cc s 3, 5, 7 li rt c a chung. Nhng ngi nh c s m khi phn tch ra tha s nguyn t ch cha cc tha s
3, 5, 7 c coi l may mn v c mua rt nhanh.
Sau mt thi gian di tho lun, Hi ng thnh ph quyt nh nh s tt c cc ngi nh trn mt ng ph mi m bng cc s may mn lin tip nhau, bin ph thnh mt ph may mn. K hiu dy cc s may mn l X1, X2, X3, X4, ... Khi cc nh bn tri s mang s X1, X3, X5. Cn dy nh bn phi s mang s X2, X4, X6, ... Ton b ng ph c khng qu 4000 nh.
Hy xac tjnh xen nt s cho trwthc c phi la nt s nha ph nay nn khng. Ntu tng thl cho bitt nha t nn bn phi hay bn trai ca ph.D liu: Vo t file vn bn STREET.INP gm khng qu 100000 dng, mi dng cha mt s
nguyn dng khng qu 18 ch s.
Kt qu: Ghi ra file vn bn STREET.OUT, gm nhiu dng, mi dng tng ng vi mt s file d liu vo v cha mt trong ba ch ci L, R, N tng ng vi nh bn tri, bn phi hay khng phi s nh ph may mn.
Lu : Dy s may mn c tnh bt u t X1=3.V d:
STREET.INPSTREET.OUT5R3L4N98415R12814453125LTrong mt thnh ph c:
066. TN HIU GIAO THNG m ng ph (hai chiu) song song chy thng dc theo hng Tyng, tin, ta gi cc
ng ph l H1, H2,..., Hm theo th t t Bc xung Nam. n ng ph (hai chiu) song song chy thng theo hng BcNam, ta gi cc ng ph l V1, V2, ..., Vn theo th t t Ty sang ng
Hai ng ph vung gc bt k ct nhau to thnh mt nt giao thng. Ngoi tr hai nt giao thng nm v tr gc ng-Nam v gc Ty-Bc nhng nt giao thng khc c th gn n tn hiu giao thng hai trng thi:
0. Trng thi EW: Xanh hng ng v Ty, hng Bc v Nam.
1. Trng thi NS: Xanh hng Bc v Nam, hng ng v Ty.
Mi n tn hiu c mt chu k thi gian ring, c sau mi chu k thi gian , n i trng thi mt ln. Ti thi im 0, cc n tn hiu u trng thi 0 (EW).
gi an ton, lut giao thng quy nh: Khi xe ti mt nt giao thng t mt hng no ng vo thi im n tn hiu theo hng ang hay chuyn sang th buc phi dng li, ng vo thi im n tn hiu theo hng ang Xanh hay chuyn sang Xanh th c th i thng, r phi hay r tri tu .
Trn mt ng ph, thi gian xe i gia hai nt giao thng lin tip c nh l 1 n v thi gian. Yu cu: Cho bitt s t giao thng va cac tn tIn hiu. Cho nt xe xuit phat tni thi titn 0 t nt giao thng gc Ty-Bc. Tln hanh trlnh va thi titn sthn nhit tt xe tthi nt giao thng gc ng-Nan.D liu: Vo t file vn bn TRAFFIC.INP
Dng 1: Ghi hai s nguyn dng m, n (m, n 100)
Dng 2: Ghi s k l s n hiu giao thng k dng tip theo, dng th i gm 3 s nguyn dng x, y, t cho bit n hiu th i nm giaoim ca ng Hx v Vy c chu k l t (t 10000).Kt qu: Ghi ra file vn bn TRAFFIC.OUT
Dng 1: Ghi thi im sm nht xe chy t gc Ty-Bc ti gc ng-Nam
Dng 2: Ghi mt dy k t, k t th p {w, E, W, S, N} cho bit trong khong thi gian t p-1 ti p, xe trong trng thi ng i hay chy theo hng ng, Ty, Nam hay Bc (theo th t
w, E, W, S, N ).
Cc s trn mt dng ca Input File c ghi cch nhau t nht mt du cch.
V d:TRAFFIC.INPTRAFFIC.OUT3 491 2 2
6ESEwSE223N
1 4 32 1 42 2 22 3 12 4 23 1 103 3 4
42w 12W
E S
104067. PHN NHMCho n hc sinh v m c im (n 100), (m 10).
Cn phn cac hc sinh nay thanh nt s It cac nhn nhit tt tn bo rng ta ch cn quan tn tthi nt s It nhit cac tc titn la c tht phn bit twic cac hc sinh trong ni b nt nhn.Ch :1. Trwthc tin phi tho nn yu cu It nhn nhit, trong cac cach chia It nhn nhit na vn c tht phn bit twic cac hc sinh trong nt nhn thl ch ra nt cach chia phi dung It tc titn nhit.2. Tp cac tc titn twic chn phi s dng twic trn tit c cac nhn tt phn bit hc sinh.D liu: Vo t file vn bn GROUP.INP
Dng 1 ghi hai s n, m
n dng tip theo, dng th i m t c im ca hc sinh th i: Gm c m s nguyn m s th j l 1 hay 0 tu theo hc sinh th i c hay khng c c im j.
Kt qu: Ghi ra file vn bn GROUP.OUT Dng 1: Ghi s k l s nhm chia ra c
Dng 2: Ghi cc c im c chn phn bit cc hc sinh trong ni b cc nhm k dng tip theo, dng th p ghi cc hc sinh trong nhm p
Cac s trn nt dng ca Input/Output File twic ghi cach nhau It nhit nt diu cach.V d:GROUP.INPGROUP.OUT
10 40 0 0 1
0 0 1 0
0 1 1 01 0 0 01 0 0 0
1 0 0 11 0 1 11 1 0 11 1 1 01 1 1 021 2 42 5 10 1 64 3 9 7 8
068. TUA DU LCH R NHTMt khu thng cnh gm n im nh s t 1 ti n (n 100) v m ng i hai chiu gia cc cp
a im , chi ph i trn cc ng i l bit trc ( 10000).Mt Tour du lch l mt hnh trnh xut pht t mt a im i thm 2 a im khc v quay tr v im xut pht, ngoi tr a im xut pht, khng a im no b thm ti hai ln. Chi ph ca mt Tour du lch l tng chi ph cc qung ng i qua.
Yu cu: Hy tln Tour du ljch c chi phI r nhit.D liu: Vo t file vn bn TOUR.INP
Dng 1: Ghi hai s nguyn dng n, m
m dng tip theo mi dng c dng x y c. Cho bit c ng i trc tip ni a im x vi aim y v chi ph i qung ng l c.
Kt qu: Ghi ra file vn bn TOUR.OUT
Dng 1: Ghi s 1 nu nh tn ti hnh trnh theo yu cu, ghi s 0 nu khng tn ti hnh trnh.
Nu dng u tin ghi s 1:
Dng th 2 ghi chi ph ca tour tm c Dng th 3 ghi s k l s a im ti thm Dng th 4 gm k s, s th i l a im ti thm th i trong tour, quy c a im thm u tin l a im xut pht, a im thm th k (a im cui cng) l a im m t quay tr li im xut pht kt thc hnh trnh.
Cac s trn nt dng ca Input/Output File twic ghi cach nhau It nhit nt diu cach.V d:
1910252
2282294103069. DU LCH NHIU TUA NHTMt khu thng cnh gm n im nh s t 1 ti n (n 200) v m ng i hai chiu gia cc cp
a im .
Mt Tour du lch l mt hnh trnh xut pht t mt a im i thm 2 a im khc v quay tr
v im xut pht, ngoi tr a im xut pht, khng a im no b thm ti hai ln.
Yu cu: Hy tln nt s tour du ljch nhiu nhit sao cho ni tour du ljch tln twic tu c nttonn twng ring hoan toan khng c nt trong cac tua du ljch cn lni.D liu: Vo t file vn bn TOURS.INP
Dng 1: Ghi hai s n, m
m dng tip theo mi dng c dng x y cho bit gia hai a im x v y c ng i trc tip.Kt qu: Ghi ra file vn bn TOURS.OUT
Dng 1: Ghi s k l s tour du lch tm c
k dng tip theo, dng th i m t tour du lch th i: bt u l s a im thm c trong tour, tip theo l danh sch cc a im theo th t trong hnh trnh bt u t a im xut pht cho ti kt thc l a im m t quay li im xut pht kt thc hnh trnh
Cac s trn nt dng ca Input/Output file twic ghi cach nhau It nhit nt diu cachV d:152
43
070. PHN CNGC m th v n cng vic, cc th nh s t 1 ti m v cc vic nh s t 1 ti n. Mi th c kh
nng thc hin mt s cng vic no .
Khi giao vic cho cc th thc hin, i vi mt ngi th th h s thc hin cc cng vic c giao mt cch tun t v lin tc (sequence), lm mi vic mt mt n v thi gian. Nhng i vi nhiu th th cc cng vic ca h c thc hin song song (paralell), vic ca ai ngi y lm, khng nh hng ti tin ca ngi khc.
Hy tln cac phn cng cng vic cho cac thi tt tit c cac cng vic twic thc hin, ni vic chphn cho nt thi va thi gian hoan thanh tit c cac cng vic la nhanh nhit.D liu: Vo t file vn bn ASSIGN.INP
Dng 1: Cha hai s nguyn dng m v n (1 m 100; 1 n 500)
m dng tip theo, dng i cha danh sch cc cng vic m th i c th thc hin, c thm mt k hiu kt thc l s 0.
Kt qu: Ghi ra file vn bn ASSIGN.OUT
Dng 1: Ghi t YES hay NO tu theo c tn ti cch phn cng thc hin tt c cc cng vic hay khng.
Nu dng 1 ghi t YES: Dng 2: Ghi thi gian nhanh nht c th hon thnh cc cng vic
m dng tip theo, dng i ghi danh sch cc cng vic c phn cho th i, ghi thm mt k hiu kt thc l s 0.
Cac s trn nt dng ca Input/Output File twic ghi cach nhau It nhit nt diu cachV d:
ASSIGN.INPASSIGN.OUT4 101 2 3 4 5 04 5 6 7 8 01 2 3 4 5 7 8 9 01 2 3 4 5 6 7 8 9 10 0
YES33 4 5 06 7 8 02 9 01 10 0071. NHN TINMt kho hc c n hc vin nh s t 1 ti n, mi hc vin c th bit s in thoi ca mt vi hc vin khc.
Hc vin A c th nhn tin cho hc vin B nu nh hc vin A bit s in thoi ca hc vin B. Lu rng vic bit s in thoi y khng phi quan h i xng: C th hc vin A bit s in thoi ca hc vin B nhng hc vin B hon ton khng bit s in thoi ca hc vin A.
Thy giao nn twic tit c s tin thoni ca cac hc vin trong h s ca trung, hi khi thy giao nun nhn tin tthi tit c cac hc vin trong khoa, thy giao s phi nhn trc titp tthi nt s It nhit cac hc vin nao tt thng tip t ttn twic tit c cac hc vin khac.D liu: Vo t file vn bn MESSAGE.INP
Dng 1 cha s n (n 700)
Cc dng tip theo, mi dng cha hai s nguyn dng x, y (x y: 1 x, y n) cho ta thng tin: hc vin x bit s in thoi ca hc vin y
Kt qu: Ghi ra file vn bn MESSAGE.OUT
Dng 1: Ghi s k l s hc sinh c thy gio nhn tin trc tip khi cn
Dng 2: Ghi k s hiu ca cc hc sinh c thy gio nhn tin trc tipCac s trn nt dng ca Input/Output File twic ghi cach nhau It nhit nt diu cach.V d:214356789101211Gii hn khng gian v thi gian: 512KB - 1 giy
072. CC S IN THOINgy nay bn phi nh qu nhiu s in thoi m chng li ngy cng di hn. Mt trong nhng cch d ghi nh cc con s nh vy l thay th cc ch s bng ch ci theo mt qui c no . V d nh ta c th thay:
1 = ij2 = abc3 = def4 = gh5 = kl6 = mn7 = prs
8 = tuv9 = wxy0 = oqz
Bng cch ny, mi t hoc mt nhm t c th gn cho mt s duy nht, v v th bn c th nh cc t thay v cc con s. V d s in thoi ca ngi bn chi c 941837296 th c th nh bi t WHITE PAWN cn s in thoi ca mt thy gio 8322437 th c th nh bng t TEACHER th d nh hn nhiu so vi cc con s di dng .
Cho bitt cac php thay tht s bng ch cai, va nt t titn. Hy tln nt dy gn It nhit cac t tt gan cho con s cn ghi nhth cho trwthc. Mi t c tht dung nhiu ln.D liu: Vo t file vn bn PHONE.INP
10 dng u tin, dng th i ghi danh sch cc ch ci c th dng thay cho s i - 1.
Dng 11 ghi con s cn ghi nh (khng qu 100 ch s) Cc dng tip theo, mi dng ghi mt t trong t in, mi t gm khng qu 50 ch ci ting Anh in thng. K hiu kt thc t in l dng cui cng ghi du #. S t trong t in khng qu 50000.
Trong Input File hon ton khng cha du cch.
Kt qu: Ghi ra file vn bn PHONE.OUT
Dng th nht: Ghi t YES hay NO tu theo c php gn dy t cho s cho hay khng ?
Nu dng th nht ghi t YES, dng th hai, ghi danh sch cc t ghp li theo ng th t s c s cho, cc t ghi cch nhau t nht mt du trng.
V d:
PHONE.INPPHONE.OUToqz ij abc def gh kl mn prs tuv wxy7325189087 ityour reality realour#
YESreality our073. GI TR LN NHTMt s nguyn dng x gi l con ca s nguyn dng y nu ta c th xo bt mt s ch s ca y
c x.
Cho hai s a va b hy tln s c la con ca c a va b sao cho gia trj ca c la lthn nhit c tht.Rng buc: 1 a, b 10100
D liu vo lun c nghim.
D liu: Vo t file vn bn NUMBER.INP
Dng th nht cha s a
Dng th hai cha s bKt qu: Ghi ra file vn bn NUMBER.OUT
Ghi ra trn mt dng s c.
V d:NUMBER.INPNUMBER.OUT
12345678123456781234567856781234
074. NT GIAO THNG TRNG IMTrong mt ng ph c n nt giao thng v m ng hai chiu ni trc tip cc cp nt giao thng
, gia hai nt giao thng bt k c khng qu mt ng i trc tip.
Mt nt giao thng c c gi l trng im nu tn ti hai nt giao thng a v b (a, b, c i mt khc nhau) sao cho:
Gia a v b c t nht mt ng i theo cc ng ph cho
Nu nt c b tc th khng c cch no i t a sang b. Hay ni cch khc, mi ng i t a ti b chc chn phi qua c.
Cho bitt s t giao thng ca thanh ph, hy xac tjnh cac nt giao thng trng titn.D liu: Vo t file vn bn CNODE.INP
Dng 1: Ghi hai s nguyn dng n, m (n 1000; m 10000)
m dng tip theo, mi dng ghi hai s nguyn dng u v, cho ta thng tin: Gia hai nt giao thng u v v c mt ng i trc tip.
Kt qu: Ghi ra file vn bn CNODE.OUT
Dng 1: Ghi s nt giao thng trng im
Dng 2: Ghi ch s ca cc nt giao thng trng im, cc ch s ny phi lit k i mt khc nhau.
Cac s trn nt dng ca Input/Output File twic ghi cach nhau It nhit nt diu cachV d:1 23 4 56 712118 139 10075. TP KTMt bn c kch thc nxn (2 n 100) trong nh du mt s cm. Trn bn c c k qun m ang ng nhng v tr no (1 k 100). Cn i nhng qun m ny n k v tr tp kt (mi qun m mt v tr). Trong qu trnh di chuyn, m khng c nhy n cc cm nhng c th nhy n c nhng qun m khc ang ng. Vai tr ca cc qun m v cc v tr tp kt l nh nhau (mt qun m c th cho i ti bt k v tr tp kt no nu c ng nhy). trng thi ban u k v tr xut pht v k v tr tp kt c cho hon ton phn bit
Yu cu: Lp chwng trlnh xac tjnh cach ti cac qun n sao cho tng s bwthc ti ca cac qun n la nh nhit.CCS
SD
C
SC
CCSDD
CD
D liu: Vo t file vn bn HORSES.INP
Dng 1: Ghi s n (n 100
n dng tip theo, dng i, ghi n k t th hin hng i ca bn c. K t th i l:
".": Th hin trng
"C": Th hin cm "S": Th hin c m ang ng
"D": Th hin v tr tp kt
Kt qu: Ghi ra file vn bn HORSES.OUT
Dng 1: Ghi s m l tng bc di chuyn a cc qun m v v tr tp kt. Nu khng c cch tp kt th ghi s -1.
m dng tip theo, dng th i ghi 4 s x1 y1 x2 y2 cch nhau t nht mt du cch, cho bit ti bc th i s di chuyn mt qun m t (x1, y1) n (x2, y2)
V d:
HORSES.INPHORSES.OUT6C.C..S...SD...C.....SC..CC.SDD C....D
75 4 4 64 6 2 54 3 5 51 6 3 53 5 5 62 4 4 54 5 6 6076. MI KHCH D TICCng ty trch nhim hu hn "Vui v" c n cn b nh s t 1 ti n. Cn b th i c nh gi
vui tnh l hi. Ngoi tr gim c cng ty, mi ngi u c mt th trng trc tip ca mnh.
Bnn cn gip cng ty ni nt nhn can b ttn d dn tic "Nhng ngwi thIch tua" sao cho tng tanh gia t vui tInh ca nhng ngwi d tic la lthn nhit, vthi yu cu: trong s nhng ngwi twic ni khng tng thi c nt nhn vin cung th trwng trc titp ca ngwi t.D liu: Vo t file vn bn GUEST.INP
Dng u tin ghi s cn b cng ty: n (2 n 10000)
n dng tip theo, dng th i gm hai s t nhin bi, hi cho ta thng tin, ngi th i c th trng trc tip l bi v vui tnh l hi. Nu nh bi = 0 th ta hiu i l gim c cng ty.
Kt qu: Ghi ra file vn bn GUEST.OUT
Dng 1: Ghi s ngi c mi (k) v tng vui tnh ca nhng ngi (m)
k dng tip, mi dng ghi s hiu mt ngi c mi ti d tic. Cac s trn nt dng ca Input/Output File twic ghi cach nhau It nhit nt diu cach D liu vao twic cho tng tn: khng tn tni nt dy x1, x2, ..., xp, xp+1 = x1 na ngwi i la th trwng trc titp ca ngwi i + 1 (i: 1 i p) . Khng nhit thitt phi ni gian tc cng tyV d:GUEST.INPGUEST.OUT102 93 74 80 104 25 116 66 44 69 6
4 3614610077. KHI PHC NGOCMt dy du ngoc hp l l mt dy cc k t "(" v ")" c nh ngha nh sau:
i.Dy rng (khng c k t no) l mt dy du ngoc hp l
ii.Nu A l mt dy du ngoc hp l th (A) l dy du ngoc hp l. Du ngoc m v du ngoc ng hai bn dy A c gi l tng ng vi nhau
iii.Nu A v B l hai dy du ngoc hp l th AB l dy du ngoc hp l.
V d: ((()))(())()() l mt dy du ngoc hp l. cc du m ngoc cc v tr: 1, 2, 3, 7, 8, 11, 13 tng ng ln lt vi cc du ng ngoc cc v tr: 6, 5, 4, 10, 9, 12, 14.
Ban u c mt dy du ngoc hp l, ngi ta vit vo di mi du ngoc m mt s l s du ngoc (c ng v m) nm gia du ngoc m v du ngoc ng tng ng:
((()))(())()()
4202000
Sau xo i dy ngoc.
Yu cu: Cho bitt dy s cn lni, hy khi phc lni dy ngoc ban tuD liu: Vo t file vn bn BRACKETS.INP
Dng 1: Ghi s n l s phn t ca dy s cn li (n 10000)
Dng 2: Ghi ln lt cc s trong dy
Kt qu: Ghi ra file vn bn BRACKETS.OUT Gm 1 dng ghi dy du ngoc khi phc c
V d:BRACKETS.INPBRACKETS.OUT
74 2 0 2 0 0 0((()))(())()()
078. DY XCHMt dy xch l mt cy c tnh cht: Tn ti mt ng i sao cho mi nh treo phi k vi ng mt nh trn ng i . Vi mi dy xch, ng i ny khng nht thit phi duy nht.
8567
1234
91011
1213
Cho nt dy xIch vthi cac nt twic tanh s 1..n (2 n 10000). Hy tln cach gan cho ni tnh i nt nhn Lab(i); 1 Lab(i) n sao cho cac tiu kin sau twic tho nn: Hai tnh khac nhau c hai nhn khac nhau Khng c hai cnnh nao c cung gia trj tuyt ti ca hiu cac nt hai tu nt11658
72101
439
1213
D liu: Vo t file vn bn CHAIN.INP
Dng 1: ghi s n
n - 1 dng tip theo, mi dng ghi hai u mt ca mt cnh thuc xch
Kt qu: Ghi ra file vn bn CHAIN.OUT (Nu c nhiu li gii th ch cn chn mt)
Mt dng n s, s th i l Lab(i)V d:
CHAIN.INPCHAIN.OUT7 2 10 1 6 5 8 11 4 3 9 12 13079. PHN CNGC n th v n vic (n 200), cc th c nh s t 1 ti n v cc vic cng c nh s t 1 ti n. Vi th i v vic j no th c hai kh nng: Hoc th i khng lm c vic j, hoc lm c vi chi ph l cij. (cij l s t nhin 109).
Hy phn cng cho ni thi lan tng nt vic sao cho c tht thc hin tit c cac cng vic vthi tng chi phI It nhit c tht.D liu: Vo t file vn bn ASSIGN.INP
Dng 1: Ghi s n
Cc dng tip, mi dng ghi ba s i j cij cho ta thng tin: Th i lm c vic j vi chi ph cij.
Kt qu: Ghi ra file vn bn ASSIGN.OUT
Dng 1: Ghi tng chi ph thc hin cc cng vic, nu khng tn ti cch phn cng th dng ny ghi s -1.
Nu c phng n phn cng, n dng tip theo, dng th i ghi s hiu vic c phn cho th i.Cac s trn nt dng ca Input File twic ghi cach nhau It nhit nt diu cachV d:ASSIGN.INPASSIGN.OUT
41 1 1
1 2 22 1 22 2 52 3 1
3 2 1
3 3 104 3 104 4 7101324
080. DY CUNGTrn mt phng vi h trc to Decattes vung gc, cho ng trn c tm O l gc to , bn knh R. Trn ng trn O xt n im xanh v n im u c honh nguyn, tung khc 0. Cc im c nh s th t t 1 n 2n v nm cc v tr hon ton phn bit.
Theo gi thit trn, thng tin v im th i c th cho bi b ba (Ci, Xi, Di) vi:
K t Ci {R, B}; Ci = R c ngha l im , Ci = B c ngha l im xanh S nguyn Xi l honh im . S nguyn Di {-1, 1}; Di = -1 tc l tung m (nm di trc honh), Di = 1 tc