PRE ACM PTIT 2015 ROUND 1
Problem A: Cc cp giai tha
Time limit: 1s
Axe chi mt tr chi vi Lina.
H nh ngha hm F(x) vi s x nguyn dng l tch giai tha cc ch s ca x. V d
F(135) = 1! * 3! * 5! = 720.
u tin, h chn mt s a c n ch s v c t nht mt ch s ln hn 1, c th c ch s
khng u. Sau h tm mt s nguyn dng x ln nht tha mn:
1. X khng cha ch s 0 hoc 1
2. F(x) = F(a)
Hy gip Axe v Lina tm ra c s .
Input:
Dng u tin cha s b test T ( T < 100 ).
Mi test gm mt dng cha s n v s a (1
PRE ACM PTIT 2015 ROUND 1
Problem B: Rubik i siu th
Time limit: 1s
Rubik i siu th mua n mn v vo trong xe y ri mang ra quy thanh ton. Bit mt
hng th i c gi l C_i v ngi thu ngn cn thi gian T_i c th xc nhn mt hng ny.
Nhng Rubik l thnh n trm nn anh ta sp xp th t cc mt hng cho ngi thu ngn
xc nhn theo ca mnh, khi ngi thu ngn bn lm th tc l Rubik s c th n trm 1
mn t chnh xe ca mnh v mt 1 giy.
Bn hy tnh xem s tin ti thiu m Rubik phi tr l bao nhiu?
Input:
Dng u tin cha s mt hng n (1
PRE ACM PTIT 2015 ROUND 1
Problem C: Tr chi tr tu
Time limit: 5s
Tide v Kunkka thch thc nhau v mt tr chi. H vit tt c cc s nguyn dng t 1 n
n. Ti lt ca mi ngi, ngi s chn mt s nguyn trong cc s h va vit ra, nu
chn s x th cc s l ly tha (nguyn dng) ca x s khng c chn cho cc lt tip
theo.
Tt c u chi vi chin thut ti u, vy nu Tide chn trc th bn hy cho bit ai s l
ngi chin thng?
Ngi thua cuc l ngi m n lt ca mnh khng cn s no chn.
Input:
Dng u tin cha s b test T (1
PRE ACM PTIT 2015 ROUND 1
Problem D: Du hnh gia cc v sao
Time limit: 1s
Sau chuyn du hnh gia cc v sao nhm Cooper tm c hnh tinh Edmunds ph hp vi
s sng thin h Blabla, anh gi thng tin v cho con ngi Ngn H qua l su. V di
chuyn sang thin h Blabla tn kh nhiu ti nguyn nn cn tp hp tt c ngi dn trn
mt trm bt k.
C n trm ang trn qu o ca n hnh tinh hay thin th khc nhau ln cn trong h mt
tri, mi hnh tinh c d_i c dn ang sinh sng, v c n-1 khng gian 5 chiu di chuyn
trc tip gia hai trm v ch c mt cch duy nht di chuyn gia hai trm bt k. Mi
khng gian nh vy ni hai trm u v v, di chuyn 1 ngi t trm ny sang trm kia cn
mt lng ti nguyn l w.
May thay cc nh khoa hc nghin cu ra mt cch chuyn ng i trn qua mt khng
gian nhiu chiu hn, vi cch vic di chuyn gia hai trm gn nh khng tn ti
nguyn, nhng c mt rc ri l s nhiu trong khng gian trn nn ch c th chuyn ti a k
khng gian c sang khng gian mi.
Cc nh lnh o ang tm mt cch di chuyn sao cho tn t ti nguyn nht, bn hy gip
h.
Input
Dng u tin cha s b test, mi b test cu trc nh sau:
Dng u tin cha hai s nguyn n v k (1 n 1000, 0 k n 1).
Dng th hai cha n s t nhin, di l s dn ang sng trn trm th i (1 d_i
100000).
n-1 dng cn li, dng th i cha ba s nguyn dng ui, vi v wi (1 u_i, v_i n, 1
w_i 100000).
Output
In ra kt qu mi test trn mt dng.
Example
Input: Output:
1
5 3
8 5 1 8 7
1 3 8
2 3 9
3 5 7
3 4 8
45
PRE ACM PTIT 2015 ROUND 1
Problem E: Sn xut kem
Time limit: 1s
Nh my Blabla ang sn xut kem Bla. Kem c bm vo mt khay hnh ch nht kch
thc m x n nh ri a vo my lnh. My phun kem l mt cnh tay c hai u phun kem
t trn hai khc nhau. V hai u phun trn cng tay r bt nn cc bc di chuyn ca
chng ng b ha vi nhau, nu my th nht di chuyn theo mt vec t, th tay th hai
cng c di chuyn theo vect y. Ban u cc trn khay khng cha kem.
Tay r bt di chuyn theo quy lut sau:
C 2 my phun u t trn 2 khc nhau v u hot ng.
My phun di chuyn qua no th y c phun kem.
Tay r bt di chuyn song song vi cc cnh ca khay.
Cc my phun khng c di chuyn ra bn ngoi khay.
Blab l nhn vin k thut ca nh my Blabla, anh c giao nhim v vit chng trnh
tnh s khng c phun kem, cc bn hy gip anh y.
Input
Dng u tin cha s b test T (khng qu 150 test), T dng sau mi dng cha 1 b test
cha 6 s nguyn dng ln lt m, n, x1, y1, x2, y2.
Trong m, n ln lt l s ct v s hng ca khay, (x1, y1) l ta ca my phun th
nht (x1, y1 l v tr ct, hng), (x2, y2) l ta ca my phun th hai (x2, y2 l v tr ct,
hng). Cc ct c nh du t tri sang phi, cc hng c nh du t trn xung di.
Gii hn: 2 n, m 10^9, 1 x1, x2 m, 1 y1, y2 n.
Output
Vi mi b test in ra kt qu trn 1 dng.
Example
Input: Output:
2
4 4 1 1 3 3
4 3 1 1 2 2
8
2
PRE ACM PTIT 2015 ROUND 1
Problem F: Cipher
Time limit: 1s
0xb0b0 team l 1 i ca PTIT ang tham gia cuc thi CTF(Capture The Flag). tm
c Flag ca mt cu hi, bn phi tri qua rt nhiu th thch. i ang tin hnh gii
quyt 1 bi Cipher. Sau 1 hi thi c rt quyt lit, 0xb0b0 team i n kt lun:
Secret key (kha b mt) c th ly c bng cch ct kha Public key (cng khai)
thnh 2 phn. Kha cng khai l 1 s t nhin rt ln, c th c ti 1 triu ch s.
0xb0b0 team mun tm mt cch sao cho c th ct publickey thnh 2 s nguyn dng
x v y sao cho x chia ht cho a v y chia ht cho b (vi a v b l 2 s cho trc). C x v y
u khng c c ch s 0 u.
Hy gip 0xb0b0 team tm cch ct public key.
Input
Dng th nht cha public key 1 s nguyn dng (khng cha ch s 0 u) c
di t 1 n 10^6 ch s.
Dng tip theo bao gm 2 s nguyn dng cch nhau bi 1 du cch a, b
(1a,b10^8).
Output
Dng u tin in "YES" nu c cch ct c public key. Trong trng hp ny, in 2 dng
tip theo l 2 s x, y sao cho x b nht c th.
Trng hp cn li, tc l khng tn ti cch ct, in "NO" v khng in g thm.
Example
Test 1 Test 2 Test 3
Input:
116401024
97 1024
Output:
YES
11640
1024
Input:
284254589153928171911281811000
1009 1000
Output:
YES
2842545891539
28171911281811000
Input:
120
12 1
Output:
NO
PRE ACM PTIT 2015 ROUND 1
Problem G: Xp hng
Time limit: 1s
Trong gi n tra ti Hc vin Cng ngh Bu chnh Vin thng, c n sinh vin ang xp
hang ly .
Cm thy chn v phi ng i mt mnh, v vy mi sinh vin vit ra m sinh vin ca
mnh ng ngay trc v ngay sau ca mnh. Nu khng c ai ng trc hoc khng c
ai ng sau th vit ra 0.
t nhin, xe ch nc si i qua, tt c sinh vin phi trnh. Khi h tr li, h khng
nh v tr ca mnh m ch nh m sinh vin ca ngi n trc v ngi ng sau.
Hy gip cc sinh vin PTIT tm li v tr ca mnh!!!!
Input
Dng u tin gm s t nhin n (2n210^5) s lng sinh vin.
n dng tip theo, dng th i gm cp s t nhin ai, bi (0ai,bi10^6), vi ai l m sinh
vin ca ngi ng trc, bi l m sinh vin ca ngi ng sau 1 sinh vin no .
Nu khng c ai ng trc hoc khng c ai ng sau nhp 0.
M sinh vin ca mi sinh vin l khc nhau.
Output
Trn 1 dng, in ra n s x1,x2,...,xn, danh sch ca cc sinh vin theo th t ban u.
Example
Input: Output: 4
92 31
0 7
31 0
7 141
92 7 31 141
Gii thch test bi:
PRE ACM PTIT 2015 ROUND 1
Problem H: S ma thut
Time limit: 1s
Mt s ma thut l s m c ghp bi cc s 1, 14, 144. S ma thut khng nht thit
phi c ghp bi c 3 s trn. Cc bn gip kim tra gip xem mt s c l s ma
thut khng nh!
Input
Mt dng duy nht cha s n (1
PRE ACM PTIT 2015 ROUND 1
Problem I: Ch s cui cng
Time limit: 1s
Thy T rt thch th vi nhng con s, c gio giao cho T mt bi tp v rt gn cc
con s. Php rt gn c thc hin nh sau: t mt s ban u, s mi c to thnh
bng cch cng cc ch s ca s ban u vi nhau. Sau T phi thc hin tip tc vi
con s va mi thu c.
Qu trnh rt gn kt thc khi s thu c ch c duy nht 1 ch s.
Cc bn hy cng T i tm ch s cui cng ca php rt gn!
Input
Dng u tin gm s lng test T (T
PRE ACM PTIT 2015 ROUND 1
Problem J: m s ng i
Cho mt ma trn N x M, trong c K b chn khng c php i qua. Bn ch c php
i sang phi hoc i xung di.
Nhim v ca bn l tm cc ng i t (1, 1) ti (N, M).
Input:
Dng u tin gm s test T (T