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2018年浙江省大学生程序设计竞赛试题

2018年浙江省大学生程序设计竞赛试题
2018年浙江省大学生程序设计竞赛试题

The 15th Zhejiang Provincial Collegiate Programming Contest

Sponsored by

Contest Section

April 29, 2018

Problem List

This problem set should contain 13 (thirteen) problems on 17 (seventeen) numbered pages. Please inform a runner immediately if something is missing from your problem set.

Prepared by Zhejiang University ACM/ICPC Problem Setter Team.

Problem A.Peak

Description

A sequence of n integers a1,a2,...,a n is called a peak,if and only if there exists exactly one integer k such that1a i for all k

Given an integer sequence,please tell us if it’s a peak or not.

Input

There are multiple test cases.The?rst line of the input contains an integer T,indicating the number of test cases.For each test case:

The?rst line contains an integer n(3≤n≤105),indicating the length of the sequence.

The second line contains n integers a1,a2,...,a n(1≤a i≤2×109),indicating the integer sequence. It’s guaranteed that the sum of n in all test cases won’t exceed106.

Output

For each test case output one line.If the given integer sequence is a peak,output“Yes”(without quotes), otherwise output“No”(without quotes).

Example

standard input standard output

7

5

15732 5

12121 4

1234 4

4321 3

121

3

212

5

12312Yes No No No Yes No No

Problem B.King of Karaoke

Description

It’s Karaoke time!DreamGrid is performing the song Powder Snow in the game King of Karaoke.The song performed by DreamGrid can be considered as an integer sequence D1,D2,...,D n,and the standard version of the song can be considered as another integer sequence S1,S2,...,S n.The score is the number of integers i satisfying1≤i≤n and S i=D i.

As a good tuner,DreamGrid can choose an integer K(can be positive,0,or negative)as his tune and add K to every element in D.Can you help him maximize his score by choosing a proper tune? Input

There are multiple test cases.The?rst line of the input contains an integer T(about100),indicating the number of test cases.For each test case:

The?rst line contains one integer n(1≤n≤105),indicating the length of the sequences D and S. The second line contains n integers D1,D2,...,D n(?105≤D i≤105),indicating the song performed by

DreamGrid.

The third line contains n integers S1,S2,...,S n(?105≤S i≤105),indicating the standard version of the song.

It’s guaranteed that at most5test cases have n>100.

Output

For each test case output one line containing one integer,indicating the maximum possible score. Example

standard input standard output

2

4

1234

2346

5

-5-4-3-2-1 543213 1

Note

For the?rst sample test case,DreamGrid can choose K=1and changes D to{2,3,4,5}.

For the second sample test case,no matter which K DreamGrid chooses,he can only get at most1match.

Problem C.Magic12Months

Description

It’s New Year’s Eve,and it’s also the best time of the year to play the card game Magic12Months to pray for good luck of the coming year.BaoBao has just found a deck of standard52playing cards(without Jokers)in his pocket and decides to play the game.The rules are as follows:

1.Setup

1.1.Remove the four‘K’s from the52cards.

1.2.Shu?e the remaining48cards and divide them face down into12piles(4cards per pile)with

equal probability.

2.Gameplay

2.1.Let p=1.

2.2.Flip the card on the top of the p-th pile,check its rank r,and discard the card.

2.3.If r is a number,let p=r;If r=‘A’,let p=1;If r=‘J’,let p=11;If r=‘Q’,let p=12.

2.4.If the p-th pile is empty,the game ends;Otherwise go back to step2.2.

When the game ends,having all the4cards of rank m?ipped and discarded indicates that the m-th month in the coming year is a lucky month.

BaoBao is in the middle of the game and has discarded n cards.He wants to know the probability that the i-th month of the coming year is a lucky month for all1≤i≤12when the game ends.Given these n cards,please help him calculate the answer.

Input

There are multiple test cases.The?rst line of input contains an integer T(about100)–the number of test cases.For each test case:

The?rst and only line contains an integer n(0≤n≤48)–the number of?ipped cards,followed by the rank of the n cards r1,r2,...,r n(r i∈{A,2,3,4,5,6,7,8,9,10,J,Q})separated by a space in the order they are?ipped.It’s guaranteed that the input describes a valid and possible situation of the game.

Output

For each test case output one line containing12numbers separated by a space,where the i-th number indicates the probability that the i-th month of the coming year is a lucky month.

You should output a probability in its simplest fraction form A/B where A and B are coprime.Speci?cally, if the probability equals0,you should output0;If the probability equals1,you should output1. Please,DO NOT output extra spaces at the end of each line,or your answer may be considered incorrect! Example

standard input

3

309Q10J Q10J10J J85765767663A24A24244

72A3A4A A

standard output

12/32/511/212/32/52/52/311/2

11/21/21/21/21/21/21/21/21/21/21/2

100000000000

Problem D.Sequence Swapping

Description

BaoBao has just found a strange sequence{,,...,}of length n in his pocket. As you can see,each elementin the sequence is an ordered pair,where the?rst element s i in the pair is the left parenthesis‘(’or the right parenthesis‘)’,and the second element v i in the pair is an integer.

As BaoBao is bored,he decides to play with the sequence.At the beginning,BaoBao’s score is set to 0.Each time BaoBao can select an integer k,swap the k-th element and the(k+1)-th element in the sequence,and increase his score by(v k×v k+1),if and only if1≤k

Input

There are multiple test cases.The?rst line of the input contains an integer T,indicating the number of test cases.For each test case:

The?rst line contains an integer n(1≤n≤103),indicating the length of the sequence.

The second line contains a string s(|s|=n)consisting of‘(’and‘)’.The i-th character in the string indicates s i,of which the meaning is described above.

The third line contains n integers v1,v2,...,v n(?103≤v i≤103).Their meanings are described above. It’s guaranteed that the sum of n of all test cases will not exceed104.

Output

For each test case output one line containing one integer,indicating the maximum possible score BaoBao can get.

Example

standard input standard output

4

6

)())()

135-132 6

)())()

135-10032 3

())

1-1-1

3

())

-1-1-124 21 0 2

Note

For the?rst sample test case,the optimal strategy is to select k=2,3,5,4in order. For the second sample test case,the optimal strategy is to select k=2,5in order.

Problem E.LIS

Description

DreamGrid is learning the LIS(Longest Increasing Subsequence)problem and he needs to?nd the longest increasing subsequence of a given sequence a1,a2,...,a n of length n.

Recall that

?A subsequence b1,b2,...,b m of length m is a sequence satisfying b1=a k

1,b2=a k

2

,...,b m=a k

m

and1≤k1

?An increasing subsequence b1,b2,...,b m is a subsequence satisfying b1

procedure lis_helper(a:original sequence)

{Let n be the length of the original sequence,

f(i)be the i-th element in sequence f,and a(i)

be the i-th element in sequence a}

for i:=1to n

f(i):=1

for j:=1to(i–1)

if a(j)f(i)

f(i):=f(j)+1

return f{f is the helper sequence}

DreamGrid has derived the helper sequence using the program,but the original sequence a1,a2,...,a n is stolen by BaoBao and is lost!All DreamGrid has in hand now is the helper sequence and two range sequences l1,l2,...,l n and r1,r2,...,r n indicating that l i≤a i≤r i for all1≤i≤n.

Please help DreamGrid restore the original sequence which is compatible with the helper sequence and the two range sequences.

Input

There are multiple test cases.The?rst line of the input contains an integer T,indicating the number of test cases.For each test case:

The?rst line contains an integer n(1≤n≤105),indicating the length of the original sequence.

The second line contains n integers f1,f2,...,f n(1≤f i≤n)seperated by a space,indicating the helper sequence.

For the following n lines,the i-th line contains two integers l i and r i(0≤l i≤r i≤2×109),indicating the range sequences.

It’s guaranteed that the original sequence exists,and the sum of n of all test cases will not exceed5×105. Output

For each test case output one line containing n integers separated by a space,indicating the original sequence.If there are multiple valid answers,print any of them.

Please,DO NOT print extra spaces at the end of each line,or your solution may be considered incorrect!

Example

standard input standard output

4

6

123243 05

24

33

12

35

15

5

12131 100200 200300 200400 400500 100500

7

1231142 03

03

03

03

03

03

03

2

11

12

23123253 200300200500200 0120031

22

Problem F.Now Loading!!!

Description

DreamGrid has n integers a1,a2,...,a n.DreamGrid also has m queries,and each time he would like to

know the value of∑

1≤i≤n ?a

i

?log p a i?

?

for a given number p,where?x?=max{y∈Z|y≤x},?x?=min{y∈Z|y≥x}.

Input

There are multiple test cases.The?rst line of input is an integer T indicating the number of test cases. For each test case:

The?rst line contains two integers n and m(1≤n,m≤5×105)–the number of integers and the number of queries.

The second line contains n integers a1,a2,...,a n(2≤a i≤109).

The third line contains m integers p1,p2,...,p m(2≤p i≤109).

It is guaranteed that neither the sum of all n nor the sum of all m exceeds2×106.

Output

For each test case,output an integer(m ∑

i=1

i·z i)mod109,where z i is the answer for the i-th query. Example

standard input standard output

2

32 100100010000 10010

45 2323223123123 123232423511366 45619

Problem G.JUMPin’JUMP UP!!!

Description

Tired of solving mathematical equations,DreamGrid starts to solve equations related to strings:for two strings x and y with the same length consisting of lowercase English letters,calculate f(x,y,n),which is de?ned as the number of nonempty strings z consisting of lowercase English letters such that xz=zy and the length of z does not exceed n.

DreamGrid has two strings s=s1s2...s n and t=t1t2...t m.He would like to ask several questions about the value of f(t,s[x..(x+m?1)],y),where s[x..(x+m?1)]is the substring of s starting from s x with length m and y is a given number.

Input

There are multiple test cases.The?rst line of input contains an integer T,indicating the number of test cases.For each test case:

The?rst line contains three integers n and m and q(1≤n,m,q≤105,m≤n)–the length of s,the length of t and the number of questions.

The second line contains n lowercase English letters denoting the string s.The third line contains m lowercase English letters denoting the string t.

Each of the next q lines contains two integers x i and y i(1≤x i≤n+1?m,1≤y i≤1018)denoting the i-th question.

It is guaranteed that neither the sum of all n nor the sum of all q exceeds106.

Output

For each question,output an integer denoting the answer.

Example

standard input standard output

1 423 abcd ba

12 22 321 0 0

Problem H.Game on a Tree

Description

BaoBao is playing a game on a rooted tree with n vertices and(n?1)weighted edges.At the beginning of the game,a chess piece is placed on the root of the tree,which is vertex1.

In each step,BaoBao can perform one of the four operations:

1.Move the chess piece along an edge from its current vertex to a child vertex.This operation will

cost BaoBao w units of value,where w is the weight of the edge.

2.Jump the chess piece back to vertex1.This operation is free and won’t cost BaoBao any unit of

value.

3.Set a“save point”on the current vertex of the chess piece.If a save point has been set on some

other vertex before,the save point on the old vertex will be removed(so there will be at most one save point on the tree at the same time).This operation is free and won’t cost BaoBao any unit of value.

4.Jump the chess piece back to the save point(the save point must be set before this operation).This

operation is free and won’t cost BaoBao any unit of value.

The goal of the game is to visit every leaf vertex of the tree using the chess piece.Please help BaoBao calculate the minimum units of value he has to spend to achieve the goal.

Recall that a leaf vertex of a tree is a vertex with no child.

Input

There are multiple test cases.The?rst line of the input contains an integer T,indicating the number of test cases.For each test case:

The?rst line contains one integer n(2≤n≤200),indicating the size of the tree.

The following(n?1)lines each contains three integers u i,v i and w i(1≤u i,v i≤n,1≤w i≤109), indicating an edge connecting vertex u i and vertex v i with weight w i in the tree.

It’s guaranteed that the given graph is a tree,and the sum of n over all test cases will not exceed2000. Output

For each test case output one line containing one integer,indicating the minimum units of value BaoBao has to spend to achieve the goal.

Example

standard

input

standard output

3812131124254262237383381212313413512616716818121002313413512616716

8

1

148107

Note

The trees of the sample test cases are shown above.

For the ?rst sample test case,BaoBao should perform the following operations:go to 2,save on 2,go to 4,go to 5,back to save (2),go to 6,back to root (1),go to 3,save on 3,go to 7,back to save (3),go to 8.For the second sample test case,BaoBao should perform the following operations:go to 2,go to 3,save on 3,go to 4,back to save (3),go to 5,back to root (1),go to 2,go to 6,save on 6,go to 7,back to save (7),go to 8.

For the third sample test case,BaoBao should perform the following operations:go to 2,save on 2,go to 3,go to 4,back to save (2),go to 3,go to 5,back to save (2),go to 6,save on 6,go to 7,back to save (6),go to 8.

Problem I.Magic Points

Description

Given an integer n ,we say a point (x,y )on a 2D plane is a magic point,if and only if both x and y are integers,and exactly one of the following conditions is satis?ed:

?0≤x

It’s easy to discover that there are 4n ?4magic points in total.These magic points are numbered from 0to 4n ?5in counter-clockwise order starting from (0,0).

DreamGrid can create n magic lines from these magic points.Each magic line passes through exactly two magic points but cannot be parallel to the line x =0or y =0(that is to say,the coordinate axes).The intersections of the magic lines are called dream points,and for some reason,DreamGrid would like to make as many dream points as possible.Can you tell him how to create these magic lines?

Input

There are multiple test cases.The ?rst line of input contains an integer T (about 100),indicating the number of test cases.For each test case,there is only one integer n (2≤n ≤1000).

Output

For each case output 2n integers p 1,p 2,...,p 2n in one line separated by one space,indicating that in your answer,point p 2k ?1and point p 2k is connected by a line for all 1≤k ≤n .If there are multiple answers,you can print any of them.

Example

standard input

standard output

3234

0213

142536

061938410

Note

The sample test cases are shown as follow:

Problem J.CONTINUE...?

Description

DreamGrid has n classmates numbered from1to n.Some of them are boys and the others are girls.Each classmate has some gems,and more speci?cally,the i-th classmate has i gems.

DreamGrid would like to divide the classmates into four groups G1,G2,G3and G4such that:?Each classmate belongs to exactly one group.

?Both G1and G2consist only of girls.Both G3and G4consist only of boys.

?The total number of gems in G1and G3is equal to the total number of gems in G2and G4.

Your task is to help DreamGrid group his classmates so that the above conditions are satis?ed.Note that you are allowed to leave some groups empty.

Input

There are multiple test cases.The?rst line of input is an integer T indicating the number of test cases. For each test case:

The?rst line contains an integer n(1≤n≤105)–the number of classmates.

The second line contains a string s(|s|=n)consisting of0and1.Let s i be the i-th character in the string s.If s i=1,the i-th classmate is a boy;If s i=0,the i-th classmate is a girl.

It is guaranteed that the sum of all n does not exceed106.

Output

For each test case,output a string consists only of{1,2,3,4}.The i-th character in the string denotes the group which the i-th classmate belongs to.If there are multiple valid answers,you can print any of them;If there is no valid answer,output“-1”(without quotes)instead.

Example

standard input standard output

5

1

1

2

10

3

101

4

0000

7 1101001-1

-1

314 1221 3413214

Problem K.Mahjong Sorting

Description

DreamGrid has just found a set of Mahjong with3M suited tiles and a White Dragon tile in his pocket. Each suited tile has a suit(Character,Bamboo or Dot)and a rank(ranging from1to M),and there is exactly one tile of each rank and suit combination.

Character tiles whose rank ranges from1to9

Bamboo tiles whose rank ranges from1to9

Dot tiles whose rank ranges from1to9

White Dragon tile

As DreamGrid is bored,he decides to play with these tiles.He?rst selects one of the3M suited tiles as the“lucky tile”,then he picks N tiles from the set of(3M+1)tiles and sorts these N tiles with the following rules:

?The“lucky tile”,if contained in the N tiles,must be placed in the leftmost position.

?For two tiles A and B such that neither of them is the“lucky tile”,if

–A is a Character tile and B is a Bamboo tile,or

–A is a Character tile and B is a Dot tile,or

–A is a Bamboo tile and B is a Dot tile,or

–A and B have the same suit and the rank of A is smaller than the rank of B, then A must be placed to the left of B.

White Dragon tile is a special tile.If it’s contained in the N tiles,it’s considered as the original(not-lucky)version of the lucky tile during the sorting.For example,consider the following sorted tiles,where “3Character”is selected as the lucky tile.White Dragon tile,in this case,is considered to be the original not-lucky version of“3Character”and should be placed between“2Character”and“4Character”.

As DreamGrid is quite forgetful,he immediately forgets what the lucky tile is after the sorting!Given N sorted tiles,please tell DreamGrid the number of possible lucky tiles.

Input

There are multiple test cases.The?rst line of the input contains an integer T,indicating the number of test cases.For each test case:

The?rst line contains two integers N and M(1≤N,M≤105,N≤3M+1),indicating the number of sorted tiles and the maximum rank of suited tiles.

For the next N lines,the i-th line describes the i-th sorted tile counting from left to right.The line begins with a capital letter s i(s i∈{C,B,D,W}),indicating the suit of the i-th tile:

?If s i=C,then an integer r i(1≤r i≤M)follows,indicating that it’s a Character tile with rank r i;

?If s i=B,then an integer r i(1≤r i≤M)follows,indicating that it’s a Bamboo tile with rank r i;

?If s i=D,then an integer r i(1≤r i≤M)follows,indicating that it’s a Dot tile with rank r i;

?If s i=W,then it’s a White Drangon tile.

It’s guaranteed that there exists at least one possible lucky tile,and the sum of N in all test cases doesn’t exceed106.

Output

For each test case output one line containing one integer,indicating the number of possible lucky tiles. Example

standard input standard output

4

39 C2 W

C4 69 C2 C7 W

B3 B4 D2 3100 C2 W

C9 39 C1 B2 D32 4 7 25

Note

For the?rst sample,“2Character”and“3Character”are possible lucky tiles.

For the second sample,“8Character”,“9Character”,“1Bamboo”and“2Bamboo”are possible lucky tiles.

Problem L.Doki Doki Literature Club

Description

Doki Doki Literature Club!is a visual novel developed by Team Salvato.The protagonist is invited by his childhood friend,Sayori,to join their high school’s literature club.The protagonist then meets the other members of the club:Natsuki,Yuri,and the club president Monika.The protagonist starts to participate in the club’s activities such as writing and sharing poetry,and grows close to the four girls.What a lovely story!

A very important feature of the game is its poetry writing mechanism.The player is given a list of various words to select from that will make up his poem.Each girl in the Literature Club has di?erent word preferences,and will be very happy if the player’s poem is full of her favorite words.

The poem writing mini-game(from wikipedia)

BaoBao is a big fan of the game and likes Sayori the most,so he decides to write a poem to please Sayori.

A poem of m words s1,s2,...,s m is nothing more than a sequence of m strings,and the happiness of Sayori after reading the poem is calculated by the formula

H=

m

i=1

(m?i+1)·f(s i)

where H is the happiness and f(s i)is Sayori’s preference to the word s i.

Given a list of n words and Sayori’s preference to each word,please help BaoBao select m words from the list and?nish the poem with these m words to maximize the happiness of Sayori.

Please note that each word can be used at most once!

Input

There are multiple test cases.The?rst line of input contains an integer T(about100),indicating the number of test cases.For each test case:

The?rst line contains two integers n and m(1≤m≤n≤100),indicating the number of words and the length of the poem.

For the following n lines,the i-th line contains a string consisting of lowercased English letters w i (1≤|w i|≤15)and an integer f(w i)(?109≤f(w i)≤109),indicating the i-th word and Sayori’s preference to this word.It’s guaranteed that w i=w j for all i=j.

Output

For each test case output one line containing an integer H and m strings s1,s2,...,s m separated by one space,indicating the maximum possible happiness and the corresponding poem.If there are multiple poems which can achieve the maximum happiness,print the lexicographically smallest one.

Please,DO NOT output extra spaces at the end of each line,or your answer may be considered incorrect!

A sequence of m strings a1,a2,...,a m is lexicographically smaller than another sequence of m strings b1,b2,...,b m,if there exists a k(1≤k≤m)such that a i=b i for all1≤i

A string s1=a1a2...a x is lexicographically smaller than another string s2=b1b2...b y,if there exists a k(1≤k≤min(x,y))such that a i=b i for all1≤i

Example

standard input standard output

4

108

hello0

world0 behind0

far1

be2

spring10

can15

comes20 winter25

if200

55

collegiate0 programming-5 zhejiang10 provincial5 contest-45

32

bcda1

bcd1

bbbbb1

32

a1

aa1

aaa12018if winter comes can spring be far behind

15zhejiang provincial collegiate programming contest 3bbbbb bcd

3a aa

Problem M.Lucky7

Description

BaoBao has just found a positive integer sequence a1,a2,...,a n of length n from his left pocket and another positive integer b from his right pocket.As number7is BaoBao’s favorite number,he considers a positive integer x lucky if x is divisible by7.He now wants to select an integer a k from the sequence such that(a k+b)is lucky.Please tell him if it is possible.

Input

There are multiple test cases.The?rst line of the input is an integer T(about100),indicating the number of test cases.For each test case:

The?rst line contains two integers n and b(1≤n,b≤100),indicating the length of the sequence and the positive integer in BaoBao’s right pocket.

The second line contains n positive integers a1,a2,...,a n(1≤a i≤100),indicating the sequence. Output

For each test case output one line.If there exists an integer a k such that a k∈{a1,a2,...,a n}and(a k+b) is lucky,output“Yes”(without quotes),otherwise output“No”(without quotes).

Example

standard input standard output

4

37

456

37

476

52 25252 426 100124No Yes Yes Yes

Note

For the?rst sample test case,as4+7=11,5+7=12and6+7=13are all not divisible by7,the answer is“No”.

For the second sample test case,BaoBao can select a7from the sequence to get7+7=14.As14is divisible by7,the answer is“Yes”.

For the third sample test case,BaoBao can select a5from the sequence to get5+2=7.As7is divisible by7,the answer is“Yes”.

For the fourth sample test case,BaoBao can select a100from the sequence to get100+26=126.As 126is divisible by7,the answer is“Yes”.

2018年4月浙江省普通高中学业水平考试语文试卷

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