Find them, Catch them

The police office in Tadu City decides to say ends to the chaos, as launch actions to root up the TWO gangs in the city, Gang Dragon and Gang Snake. However, the police first needs to identify which gang a criminal belongs to. The present question is, given two criminals; do they belong to a same clan? You must give your judgment based on incomplete information. (Since the gangsters are always acting secretly.) Assume N (N <= 10^5) criminals are currently in Tadu City, numbered from 1 to N. And of course, at least one of them belongs to Gang Dragon, and the same for Gang Snake. You will be given M (M <= 10^5) messages in sequence, which are in the following two kinds:

1. D [a] [b]
where [a] and [b] are the numbers of two criminals, and they belong to different gangs.

2. A [a] [b]
where [a] and [b] are the numbers of two criminals. This requires you to decide whether a and b belong to a same gang.

Input

The first line of the input contains a single integer T (1 <= T <= 20), the number of test cases. Then T cases follow. Each test case begins with a line with two integers N and M, followed by M lines each containing one message as described above.

Output

For each message "A [a] [b]" in each case, your program should give the judgment based on the information got before. The answers might be one of "In the same gang.", "In different gangs." and "Not sure yet."

Sample Input

1

5 5

A 1 2

D 1 2

A 1 2

D 2 4

A 1 4

Sample Output

Not sure yet.

In different gangs.

In the same gang.

Source

POJ Monthly--2004.07.18

题目类型：带权并查集

算法分析：简化的带权并查集，rel数组中0表示两个人在同一个帮派中，1表示两个人不在同一个帮派中。注意推导出的求两个根节点关系的公式

Crossing River

A group of N people wishes to go across a river with only one boat, which can at most carry two persons. Therefore some sort of shuttle arrangement must be arranged in order to row the boat back and forth so that all people may cross. Each person has a different rowing speed; the speed of a couple is determined by the speed of the slower one. Your job is to determine a strategy that minimizes the time for these people to get across.

Input

The first line of the input contains a single integer T (1 <= T <= 20), the number of test cases. Then T cases follow. The first line of each case contains N, and the second line contains N integers giving the time for each people to cross the river. Each case is preceded by a blank line. There won't be more than 1000 people and nobody takes more than 100 seconds to cross.

Output

For each test case, print a line containing the total number of seconds required for all the N people to cross the river.

Sample Input

1

4

1 2 5 10

Sample Output

17

Source

POJ Monthly--2004.07.18

题目类型：贪心

算法分析：如果n比较小则会比较容易得到答案，如果n比较大则对于每一次递推都需要判断两种方案中哪一个更优，其中一种方案是最快的来回运送最慢的，另一种方案是最快的和次快的一起过河，然后最快的回来。然后最慢的和次慢的一起过河，次快的回来

The Unique MST

Given a connected undirected graph, tell if its minimum spanning tree is unique. 阅读全文 »

Crypto Columns

The columnar encryption scheme scrambles the letters in a message (or plaintext) using a keyword as illustrated in the following example: Suppose BATBOY is the keyword and our message is MEET ME BY THE OLD OAK TREE. Since the keyword has 6 letters, we write the message (ignoring spacing and punctuation) in a grid with 6 columns, padding with random extra letters as needed:

MEETME
BYTHEO
LDOAKT
REENTH
Here, we've padded the message with NTH. Now the message is printed out by columns, but the columns are printed in the order determined by the letters in the keyword. Since A is the letter of the keyword that comes first in the alphabet, column 2 is printed first. The next letter, B, occurs twice. In the case of a tie like this we print the columns leftmost first, so we print column 1, then column 4. This continues, printing the remaining columns in order 5, 3 and finally 6. So, the order the columns of the grid are printed would be 2, 1, 4, 5, 3, 6, in this case. This output is called the ciphertext, which in this example would be EYDEMBLRTHANMEKTETOEEOTH. Your job will be to recover the plaintext when given the keyword and the ciphertext.

Input

There will be multiple input sets. Each set will be 2 input lines. The first input line will hold the keyword, which will be no longer than 10 characters and will consist of all uppercase letters. The second line will be the ciphertext, which will be no longer than 100 characters and will consist of all uppercase letters. The keyword THEEND indicates end of input, in which case there will be no ciphertext to follow.

Output

For each input set, output one line that contains the plaintext (with any characters that were added for padding). This line should contain no spacing and should be all uppercase letters.

Sample Input

BATBOY

EYDEMBLRTHANMEKTETOEEOTH

HUMDING

EIAAHEBXOIFWEHRXONNAALRSUMNREDEXCTLFTVEXPEDARTAXNAA

RYIEX

THEEND

Sample Output

MEETMEBYTHEOLDOAKTREENTH

ONCEUPONATIMEINALANDFARFARAWAYTHERELIVEDTHREEBEARSX

XXXXX

Source

East Central North America 2003

题目类型：模拟

算法分析：对于按照字典序遍历的每一个大写字母，遍历关键字串的每一个字符，若找到相同的字符则将关键字串的相应大小的字符以列优先加入到二维数组maps的指定列中。依次类推，最后按照行优先输出maps中的每一个字符

Risk

Risk is a board game in which several opposing players attempt to conquer the world. The gameboard consists of a world map broken up into hypothetical countries. During a player's turn, armies stationed in one country are only allowed to attack only countries with which they share a common border. Upon conquest of that country, the armies may move into the newly conquered country. During the course of play, a player often engages in a sequence of conquests with the goal of transferring a large mass of armies from some starting country to a destination country. Typically, one chooses the intervening countries so as to minimize the total number of countries that need to be conquered. Given a description of the gameboard with 20 countries each with between 1 and 19 connections to other countries, your task is to write a function that takes a starting country and a destination country and computes the minimum number of countries that must be conquered to reach the destination. You do not need to output the sequence of countries, just the number of countries to be conquered including the destination. For example, if starting and destination countries are neighbors, then your program should return one.

The following connection diagram illustrates the first sample input.

Input

Input to your program will consist of a series of country configuration test sets. Each test set will consist of a board description on lines 1 through 19. The representation avoids listing every national boundary twice by only listing the fact that country I borders country J when I < J. Thus, the Ith line, where I is less than 20, contains an integer X indicating how many "higher-numbered" countries share borders with country I, then X distinct integers J greater than I and not exceeding 20, each describing a boundary between countries I and J. Line 20 of the test set contains a single integer (1 <= N <= 100) indicating the number of country pairs that follow. The next N lines each contain exactly two integers (1 <= A,B <= 20; A!=B) indicating the starting and ending countries for a possible conquest.

There can be multiple test sets in the input file; your program should continue reading and processing until reaching the end of file. There will be at least one path between any two given countries in every country configuration.

Output

For each input set, your program should print the following message "Test Set #T" where T is the number of the test set starting with 1. The next NT lines each will contain the result for the corresponding test in the test set - that is, the minimum number of countries to conquer. The test result line should contain the start country code A the string " to " the destination country code B ; the string ": " and a single integer indicating the minimum number of moves required to traverse from country A to country B in the test set. Following all result lines of each input set, your program should print a single blank line.

Sample Input

1 3

2 3 4

3 4 5 6

1 6

1 7

2 12 13

1 8

2 9 10

1 11

1 11

2 12 17

1 14

2 14 15

2 15 16

1 16

1 19

2 18 19

1 20

1 20

5

1 20

2 9

19 5

18 19

16 20

Sample Output

Test Set #1

1 to 20: 7

2 to 9: 5

19 to 5: 6

18 to 19: 2

16 to 20: 2

Source

South Central USA 1997

题目类型：全源最短路(Floyd)

算法分析：直接将读入的数据建成一个无向图，每个边的权值为1，然后调用一次Floyd算法计算全源最短路，然后对于每一个查询，直接输出edge数组中相应的值即可。本题中要求的征服城市的数量(包括目标城市)其实等于求路径中边的数量，也就是求边权为1的最短路，当然本题也可以使用BFS求解，只不过对于每一个查询都要调用一次BFS

Robot Motion

A robot has been programmed to follow the instructions in its path. Instructions for the next direction the robot is to move are laid down in a grid. The possible instructions are 阅读全文 »

Polynomial Showdown

Given the coefficients of a polynomial from degree 8 down to 0, you are to format the polynomial in a readable format with unnecessary characters removed. For instance, given the coefficients 0, 0, 0, 1, 22, -333, 0, 1, and -1, you should generate an output line which displays x^5 + 22x^4 - 333x^3 + x - 1.
The formatting rules which must be adhered to are as follows:

1. Terms must appear in decreasing order of degree.

2. Exponents should appear after a caret `"^".

3. The constant term appears as only the constant.

4. Only terms with nonzero coefficients should appear, unless all terms have zero coefficients in which case the constant term should appear.

5. The only spaces should be a single space on either side of the binary + and - operators.

6. If the leading term is positive then no sign should precede it; a negative leading term should be preceded by a minus sign, as in -7x^2 + 30x + 66.

7. Negated terms should appear as a subtracted unnegated term (with the exception of a negative leading term which should appear as described above). That is, rather than x^2 + -3x, the output should be x^2 - 3x.

8. The constants 1 and -1 should appear only as the constant term. That is, rather than -1x^3 + 1x^2 + 3x^1 - 1, the output should appear as-x^3 + x^2 + 3x - 1.

Input

The input will contain one or more lines of coefficients delimited by one or more spaces. There are nine coefficients per line, each coefficient being an integer with a magnitude of less than 1000.

Output

The output should contain the formatted polynomials, one per line.

Sample Input

0 0 0 1 22 -333 0 1 -1

0 0 0 0 0 0 -55 5 0

Sample Output

x^5 + 22x^4 - 333x^3 + x - 1

-55x^2 + 5x

Source

Mid-Central USA 1996

题目类型：模拟

算法分析：按照多项式加法的过程模拟即可

Basically Speaking

The Really Neato Calculator Company, Inc. has recently hired your team to help design their Super Neato Model I calculator. As a computer scientist you suggested to the company that it would be neato if this new calculator could convert among number bases. The company thought this was a stupendous idea and has asked your team to come up with the prototype program for doing base conversion. The project manager of the Super Neato Model I calculator has informed you that the calculator will have the following neato features:

• It will have a 7-digital display.
• Its buttons will include the capital letters A through F in addition to the digits 0 through 9.
• It will support bases 2 through 16.

Input

The input for your prototype program will consist of one base conversion per line. There will be three numbers per line. The first number will be the number in the base you are converting from. The second number is the base you are converting from. The third number is the base you are converting to. There will be one or more blanks surrounding (on either side of) the numbers. There are several lines of input and your program should continue to read until the end of file is reached.

Output

The output will only be the converted number as it would appear on the display of the calculator. The number should be right justified in the 7-digit display. If the number is to large to appear on the display, then print ERROR'' (without the quotes) right justified in the display.

Sample Input

1111000  2 10

1111000  2 16

2102101  3 10

2102101  3 15

12312  4  2

1A 15  2

1234567 10 16

ABCD 16 15

Sample Output

120

78

1765

7CA

ERROR

11001

12D687

D071

Source

Mid-Central USA 1995

题目类型：简单进制转换

算法分析：直接进行任意进制之间的转换即可

Perfection

From the article Number Theory in the 1994 Microsoft Encarta: If a, b, c are integers such that a = bc, a is called a multiple of b or of c, and b or c is called a divisor or factor of a. If c is not 1/-1, b is called a proper divisor of a. Even integers, which include 0, are multiples of 2, for example, -4, 0, 2, 10; an odd integer is an integer that is not even, for example, -5, 1, 3, 9. A perfect number is a positive integer that is equal to the sum of all its positive, proper divisors; for example, 6, which equals 1 + 2 + 3, and 28, which equals 1 + 2 + 4 + 7 + 14, are perfect numbers. A positive number that is not perfect is imperfect and is deficient or abundant according to whether the sum of its positive, proper divisors is smaller or larger than the number itself. Thus, 9, with proper divisors 1, 3, is deficient; 12, with proper divisors 1, 2, 3, 4, 6, is abundant."
Given a number, determine if it is perfect, abundant, or deficient.

Input

A list of N positive integers (none greater than 60,000), with 1 <= N < 100. A 0 will mark the end of the list.

Output

The first line of output should read PERFECTION OUTPUT. The next N lines of output should list for each input integer whether it is perfect, deficient, or abundant, as shown in the example below. Format counts: the echoed integers should be right justified within the first 5 spaces of the output line, followed by two blank spaces, followed by the description of the integer. The final line of output should read END OF OUTPUT.

Sample Input

15 28 6 56 60000 22 496 0

Sample Output

PERFECTION OUTPUT

15  DEFICIENT

28  PERFECT

6  PERFECT

56  ABUNDANT

60000  ABUNDANT

22  DEFICIENT

496  PERFECT

END OF OUTPUT

Source

Mid-Atlantic 1996

题目类型：模拟

算法分析：直接按照题目对于完美数的定义直接求出完美因子的的和，将其与待测试数进行比较即可。注意输出的格式

Invitation Cards

In the age of television, not many people attend theater performances. Antique Comedians of Malidinesia are aware of this fact. They want to propagate theater and, most of all, Antique Comedies. 阅读全文 »

Word Index

Encoding schemes are often used in situations requiring encryption or information storage/transmission economy. Here, we develop a simple encoding scheme that encodes particular types of words with five or fewer (lower case) letters as integers. Consider the English alphabet {a,b,c,...,z}. Using this alphabet, a set of valid words are to be formed that are in a strict lexicographic order. In this set of valid words, the successive letters of a word are in a strictly ascending order; that is, later letters in a valid word are always after previous letters with respect to their positions in the alphabet list {a,b,c,...,z}. For example,

abc aep gwz

are all valid three-letter words, whereas

aab are cat

are not.

For each valid word associate an integer which gives the position of the word in the alphabetized list of words. That is:
a -> 1
b -> 2
.
.
z -> 26
ab -> 27
ac -> 28
.
.
az -> 51
bc -> 52
.
.
vwxyz -> 83681
Your program is to read a series of input lines. Each input line will have a single word on it, that will be from one to five letters long. For each word read, if the word is invalid give the number 0. If the word read is valid, give the word's position index in the above alphabetical list.

Input

The input consists of a series of single words, one per line. The words are at least one letter long and no more that five letters. Only the lower case alphabetic {a,b,...,z} characters will be used as input. The first letter of a word will appear as the first character on an input line.

The input will be terminated by end-of-file.

Output

The output is a single integer, greater than or equal to zero (0) and less than or equal 83681. The first digit of an output value should be the first character on a line. There is one line of output for each input line.

Sample Input

z

a

cat

vwxyz

Sample Output

26

1

0

83681

Source

East Central North America 1995

题目类型：组合数学

算法分析：求解在给定字符串之前有多少的字符串即可，详细内容可以参考：

http://blog.csdn.net/lyy289065406/article/details/6648492

COURSES

Consider a group of N students and P courses. Each student visits zero, one or more than one courses. Your task is to determine whether it is possible to form a committee of exactly P students that satisfies 阅读全文 »