2015 ICPC. Northeast North America Preliminary

Transcription

1 2015 ICPC Northeast North America Preliminary sponsored by the Clarkson Student Chapter of the ACM Saturday, October 17, :00 am 5:00 pm Applied CS Labs, Clarkson University Science Center

2 Problem A Piggy- Bank Before ACM can do anything, a budget must be prepared and the necessary financial support obtained. The main income for this action comes from Irreversibly Bound Money (IBM). The idea behind it is simple. Whenever some ACM member has any small money, he takes all the coins and throws them into a piggy-bank. You know that this process is irreversible, the coins cannot be removed without breaking the pig. After a sufficiently long time, there should be enough cash in the piggy-bank to pay everything that needs to be paid. But there is a big problem with piggy-banks. It is not possible to determine how much money is inside. So we might break the pig into pieces only to find out that there is not enough money. Clearly, we want to avoid this unpleasant situation. The only possibility is to weigh the piggy-bank and try to guess how many coins are inside. Assume that we are able to determine the weight of the pig exactly and that we know the weights of all coins of a given currency. Then there is some minimum amount of money in the piggy-bank that we can guarantee. Your task is to find out this worst case and determine the minimum amount of cash inside the piggy-bank. We need your help. No more prematurely broken pigs! Input Specification The input consists of T test cases. The number of T is given on the first line of the input file. Each test case begins with a line containing two integers E and F. They indicate the weight of an empty pig and of the pig filled with coins. Both weights are given in grams. No pig will weigh more than 10 kg, that means 1 <= E <= F <= On the second line of each test case, there is an integer number N (1 <= N <= 500) that gives the number of various coin types used in the given currency. Following this are exactly N lines, each specifying one coin type. These lines contain two integers each, P and W (1 <= P <= 50000, 1 <= W <=10000). P is the value of the coin in monetary units; W is its weight in grams. Output Specification Print exactly one line of output for each test case. The line must contain the sentence "The minimum amount of money in the piggy-bank is X." where X is the minimum amount of money that can be achieved using coins with the given total weight. If the weight cannot be reached exactly, print the line "This is impossible." Sample Input

3 Output for the Sample Input The minimum amount of money in the piggy-bank is 60. The minimum amount of money in the piggy-bank is 100. This is impossible.

4 Problem B Broken Typewriter Suppose that you type out a string in lowercase on a typewriter. You show your result to a friend who retypes the string on the same typewriter. That person in turn shows their result to a friend who retypes it on the same typewriter. This happens an unspecified number of times. Let s be the initial string, and t be the string that is produced at the end of this process. If the typewriter is working correctly s and t will be the same string. But the typewriter is broken. Sometimes, but not always, the typewriter will type "ca" instead of "ab", and vice versa it will sometimes type "ab" instead of "ca". Similarly, the typewriter will sometimes type "dc" instead of "cc", and vice versa it will sometimes type "cc" instead of "dc". Given 2 strings s and t, your job is to determine if t could have been produced from s in this process. Input Specification The input consists of a positive integer N indicating how many cases there will be. Each case will be begin with a positive integer indicating the length of s, followed by a positive integer indicating the length of t, followed by s, followed by t. Output Specification Your program should print one line of output for each test case. Each line will contain the word "Yes" or "No". "Yes" means that t could be produced from s. "No" means it cannot. Sample Input abdcca caccab 6 6 abcdef abcdef 6 5 abcdef abcde 4 4 cccc cccd 3 3 ddc cdc Sample Output Yes Yes No No Yes

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6 Problem C Regular Guy Joe had a strict rule. He would make phone calls at most one day per week, but not necessarily the same day each week. He had a specific routine for each day of the week. In other words, his Tuesday routine might be to call Ann, Bill and Charles in that order. Then every Tuesday that he made phone calls, he would call the same people in the same order. Joe keeps a record of which days he made phone calls. At the end of the year you receive that record. You also receive a list of all the phone calls he made in order, but not the days on which he made the phone calls. Your job is to figure out the number of ways this could have happened. Your answer would be 0 if the results are not consistent. For example, suppose Joe's notes say that he made his first set of phone calls on a Monday, his next set on a Wednesday, and his third set on a Monday again. Also suppose the sequence of phone calls is Ann, Bill, Ann, Bill, Ann, Bill Ann. Then your answer would be 2 because you have the following possibilities: Monday: Ann Monday: Ann, Bill, Ann Wednesday: Bill, Ann, Bill, Ann, Bill Wednesday: Bill Input Specification The input consists of a positive integer N indicating how many cases there will be. Each case will begin with a positive integer C indicating how many days Joe made phone calls, followed by a positive integer D indicating how many phone calls Joe made over the year. This will be followed by a string representing the days of Joe's phone calls, using the code: M = Monday, T = Tuesday, W = Wednesday, H = Thursday, F = Friday, S = Saturday, U = Sunday. This will be followed by a string representing the list of phone calls over the year. Because this is for one year, C cannot be more than 52. Because we abbreviate people Joe called by letters of the alphabet, you can assume he did not call more than 26 different people. Output Specification Your program should print one line of output for each test case. Each line will contain a number indicating the number of ways that test case could have happened. Sample Input MWM abababa 3 7 TTH abababa 3 8 MWM abababab

7 4 9 SUSU abcabcabc 4 10 TWTW aaaaaaaaaa Sample Output

8 Problem D Pangram A pangram is a phrase that includes at least one occurrence of each of the 26 letters, a... z. You re probably familiar with this one: The quick brown fox jumps over the lazy dog. Your job is to recognize pangrams. For phrases that don t contain every letter, report what letters are missing. We ll say that a particular letter occurs in the phrase if it occurs as either uppercase or lowercase. Input Input starts with a line containing an integer 1 N 50. The next N lines are each a single phrase, possibly containing upper and lower case letters, spaces, decimal digits and the punctuation characters.,,,?,!, and ". Each phrase contains at least one and no more than 100 characters. Output For each input phrase, output pangram if it qualifies as a pangram. Otherwise, output the word missing followed by a space and then the list of letters that didn t occur in the phrase. The list of missing letters should be reported in lower case and should be sorted alphabetically Sample Input 3 The quick brown fox jumps over the lazy dog. ZYXW, vu TSR Ponm lkj ihgfd CBA..,?! " abcde FGHIJ Sample Output pangram missing eq missing klmnopqrstuvwxyz

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10 Problem E Island of Logic The Island of Logic has three kinds of inhabitants: divine beings that always tell the truth, evil beings that always lie, and human beings that are truthful during the day and lie at night. Every inhabitant recognizes the type of every other inhabitant. A social scientist wants to visit the island. Because he is not able to distinguish the three kinds of beings only from their looks, he asks you to provide a communication analyzer that deduces facts from conversations among inhabitants. The interesting facts are whether it is day or night and what kind of beings the speakers are. Input The input file contains several descriptions of conversations. Each description starts with an integer n, the number of statements in the conversation. The following n lines each contain one statement by an inhabitant. Every statement line begins with the speaker s name, one of the capital letters A, B, C, D, E, followed by a colon :. Next is one of the following kinds of statements: I am [not] (divine human evil lying). X is [not] (divine human evil lying). It is (day night). Square brackets [] mean that the word in the brackets may or may not appear, round brackets () mean that exactly one of the alternatives separated by must appear. X stands for some name from A, B, C, D, E. There will be no two consecutive spaces in any statement line, and at most 50 statements in a conversation. The input is terminated by a test case starting with n = 0. Output For each conversation, first output the number of the conversation in the format shown in the sample output. Then print This is impossible., if the conversation cannot happen according to the rules or No facts are deducible., if no facts can be deduced. Otherwise print all the facts that can be deduced. Deduced facts should be printed using the following formats: X is (divine human evil). It is (day night). X is to be replaced by a capital letter speaker name. Facts about inhabitants must be given first (in alphabetical order), then it may be stated whether it is day or night. The output for each conversation must be followed by a single blank line. Sample Input 1 A: I am divine.

11 1 A: I am lying. 1 A: I am evil. 3 A: B is human. B: A is evil. A: B is evil. 0 Sample Output Conversation #1 No facts are deducible. Conversation #2 This is impossible. Conversation #3 A is human. It is night. Conversation #4 A is evil. B is divine. Reasoning made easy To make things clearer, we will show the reasoning behind the third input example, where A says I am evil.. What can be deduced from this? Obviously A cannot be divine, since she would be lying, similarly A cannot be evil, since she would tell the truth. Therefore, A must be human, moreover, since she is lying, it must be night. So the correct output is as shown. In the fourth input example, it is obvious that A is lying since her two statements are contradictory. So, B can be neither human nor evil, and consequently must be divine. B always tells the truth, thus A must be evil. Voila!

12 Problem F Factorial The most important part of a GSM network is the so-called Base Transceiver Station (BTS). These transceivers form the areas called cells (this term gave the name to the cellular phone) and every phone connects to the BTS with the strongest signal (in a slightly simplified view). Of course, BTSes need some attention and technicians need to check their function periodically. ACM technicians faced a very interesting problem recently. Given a set of BTSes to visit, they needed to find the shortest path to visit all of the given points and return back to the central company building. Programmers have spent several months studying this problem but with no results. They were unable to find the solution fast enough. After a long time, one of the programmers found this problem in a conference article. Unfortunately, he found that the problem is the socalled "Travelling Salesman Problem" and it is very hard to solve. If we have N BTSes to be visited, we can visit them in any order, giving us N! possibilities to examine. The function expressing that number is called the factorial and can be computed as a product 1*2*3*4*...*N. The number is very large even for a relatively small N. The programmers understood they had no chance to solve the problem. But because they have already received the research grant from the government, they needed to continue with their studies and produce at least some results. So they started to study the behavior of the factorial function. For example, they defined the function Z. For any positive integer N, Z(N) is the number of zeros at the end of the decimal form of the number N!. They noticed that this function never decreases. If we have two numbers N 1 <N 2, then Z(N 1 ) <= Z(N 2 ). It is because we can never "lose" any trailing zero by multiplying by any positive number. We can only get new zeros. The function Z is very interesting, so we need a computer program that can determine its value efficiently. Input Specification There is a single positive integer T on the first line of input. It stands for the number of numbers to follow. Then there is T lines, each containing exactly one positive integer N, 1 <= N <= 1,000,000,000. Output Specification For every number N, output a single line containing the single non-negative integer Z(N). Sample Input Sample Output

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