Westminster College 2016 High School Programming Contest. March 7, 2016

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1 Westminster College 2016 High School Programming Contest March 7, 2016 Rules: 1. There are six questions to be completed in two and 1/2 hours. 2. All questions require you to read the test data from standard input and write results to standard output. You should not use files for input or output. 3. The allowed programming languages are C++ and Java. 4. All programs will be re-compiled prior to testing with the judges data. 5. Programming style is not considered in this contest. You are free to code in whatever style you prefer. Documentation is not required. 6. from your solutions should follow the format used in the section for each problem. Unless stated otherwise, single blanks are used to seperate all output, and no blanks should appear at the end of any line. 7. Cheating is allowed and encouraged. 8. The previous statement is a lie!!! No cheating will be tolerated, and those caught cheating will be disqualified from the competition. 9. All judges decisions are final.

2 2016 Westminster High School Programming Contest 1 Problem A: Dinoscan Sarah Tops is a paleontologist who specializes in the reconstruction of dinosaur skeletons. One problem which she faces is determining whether two bones mesh together correctly. She has taken scans of all the bones in her collection, so instead of physically trying to put bones together she plans to use the scans to determine the appropriate connections between bones. Below on the left are scans of the ends of two different bones: Scan Scan 2 Combined In each scan, a 1 indicates bone and a 0 indicates empty space. Two bones mesh together if the two scans can be put together to form a solid rectangle of 1 s with no overlap. Scan 1 above can mesh with Scan 2 (as shown above on the right), but Scan 1 cannot mesh with either scans 3 or 4 shown below: Scan Scan 4 The input file contains multiple test cases. Each case starts with a line containing three positive integers r c 1 c 2, indicating the number of rows in both scans and the number of columns in the first and second scans. Following this are r lines each containing c 1 characters this is the first scan. All characters in the scan are either a 0 or a 1. Following this are r lines each with c 2 characters specifying the second scan. The maximum value for r, c 1 and c 2 is 20. In all test cases, the first column of scan 1 and the last column of scan 2 contain all 1 s. A line containing three zeros terminates input. For each test case, output the case number followed by Yes if the two scans can be meshed together, or No otherwise. When combining two scans, always try to connect the right hand side of the first scan with the left hand side of the second scan.

3 2016 Westminster High School Programming Contest 2 Note: the first uses scans 1 and 2 above, and the second uses scans 1 and Case 1: Yes Case 2: No

4 2016 Westminster High School Programming Contest 3 Problem B: Getting in Line with Art Mike and Angelo are arguing about a recent sculpture exhibit they attended (I m sure you get into these types of arguments all the time). Both of them are aspiring artists, and as soon as they got to the exhibit they each set up an easel and starting sketching the various sculptures they could see. Their argument involves the number of sculptures in the exhibit. Mike insists there were only three while Angelo swears there were five. After examining the layout of the sculpture from a map in the exhibition brochure they realized the problem: from where Mike had set up his easel, one of the statues (A) blocked his view of two others (C and E), as shown in the diagram below. Both Mike and Angelo wonder how likely something like this can happen, so they ve turned to you to run some simulations. For simplicity you decide to represent each sculpture by a point on the x-y plane. In this model, one sculpture can block the view of other sculptures only when they lie on the same line. All you have to do now is write code which when given a set of points determines the maximum number of those points that lie on a single line. Well...what are you waiting for? The input file contains multiple test cases. Each test case starts with a line containing a single integer n indicating the number of points, where n 100. After this are n pairs of integers x i y i indicating the location of the points. These pairs of numbers are across one or more input lines. All coordinate values lie in the range and no two points are the same. A line containing a single zero terminates input For each test case, output the case number followed by the maximum number of points on any one line.

5 2016 Westminster High School Programming Contest Case 1: 3 Case 2: 6

6 2016 Westminster High School Programming Contest 5 Problem C: Hidden Words Danny is a partial paranoid he thinks only half the world is out to get him! He s convinced that this vast anti-danny conspiracy is sending secret messages to each other via on-line media, so he scours websites looking for clues to their evil plan. So for example, the other day he found the words omega and theta in the following snippet from a restaurant review site:... feeling at home, Gary ate the taco he bought... and later found the word pascal in another line in the same article:... after you dip a scallop in the sauce... Notice how devilish Danny s enemies are, hiding these words by splitting them over multiple words while ignoring punctuation and capitalization. The fiends! Now, what omega, theta, and pascal actually mean Danny has no idea, but he s sure it can t be good. The problem for Danny is that there are just too many articles in too many websites for him to handle on his own. He s asked you to write a program that will scan a given sentence to see if a specific word is hidden in it somewhere. And he knows they re there! The input file contains multiple test cases. The first line contains a single integer n indicating the number of test cases. Each test case consists of two lines. The first line contains a single non-empty word in lowercase letters this is the word to search for. The second line contains the sentence to search. (NOTE: instructions on how to read in an entire line from a file are given at the end of this problem.) This line will contain only lower and upper case letters, blanks and punctuation. The maximum length of both the word and the line will be 80 characters each. For each test case, output the case number followed by the index of where the word starts in the sentence, or the phrase not found if the word is not in the sentence. The index of the first character in the sentence is 0, and you should count all characters in the sentence including blanks and punctuation when calculating the index. If there is more than one occurrence, output the first location. 3 omega feeling at home, Gary ate the taco he bought pascal... after you dip a scallop in the sauce... java... after you dip a scallop in the sauce... Case 1: 12 Case 2: 16 Case 3: not found

7 2016 Westminster High School Programming Contest 6 Reading in Lines C++: To read in an entire line into a string variable s use the global function getline() found in the string library. using namespace std;... string s;... getline(cin,s); Java: To read in an entire line into a String variable s, use the nextline method of a Scanner object. import java.util.scanner;... Scanner in = new Scanner(System.in); String s;... s = in.nextline(); WARNING: Suppose you want to read in an integer on one line and then read in the entire second line of input. In this case you must perform one getline or in.nextline call before reading in the second line of input. This is because after reading in the integer using cin >> n or n = in.nextint(), there is still an empty string remaining on that line which will be read in by the next getline or in.nextline. So to read in an integer and then read in the entire next line, you must do something like the following: C++ Java int n; int n; string s; String s; cin >> n; n = in.nextint(); getline(cin, s); reads in blank line s = in.nextline(); getline(cin, s); reads in next line s = in.nextline();

8 2016 Westminster High School Programming Contest 7 Problem D: Hoop Yourself Kathy is a basketball player on a mission. Her school uses basketballs from three different manufacturers and she s convinced that one of these companies produces a better product than the other two. To test this theory, she has amassed a wealth of data from various practices and hopes that she can use this data to convince the athletic department to only use one type of ball. The data she has is the following: For each jump shot taken at practice she knows the type of ball used and whether or not the shot was successful. For example, if the three types of balls are identified with the letters A, B and C, then the data (A,yes), (C,no), C(yes), B(no) indicates that one successful shot was take with ball type A, one unsuccessful shot was take with ball type B and two shots were take with ball type C, one successful and one not. Based on this (very small) sample Kathy would say that type A has a 100% rate of success, type C has a 50% rate and type B has a 0% rate. If that was all the data Kathy had, then she would say that type A is the ball to go with, but she has much more data than this data from 100 s of practices where in each practice 100 s of shots are taken. She has come to you to help automate the ranking process. The input file contains multiple test cases. Each test case starts with a line containing a single integer n 1000 indicating the number of data points in the sample. After this are n pairs t i s i where each pair represents one data point. In each pair t i is either the character A, B or C, and s i is either 1 (for a successful shot) or 0 (for an unsuccessful shot). These pairs are given across one or more input lines and there is at least one data point for each basketball type. A line containing a single zero terminates input For each test case, output each of the data types and their success rates, one pair per line. the pairs in sorted order, from most successful to least successful (there will never be a tie). the success rate as a percentage, using the standard floating point output in your language of choice. 4 A 1 C 0 C 1 B 0 17 C 1 A 0 A 1 B 1 B 1 B 0 C 1 C 0 B 1 C 1 B 1 A 0 C 0 C 1 B 0 B 1 A 0 0 Using C++ Using Java Case 1: Case 1: A 100 A 100 C 50 C 50 B 0 B 0 Case 2: Case 2: B B C C A 25 A 25.0

9 2016 Westminster High School Programming Contest 8 Problem E: Prime Driving Conditions Gabby has just bought a new car and needs license plates. In Pennsylvania license plates consists of three uppercase letters followed by four digits. License plates are given out in lexicographic order, meaning that plate AAA 0000 is first, followed by AAA 0001, AAA 0002, etc,. After AAA 9999 comes plates AAB 0000, AAB 0001, etc., and after plate AZZ 9999 comes plate BAA The very last plate is ZZZ For most people, any old license plate will do, but not for Gabby. She insists that the 4 digit number on the plate must be a prime number. Recall that a prime number is a number > 1 whose only factors are 1 and the number itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23,... So if Gabby goes to the DMV to get a set of plates, and the next available plate is JPB 1285, she ll wait until plate JPB 1289 becomes available, since 1289 is the first prime greater than or equal to If the plate had been JPB 9999, she would have waited for the plate JPC Perhaps you see what we re driving at here. Starting at a given license plate, find the first plate lexicographically equal or greater that contains a prime number. As a side note, this past January the largest prime number known to date was discovered. It is equal to 2 74,207,281 1 and contains 22,338,618 digits. A little too large to fit on a license plate. The input file contains multiple test cases. Each test cases is on a single line and contains a three character string followed by a 4 digit number. The three character string consists solely of uppercase letters other than the string ZZZ. A line containing END 0000 terminates input. For each test case, output the case number followed by the license plate Gabby will accept. JPB 1285 JPB 9999 END 0000 Case 1: JPB 1289 Case 2: JPC 0002

10 2016 Westminster High School Programming Contest 9 Problem F: Time is of the Essence Do you know how long one million seconds is? How about one billion seconds? Well, the answer to the first one is 11 days, 13 hours, 46 minutes and 40 seconds Accurate, but a little over-precise. A more reasonable answer might be 11 days, 14 hours or just 12 days (after rounding). As another example, if I asked how large three million inches were, you could approximate it by saying either 47 miles or 47 miles, 613 yards. This sort of imprecision is what we re looking for in this problem! The input file contains multiple test cases. The first line of each test case is of the following form: n name 1 c 1 name 2 c 2... name n 1 c n 1 name n Each name i is a unit of measurement and each c i is a conversion rate, telling you how many units of type name i+1 are in a unit of type name i. For example, in the first sample input, this line tells you that there are 24 hours in one day, 60 minutes in each hour and 60 seconds in each minute. The value n indicates the total number of unit names and satisfies 2 n 10. All names are alphabetic strings with no blanks and always specify the plural form of the unit (which you should use for output no matter the value is associated with the unit). All conversion values are positive integers. Following this line is a single positive integer m 2, 000, 000, 000 indicating an amount of the last unit (i.e., name n ). A line containing a single zero terminates input. For each test case output the case number followed by two lines. The first line should give the closest conversion of the input amount to units specified by name 1, rounded to the nearest integer. The second line should do the same, but be a bit more precise using the two largest units name 1 and name 2. When rounding, always round up when the fraction is 0.5. Note that there are no commas in the output.

11 2016 Westminster High School Programming Contest 10 4 days 24 hours 60 minutes 60 seconds years 365 days 24 hours 60 minutes 60 seconds feet 12 inches 11 0 Case 1: 12 days 11 days 14 hours Case 2: 32 years 31 years 259 days Case 3: 1 feet 0 feet 11 inches