2008 Canadian Computing Competition: Senior Division

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Clementine Clark
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1 2008 Canadian Computing Competition: Senior Division

2 Canadian Computing Competition Hong Kong Contest Student Instructions for the Senior s 1. You may only compete in one competition. If you wish to write the Junior paper, see the other problem set. 2. Be sure to indicate on your Student Information Form that you are competing in the Senior competition.. You have three () hours to complete this competition. 4. You should assume that all input is from a file named sx.in, where X is the problem number (1 X 5). all output is to a file named sx.out, where X is the problem number (1 X 5). None of the problems require prompting: please do not prompt the user. Be sure your output matches the output in terms of order, spacing, etc. IT SHOULD MATCH EXACTLY! 5. Do your own work. Cheating will be dealt with harshly. 6. Do not use any features that the judge (your teacher) will not be able to use while evaluating your programs. 7. Books and written materials are allowed. Any machine-readable materials (like other programs which you have written) are not allowed. However, you are allowed to use standard libraries for your programming languages; for example, the STL for C++, java.util.*, java.io.*, etc. for Java, and so on. 8. Applications other than editors, compilers, debuggers or other standard programming tools are not allowed. Any use of other applications will lead to disqualification. 9. Please use file names that are unique to each problem: for example, please use s1.pas or s1.c or s1.java (or some other appropriate extension) for S1. This will make the evaluator s task a little easier. 10. Your program will be run against test cases other than the sample ones. Be sure you test your program on other test cases. 11. The contest results will be released by by February The award ceremony will be held on 5 February Please visit the CCC website for the details. The CCC website is:

3 S1. Distance In the town of Blackwood, streets either run from North to South, or from East to West. All streets are straight and the name of each street is composed of one word only. As Christmas approaches, Santa Claus is coming to the town to give some Christmas gifts. Therefore he needs to know the distance between some pairs of intersection points. He knows the names of all streets, their directions, and the distance between them. You are asked to compute the distance between given pairs of intersection points. You are given that the distance between a point and another point that is x units north of it and y units east of it is sqrt(x^2+y^2). The first line of the input consists of two integers N (1 <= N <= 5000) and M (1 <= M <= 5000), where N and M is the number of streets running in the North-South direction, and the East-West direction respectively. Each of the following N lines contains information about streets running in the North-South direction, listed from East to West. The line contains the street name and an integer indicating its distance from the street on the previous line. For the first line, this number is always zero. Each of the following M lines contains information about streets running in the East-West direction, listed from North to South. The line contains the street name and an integer indicating its distance from the street on the previous line. For the first line, this number is always zero. You may also assume that the distance between any two streets running in the same direction is no more than The (M+N+2)th line contains an integer Q (1<=Q<=20000), the number of queries from Santa Claus. Each of the following Q lines contains four street names, say A, B, C and D, each separated by a single space. Street A and Street C run from North to South, while Street B and Street D run from East to West. This means that Santa would like to know the distance from the intersection of A and B to the intersection of C and D. The output consists of Q lines, each containing the distance between the two intersections points, in the order of Santa's query. The distance should be outputted with 2 decimal places (rounded). Sample Yonge 0 University 00 Spadina 200 Bloor 0 Dundas 400 Queen Yonge Bloor University Dundas Yonge Bloor Spadina Queen Sample

4 S2. Cashier In a department store, customers pay for the goods they buy, and the cashier returns change to the customer if the money paid by the customer is more than the price of the goods. The currency in use is in face amounts of $100, $50, $20, $10, $5, $2, $1, $0.5, $0.2 and $0.1. In giving change, the cashier always tries to use the smallest total number of notes and coins. Given a list of daily transactions, you are asked to find out the total number of each type of notes and coins used in giving change. Note that we do not consider the incoming notes and coins from customers, because the system does not make a record of what exact notes and coins the customers give to the cashier. The first line of the input contains one integer N (1 <= N <= 0000), the number of transactions made in the day. Each of the following N lines contains information about a transaction made in the day. The line contains two numbers M and P, the money paid by the customer and the price of the goods. The numbers are given with one decimal place. You may assume M>=P, and that M <= The output consists of a single line, containing 10 integers, which is the number of $100, $50, $20, $10, $5, $2, $1, $0.5, $0.2 and $0.1 notes or coins used in giving change respectively. Sample Sample

5 S. Smart Phone book Nowadays, the features in mobile phones are very user friendly. There is a shortcut for the most frequent dialed phone number (labelled Favourite) so that you can make a phone call to that friend by just pushing that one button. And, the phone is smart enough to update the phone number of this button dynamically. You are going to write a program to simulate this feature. The input consists of two parts. The first part is the phone book showing the name of friends and their phone numbers. The second part is a set of dials/queries. The first integer R in the input (R <= 1000) represents the total number of records in the phone book. Then each of the records follows on a line by itself. Each record starts with a name with no more than 20 characters (without any whitespace) followed by a phone number with exactly 8 digits. After those (R+1) lines, another integer D (D<= ) in the input represents the total number of operations, which is either "dial" or "query". For a dial operation, a phone number follows. For each "query" operation, your program should output the name of the most frequently dialed phone number at that moment. If there are two such numbers, output the one with a smaller phone number ("smaller" being "numerically smaller"). Sample 5 Mary Susan May Ann Peter dial dial query dial dial dial dial query Sample Ann Peter

6 S4. Team formation Tom often plays chess against his computer. However, the AI of the computer game is way too intelligent for Tom to beat on his own. As a result, he decided to ask for help from his friends. Tom has ranked n of his friends in descending order of skill levels (i.e., the most skilled friend is ranked 1, the second most skilled friend is ranked 2, and so on). He wants to select some of his friends to form "a team" so that they are more or less as intelligent as the AI. Your task is to help Tom form the k-th weakest team. Here is how we rank teams. Suppose there are two teams, P and Q. We compare the strongest member in P, p1, and the strongest member in Q, q1. If p1 is stronger than q1, P is the stronger team than Q, and vice versa. If p1 and q1 is the same person, we compare the second strongest member in P, p2, to the second strongest member in Q, q2, and so on. If all members of P are also members of Q, then Q is the stronger team. You will notice that the weakest team has no members at all. The first line of input contains a single integer t (t <= 10000), the number of test cases to consider. Each of the next t lines contains two integers n and k, where 1 <= n, k <= 2^1-1. For each test case, output the k-th weakest team. Use the ranking of the team members to represent the team members. Sort the ranking in descending order. Sample Sample { } { 4 } { 1 4 }

7 S5. Tower of Hanoi with 4 poles In the classic Tower of Hanoi problem, there are n discs, each disc having a unique radius. Each of the discs are initially stacked on the first pole in decreasing order; i.e., the biggest disc is place at the bottom while the smallest one is on the top. There are two empty poles which can hold discs. Each move involves taking the topmost disc from one pole to another provided that a larger disc is not placed on top of a smaller one. It is known that we need 2 n - 1 steps to move n discs from the first pole to the third pole. We may need fewer steps if there are 4 poles. In this problem, you need to find the optimal number of moves required to move the discs from the first pole to the fourth one. Hint: You can find the optimal way to move the smallest k discs from the first pole to the third one. Then move the remaining n - k discs to the fourth pole (using poles only). Finally move the smallest k discs from the third pole to the fourth. But you have to figure out what the value k is. The first input is an integer t specifying the number of test cases (1 <= t <= 10000). On each of the next t lines there is a number n, indicating the number of discs that are to be moved in this test case. You may assume n <= 00. For each test case, output the optimal number of moves required to solve the Tower of Hanoi with 4 poles. Sample Sample 1 5 9

2007 Canadian Computing Competition: Senior Division. Sponsor:

2007 Canadian Computing Competition: Senior Division Sponsor: Canadian Computing Competition Student Instructions for the Senior Problems 1. You may only compete in one competition. If you wish to write