ACM ICPC 2012, qualification round

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Karen Weaver
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1 Task 01 Area file: area.in file: area.out Lawn design company decided to create a lawn design in front of its office to advertise its services. Initially they made a project for a convex quadrilateral form lawn ABCD (see the picture below). After seeing the plan the director of the company said that since it is done for advertising purposes they could afford a bigger lawn. He made each side two times longer and thus obtained a lawn constructed by the points QRST. The point A is right in the middle between D and Q. The point B is right in the middle between A and R. The point C is right in the middle between B and S. The point D is right in the middle between C and T. The accountants were interested in how much the cost of the new lawn would increase. Your task is to calculate the ratio of the area of QRTST and the area of ABCD. Each row has 5 decimal numbers in the interval of 1 to with 10 digits after the decimal separator. These 5 numbers correspond to AB, BC, CD, DA, AC. There are no more than 100 rows. Each row of the output file holds the ratio of the areas of the corresponding line from the input file with the precision of 10 digits after the decimal separator Q B R A T D C S 1/12

2 Task 02 Bean Language file: bean.in file: bean.out Beans (of the Fabaceae family) communicate using their own obscure language. Its universal adoption is facilitated by the fact that it subsumes a wide variety of human languages, an added bonus being that it is undecipherable in rare cases, basically when human listeners have not been paying attention. Beans will pay you a fortune though if you write a program to help them understand human messages! The rule used to translate any text into Bean language is: every maximal substring consisting of only vowels should be duplicated, inserting P before the duplicate occurrence. Thus, for example, FABACEAE becomes FAPABAPACEAEPEAE. Note: the Latin letters A, E, I, O, U, Y should be considered vowels; the others are consonants. The input file consists of one line containing a message to be translated. The message consists only of uppercase Latin letters and spaces. It starts and ends with a letter. It is at least 1 and at most characters long. The output file should contain the message translated into Bean language. PUPA YRA TOIT PUPUPAPA YPYRAPA TOIPOIT 2/12

3 Task 03 Bureaucrats file: bureaucrats.in file: bureaucrats.out A company called QuickApproval managed to rent one of the rooms in town council. Sadly the town suffers from bureaucracy and it is really hard for entrepreneurs to get approvals for their projects. QuickApproval decided to offer a project approval service for the entrepreneurs. The town council has N rooms numbered from 0 to N-1 that are connected with hallways. One room belongs to QuickApproval, one room is exit, but others belong to the bureaucrats of the town council. The bureaucrats of the town council can t stand being bothered with the same project more than once. The task is to find if QuickApproval can travel all the other rooms and exit the building while visiting each room only once (including the room owned by QuickApproval and the exit from building). The first row holds the number of testcases (not more than 20). Test case has the following layout - first row holds the number of rooms N (1<N<16), second row holds the number of room owned by QuickApproval, the third row holds the number or the exit room Y (Y X ). Last is the adjacency matrix of format N*N (N rows and N columns with 0 or 1 in each cell). If the cell on column i and row j has 1 then the rooms i and j are connected with a hallway, otherwise not. The columns and rows are in the range 0 to N-1. The output file should have a single line for each test case containing a single word Yes if the travel is possible and No, if not No Yes 3/12

4 Task 04 Cards file: cards.in file: cards.out Adam found N blank cards in his drawer. He wrote a number on each side of each card and thought of the following puzzle: what is the smallest possible value that can be obtained by reordering and possibly flipping the cards and interpreting the sequence as an expression of the following form? After a while he came up with a solution. Can you write a program to do the same? The first line contains the integer N (2 N 100,000; N is even). Each of the following N lines describes one card by giving the two integers A i and B i ( A i 2000, B i 2000) written on it. The first and only line should contain a single integer, the minimal value of the expression that can be obtained from the cards The minimal sum can be achieved by taking the cards in the following order: 1 st, 2 nd, 3 rd, 5 th, 4 th, and 6 th. Then the expression becomes (-8) (5) + (-3) (7) + (-7) (4) = /12

5 Task 05 Countries file: countries.in file: countries.out Given a list of countries (for instance, Belarus, Estonia, Latvia, Lithuania, and Russia) we need to find the two letter abbreviation for each of them. The name of the country can be perceived as a head that is the first letter of the name and the tail the rest of the name. The first letter of the abbreviation is the first letter of the name (the head). The second letter of the abbreviation can be any letter of the tail e.g. Russia can be abbreviated to Ru, Rs, Ri or Ra. The task is to find the biggest subset of the country names with valid abbreviations taken into account that different countries must have different abbreviations. The input file has no more than 40 test cases. Each test case starts with the length of the country name list N (1 N 100). Then N rows of country names follow that are 2 to 50 characters long. The names consist of upper and lower case Latin letters. The input file ends with 0 that tells that the test cases have ended. For each of the test cases in the input file the output file must contain a row with the number of the maximum countries that can have correct abbreviations. 5 Belarus Estonia Latvia Lithuania Russia 4 ABC ACD ADB ABD 6 AA AAB AABC ACABABABABABD ADE AEBC /12

6 5 Example abbreviations for the test cases above: First test case: Be, Es, La, Li, Ru Second test case: AB (for ABC), AC (for ACD), AD (for ADB or ABD) 6/12

7 Task 06 Mean file: mean.in file: mean.out In sports such as gymnastics or diving, sometimes judges tend to give biased scores depending on their likes or dislikes of an athlete. To remedy the situation, truncated or Winsorized mean is often used instead of the regular mean to compute the final score of an athlete. For example, if seven judges gave the scores 9.3, 9.5, 9.6, 9.8, 9.1, 5.0, 9.3, the mean score 8.8 is the result of one low score of 5.0 that is probably unfair to the contestant. K-truncated mean is computed by discarding K lowest and K highest scores and calculating the average of the remaining ones. For example, 2-truncated mean of the above sequence, rounded to two decimal places, would be K-Winsorized mean, on the other hand, replaces the K lowest and K highest scores with the next closest score. For the above example sequence, 5.0 and 9.1 would be replaced by 9.3 while 9.8 and 9.6 would be replaced by 9.5, giving 9.39 as the 2-Winsorized mean (again, rounded to two decimal places). Write a program to compute truncated and Winsorized means. The first line contains two integers N and K (0 2 K < N 10 6 ). The second line contains the N scores, each in the range from 0 to 100, given with exactly one decimal place. The first line should contain the K-truncated and the second line the K-Winsorized mean of the sequence given in the input file. Both means should be given with exactly two decimal places. Digits 0 4 in the third decimal place should be rounded down and 5 9 up /12

8 Task 07 Puzzle file: puzzle.in file: puzzle.out Consider the word puzzles of the type SEND + MORE MONEY where each letter must correspond to a different decimal digit, and leading zeros are not allowed in the numbers. One possible solution for the example above would be S = 9, E = 5, N = 6, D = 7, M = 1, O = 0, R = 8, Y = 2, giving = Write a program to find the number of solutions for puzzles f this type. The first and only line contains three words separated by single spaces: first addend, second addend and sum. Words consist of uppercase letters of Latin alphabet; no word is longer than 18 letters. The first and only line of output must contain the number of different solutions to the puzzle. A B A 0 A A BC 5 8/12

9 Task 08 Maximal Sum file: smax.in file: smax.out Write a program to find in the given integer sequence the subsequence with the maximal sum. The input may contain several test cases. Each test case is presented on two lines. The first line contains a single integer N (1 N 10 4 ), the number of elements in the sequence. The second line contains N integers A i ( A i 10 4 ), the elements of the sequence. The last line of input contains a zero. This is a terminator value and should not be processed. The output should contain exactly one line for each test case. Each line should contain two integers I and J (1 I J N) such that the sum of elements A I...J is the largest possible. If there are several sub-sequences with the maximal sum, output the shortest one. If there are several sub-sequences with the minimal length, output the leftmost one /12

10 Task 09 Tickets file: tickets.in file: tickets.out Ticket sales company decided to give discounts to every customer that would buy a lucky ticket. Every ticket has a sequence number of N = 2K digits that is padded with zeros up to the length N. A sequence number can consist of only zeroes. A ticket is considered to be lucky if the sum of its first K digits is equal to the sum of its last K digits. The company wants to how many discounts it will have to hand out if it sells all the tickets from number T 1 to number T 2. The first row of the input contains Q - the number of test cases (from 1 to 30). Next Q rows each hold a single test case consisting of 3 numbers. First entry of the row is number N that defines the length of the ticket sequence number (2 N 12), second and third are T 1 and T 2 - two N- digit sequence numbers that define the range of the ticket sequence number (T 1 T 2 ). The output file must have Q lines each holding the number of lucky tickets within the range given in the corresponding test case /12

11 Task 10 Trip file: trip.in file: trip.out There is a country where N cities (numbered from 1 to N) are connected by N-1 bidirectional roads so that it is possible to get from any city to any other via these roads. A traveller starts from the city S and needs to visit the cities C 1, C 2,, C M (in any order). The traveller wants to buy only as much gas as needed so that more money is left over for beer and pizza. Write a program to help him find the length of the shortest route that starts from the city K and visits each of the cities C i at least once (and possibly some others on the way). The first line contains the integers N, S, M (2 N 50,000; 1 S N; 1 M < N). Each of the following N-1 lines describes one road by the three integers A i, B i, D i (1 A i N; 1 B i N; A i B i ; 1 D i 1000) which mean that the road connects the cities A i and B i and the length of the road is D i. The last line contains the M integers C i (1 C i N; C i C j ; C i S). The first and only line should contain a single integer, the length of the shortest route starting in the city S and visiting all the cities C i The shortest route is /12

12 Task 11 XOR file: xor.in file: xor.out It is quite well known that the only encryption method that has been proven to be information theoretically secure is the one-time pad. In this method, a K-bit key is required to encrypt a K-bit plaintext, and the ciphertext is the bitwise XOR between the key and the plaintext. However, even the one-time pad can be broken when it's used carelessly and this is exactly what you're asked to do in this task. A crook has used the one-time pad to encrypt a short message sent to several accomplices. The police believes they managed to capture all the ciphertexts and also all the keys, but they do not have the plaintext and they do not know which ciphertext was produced with which key. Write a program to help them recover the plaintext. The first line contains N (1 N 1000), the number of keys/ciphertexts. Each of the following N lines contains a key. Each of the N lines after that contains a ciphertext. Both the keys and ciphertexts are given in hexadecimal, using only uppercase for the letters A Z. You can assume they all have the same even length that does not exceed 280 characters. The output should contain all possible plaintexts, one per line, in lexicographic order, or the word ERROR on the first and only line if the input data is inconsistent. The plaintexts should be given in hexadecimal, keeping the leading zeroes (if any), in uppercase AAAAAA FFFFFF BFBDB EAE8E D Indeed, encrypting the plaintext 40424D with the key gives the ciphertext , encrypting with the key AAAAAA gives the ciphertext EAE8E7, and encrypting with the key FFFFFF gives the ciphertext BFBDB2. 12/12

The 2016 ACM ICPC Vietnam National Programming Contest. The problem set consists of 11 problems: ICPC score distribution. Magical palindromic number

The 2016 ACM ICPC Vietnam National Programming Contest. The problem set consists of 11 problems: ICPC score distribution. Magical palindromic number The problem set consists of 11 problems: Problem A Problem B Problem C Problem D Problem E Problem F Problem G Problem H Problem I Problem J Problem K ICPC score distribution Magical palindromic number