ACM ICPC2009 Latin American Regionals 1. Problem A Pangram. File code name: pangram

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1 ACM ICPC29 Latin American Regionals Problem A Pangram File code name: pangram Pangram Show is an exciting new television quiz show which offers very large cash prizes for correctly detecting if a sentence is a pangram. A pangram is a sentence that contains at least once each of all 26 letters of the English alphabet. Pangram examples: the quick brown fox jumps over a lazy dog jackdaws loves my big sphinx of quartz Each contestant must indicate if each sentence is a pangram or not. During the ACM Contest, you may play along with actual contestants from the show! You ll be given the same sentences as they appeared on the show. Can you do as well as the contestant? The input contains several test cases. Each test case is given in a single line that contains a non-empty string of at most 2 characters. Each string represents a sentence. The words of the sentence are separated with a single space. Only lowercase letters of the English alphabet and spaces appear in each line of the input. The last test case is followed by a line containing a single asterisk. For each test case your program must output a single line, containing an uppercase Y if the sentence is a pangram or an uppercase N if the sentence is not a pangram. jackdawf loves my big quartz sphinx abcdefghijklmnopqrstuvwxyz hello world * for the sample input Y Y N

2 ACM ICPC29 Latin American Regionals 2 Problem B Hexagonal Tiles File code name: hexagonal The path to Mary s school is a straight line paved with hexagonal tiles. The picture below shows an example of the path with 2 numbered tiles Mary loves mathematics. When going to school, she steps on the tiles of that path following these rules: She always starts from the tile with the smiling face (as nothing matches starting anything with a smile!). This tile is always present at the beginning of the path. The other tiles are numbered consecutively, in ascending order, starting from, as shown in the figure. She is not allowed to go back, that is, she must not step on a tile which bears a lower number than the tile she is on (when decided to go to school, there she goes!). She always steps from a tile to a neighboring one (no jumps in order to keep out of harm s way!). She must always finish on the highest numbered tile. When classes are over, she is so tired that she avoids the path and walks on the lawn. Mary does not want to repeat any sequence of steps on the tiles and she would like to know, if the path is paved with N numbered tiles and a tile with the face, how many days will it take to make each possible sequence once. For example, five days will be needed for her to try all possible step sequences if the path has N = 4 tiles, one day for each of the sequences: , -2-4, -3-4, and 2-4. Write a program to determine how many different step sequences there are for a path with a given number N of tiles. The input contains several test cases. Each test case is composed by a line containing an integer N( N 4), the number of tiles in the path. The last test case is followed by a line containing a single zero.

3 ACM ICPC29 Latin American Regionals 3 For each test case, print a line containing a single integer, the number of different step sequences. 4 2 for the sample input

4 ACM ICPC2 Latin American Regional Problem A Mean Median Problem Problem code name: mean The mean of three integers A, B and C is (A + B + C)/3. The median of three integers is the one that would be in the middle if they are sorted in non-decreasing order. Given two integers A and B, return the minimum possible integer C such that the mean and the median of A, B and C are equal. Each test case is given in a single line that contains two integers A and B ( A B 9 ). The last test case is followed by a line containing two zeros. For each test case output one line containing the minimum possible integer C such that the mean and the median of A, B and C are equal. 2 6 for the sample input

5 ACM ICPC2 Latin American Regional 2 Problem B Factorial Again! Problem code name: factorial Mathew, an engineering freshman, is developing an original positional notation for representing integer numbers. He called it A Curious Method (ACM for short). The ACM notation uses the same digits as the decimal notation, i.e., through 9. To convert a number A from ACM to decimal notation you must add k terms, where k is the number of digits of A (in the ACM notation). The value of the i-th term, corresponding the i-th digit a i, counting from right to left, is a i i!. For instance 79 ACM is equivalent to 53, since 7 3! + 2! + 9! = 53. Mathew has just begun studying number theory, and probably does not know which properties a numbering system should have, but at the moment he is only interested in converting a number from ACM to decimal. Could you help him? Each test case is given in a single line that contains a non-empty string of at most 5 digits, representing a number in ACM notation. The string does not have leading zeros. The last test case is followed by a line containing one zero. For each test case output a single line containing the decimal representation of the corresponding ACM number for the sample input

6 ACM ICPC29 Latin American Regionals 6 Problem J Jingle Composing File code name: jingle A. C. Marcos is taking his first steps in the direction of jingle composition. He is having some troubles, but at least he is achieving pleasant melodies and attractive rhythms. In music, a note has a pitch (its frequency, resulting in how high or low is the sound) and a duration (for how long the note should sound). In this problem we are interested only in the duration of the notes. A jingle is divided into a sequence of measures, and a measure is formed by a series of notes. The duration of a note is indicated by its shape. In this problem, we will use uppercase letters to indicate a note s duration. The following table lists all the available notes: Notes Identifier W H Q E S T X Duration /2 /4 /8 /6 /32 /64 The duration of a measure is the sum of the durations of its notes. In Marcos jingles, each measure has the same duration. As Marcos is just a beginner, his famous teacher Johann Sebastian III taught him that the duration of a measure must always be. For example, Marcos wrote a composition containing five measures, of which the first four have the correct duration and the last one is wrong. In the example below, each measure is surrounded with slashes and each note is represented as in the table above. /HH/QQQQ/XXXTXTEQH/W/HW/ Marcos likes computers as much as music. He wants you to write a program that determines, for each one of his compositions, how many measures have the right duration. The input contains several test cases. Each test case is described in a single line containing a string whose length is between 3 and 2 characters, inclusive, representing a composition. A composition begins and ends with a slash /. Measures in a composition are separated by a slash /. Each note in a measure is represented by the corresponding uppercase letter, as described above. You may assume that each composition contains at least one measure and that each measure contains at least one note. All characters in the input will be either slashes or one of the seven uppercase letters used to represent notes, as described above. The last test case is followed by a line containing a single asterisk.

7 ACM ICPC29 Latin American Regionals 7 For each test case your program must output a single line, containing a single integer, the number of measures that have the right duration. /HH/QQQQ/XXXTXTEQH/W/HW/ /W/W/SQHES/ /WE/TEX/THES/ * for the sample input 4 3