Kemija. Write a program that decodes Luka s sentence. Input

Transcription

1 Kemija Luka is fooling around in chemistry class again! Instead of balancing equations he is writing coded sentences on a piece of paper. Luka modifies every word in a sentence by adding, after each vowel (letters a, e, i, o and u ), the letter p and then that same vowel again. For example, the word kemija becomes kepemipijapa and the word paprika becomes papapripikapa. The teacher took Luka s paper with the coded sentences and wants to decode them. Write a program that decodes Luka s sentence. The coded sentence will be given on a single line. The sentence consists only of lowercase letters of the English alphabet and spaces. The words will be separated by exactly one space and there will be no leading or trailing spaces. The total number of character will be at most 100. the decoded sentence on a single line. zepelepenapa papapripikapa Sample 1 zelena paprika Sample 2 bapas jepe doposapadnapa opovapa kepemipijapa Sample 2 bas je dosadna ova kemija Source: Croatian Open Competition in Informatics 2008/2009, contest #3. License: For educational use only

2 Dice game Gunnar and Emma play a lot of board games at home, so they own many dice that are not normal 6-sided dice. For example they own a die that has 10 sides with numbers 47,48,,56 on it. There has been a big storm in Stockholm, so Gunnar and Emma have been stuck at home without electricity for a couple of hours. They have finished playing all the games they have, so they came up with a new one. Each player has 2 dice which he or she rolls. The player with a bigger sum wins. If both sums are the same, the game ends in a tie. Task Given the description of Gunnar s and Emma s dice, which player has higher chances of winning? a, a + 1,, b a b b a + 1 All of their dice have the following property: each die contains numbers, where and are the lowest and highest numbers respectively on the die. Each number appears exactly on one side, so the die has sides. a 1, b 1, a 2, b 2 i The first line contains four integers that describe Gunnar s dice. Die number contains numbers a i, a i+1,, b i on its sides. You may assume that 1 a i b i 100. You can further assume that each die has at least four sides, so a i+3 b i. The second line contains the description of Emma s dice in the same format. the name of the player that has higher probability of winning. Tie if both players have same probability of winning Sample 1 Emma Sample Sample 2 Tie

3 Sample Sample 3 Gunnar Author: Lukáš Poláček. Source: Nordic Collegiate Programming Contest License: Creative Commons License (cc by-sa)

4 Ladder You are attempting to climb up the roof to fix some leaks, and have to go buy a ladder. The ladder needs to reach to the top of the wall, which is most v h centimeters high, and in order to be steady enough for you to climb it, the ladder can be at an angle of at degrees from the ground. How long does the ladder have to be? The input consists of a single line containing two integers 1 h v 89 and that. h v and, with meanings as described above. You may assume that Write a single line containing the minimum possible length of the ladder in centimeters, rounded up to the nearest integer Sample Sample Sample Author: Per Austrin. Source: Spotify Challenge License: Creative Commons License (cc by-sa)

5 Reversed binary numbers Yi has moved to Sweden and now goes to school here. The first years of schooling she got in China, and the curricula do not match completely in the two countries. Yi likes mathematics, but now The teacher explains the algorithm for subtraction on the board, and Yi is bored. Maybe it is possible to perform the same calculations on the numbers corresponding to the reversed binary representations of the numbers on the board? Yi dreams away and starts constructing a program that reverses the binary representation, in her mind. As soon as the lecture ends, she will go home and write it on her computer. Task Your task will be to write a program for reversing numbers in binary. For instance, the binary representation of 13 is 1101, and reversing it gives 1011, which corresponds to number 11. N 1 N The input contains a single line with an integer,. one line with one integer, the number we get by reversing the binary representation of. N 13 Sample 1 11 Sample 2 47 Sample 2 61 Author: Emma Enström. Source: KTH Challenge License: Creative Commons License (cc by-sa)

6 Friday 13th On the planet Htrae Friday the 13th is a lucky day. You are going there on the next space ship and want to calculate how many times it happens during a given year. Unfortunately they change their calendar every year. Every year starts on a Sunday, but other than that, they change everything. They have released a list of calendar specifications for the next few years. A calendar specification consists of the total number of days in the year, the number of months in the year, and the number of days in each of the months. Your task is to figure out how many times there will be Friday the 13th based on the calendar specifications. The first line of the input consists of a single integer, The first line of each of the test cases is a line with two space separated integers, and, the total number of days in the year and the number of months in the year respectively. The second line of each test case consists of integers, d i, the number of days in each month. 1 T 20 1 M D di 100 i d i = D T, the number of test cases. T D M M space separated For each test case, output the number of Friday the 13ths in the specified year Sample Author: Torbjørn Morland. Source: IDI-Open License: Creative Commons License (cc by-sa)

7 Riječi One day, little Mirko came across a funny looking machine! It consisted of a very very large screen and a single button. When he found the machine, the screen displayed only the letter A. After he pressed the button, the letter changed to B. The next few times he pressed the button, the word transformed from B to BA, then to BAB, then to BABBA When he saw this, Mirko realized that the machine alters the word in a way that all the letters B get transformed to BA and all the letters A get transformed to B. Amused by the machine, Mirko asked you a very difficult question! After K times of pressing the button, how many letters A and how much letters B will be displayed on the screen? K 1 K 45 The first line of input contains the integer ( ), the number of times Mirko pressed the button. The first and only line of output must contain two space-separated integers, the number of letters A and the number of letter B. 1 Sample Sample 2 4 Sample Sample 3 10 Sample

8 Author: Marin Tomić. Source: Croatian Open Competition in Informatics 2013/2014, contest #3. License: For educational use only

9 Artichokes Fatima Cynara is an analyst at Amalgamated Artichokes (AA). As with any company, AA has had some very good times as well as some bad ones. Fatima does trending analysis of the stock prices for AA, and she wants to determine the largest decline in stock prices over various time spans. For example, if over a span of time the stock prices were 19, 12, 13, 11, 20 and 14, then the largest decline would be 8 between the first and fourth price. If the last price had been 10 instead of 14, then the largest decline would have been 10 between the last two prices. Fatima has done some previous analyses and has found that the stock price over any period of time can be modelled reasonably accurately with the following equation: p, a, b, c d price(k) = p (sin(a k + b) + cos(c k + d) + 2) where and are constants. Fatima would like you to write a program to determine the largest price decline over a given sequence of prices. Figure 1 illustrates the price function for. You have to consider the prices only for integer values of k. Figure 1:. The largest decline occurs from the fourth to the seventh price. The input consists of a single line containing 6 integers ( ),,,, ( ) and ( 1 n 106. p 1 p 1000 a b c d 0 a, b, c, d 1000 ). The first 5 integers are described above. The sequence of stock prices to consider is price(1), price(2),, price(n) n Display the maximum decline in the stock prices. If there is no decline, display the number 0. Display your output in two decimal places

10 Sample Sample Sample Close Show Valid Sample 3 Bad domain: Bad domain: Sample Bad domain: Bad domain: Bad domain: Bad domain: Bad domain: Source: ACM-ICPC World Finals License: Restricted, used with permission Bad domain: Auto-validate on refresh

11 Numbers on a Tree Lovisa is at KTH listening to Stefan Nilsson lecturing about perfect binary trees. A perfect binary tree has a distinguished node called the root which is usually drawn at the top. Each node has two children except the nodes in the lowest layer, which we call leaves. Lovisa knows all this already, so she is a bit bored. Noticing this, Stefan comes up with a new challenge for Lovisa. First, we label the nodes of a perfect binary tree with numbers as follows. We start at the bottom right leaf which gets number 1 and then label nodes on the same level in increasing order from right to left. After finishing a level, we move to the rightmost node in the level above and label all the nodes on that level from right to left. We proceed in this fashion until we reach the root. When we want to describe a node in the tree, we can do it by describing a path starting at the root and going down toward the leaves. At each non-leaf node we can either go left ( L ) or right ( R ). Figure 1: Labeled binary tree of height 3 with two marked paths from the root. Path LR leads to label 11 while path RRL leads to 2. The root has number 15. Task Lovisa s task is to calculate the label of a node, given the height of the tree H and the description of the path from the root. The only line of input contains the height of the tree, and a string consisting of the letters L and R, denoting a path in the tree starting in the root. The letter L denotes choosing the left child, and the letter R choosing the right child. The description of the path may be empty and is at most H 1 H 30 H letters. one line containing the label of the node given by the path.

12 3 LR Sample 1 11 Sample 2 3 RRL Sample 2 2 Sample 3 2 Sample 3 7 Author: Lukáš Poláček. Source: KTH Challenge License: Creative Commons License (cc by-sa)