DESENV. E IMPLEMENTAÇÃO DE ALGORITMOS 13/06/2015. Este caderno contém 11 páginas com a descrição de 11 problemas definidos a seguir:

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1 DESENV. E IMPLEMENTAÇÃO DE ALGORITMOS 13/06/2015 Este caderno contém 11 páginas com a descrição de 11 problemas definidos a seguir: A The Pony Cart problem (Valladolid 12853) B The Other Two Trees (Valladolid 10250) C Trouble with a Pentagon (Valladolid 10286) D Superman (Valladolid 10355) E The tinker's puzzlle (Valladolid 12851) F Region (Valladolid 10991) G Colourful Flowers (Valladolid 11152) H Atlhetics Track (Valladolid 11646) I Elevator (Valladolid 11834) J Little Masters (Valladolid 12704) K- Refraction (Valladolid 12901) (ver no site) Desafios: K Where Can You Hide (Valladolid 10011) L Campus Roads (Valladolid 11473) M Tunnelling the Earth (Valladolid 11817) N Trapezium Drawing (Valladolid 12404) 1. Os alunos podem trabalhar em grupos de 2, usando um micro apenas. 2. Alguns dos problemas são do site da Universidade de Valladolid. 3. Pode ser consultado qualquer material escrito. Não se pode usar pen-drives nem Internet na aula, a menos que seja expressamente permitido pelo professor. 4. Os problemas serão posteriormente checados para verificar sua originalidade. 5. Cada problema resolvido durante a aula acrescenta 0,2 na média final de cada aluno da dupla. Quando feitos em casa, na semana seguinte, acrescentam 0,1. A pontuação máxima é de 2 pontos. 6. As linguagens permitidas são: Pascal, C, C++. JAVA quando permitido expressamente, 7. Usaremos o sistema BOCA para submissão e correção dos problemas. - Cada dupla receberá um código: time1 a time40, com password inicial igual ao nome do time, que poderá ser trocada. Esse nome será usado em todo o curso. - Para acessar o sistema BOCA usar a URL xxx será informado no início de cada aula. - Logar usando os parâmetros da dupla. - Submeter cada programa com o nome correto: Ex: A.pas, C.cpp, B.c 8. Resolver e programar com calma. Boa sorte.

2 Problema A (Valladolid 12853) The Pony Cart problem What is the circumference of the outer track? While driving a speedy pony, a young boy went around a sharp turn at a gait which threatened an upset to the pony cart, as well as to his father's nerves. Fortunately no accidents occurred, and after some experimentation, the following information was gathered: In turning the pony cart around within a ring of a certain diameter, which might be said to be reasonably safe, it was found that the outer wheels made two turns to the inner wheels one; the wheels were fxed at the statutory distance of fve feet apart on the axletree. The problem is to guess the circumference of the track described by the outer wheels in making the turn. Assume that the tracks marked on the foor are perfectly circular, that the distance between a wheel on one side and its opposite on the other side is D feet, and that for one turn of the inner wheels, the outer wheels make N turns. Determine the circumference of the circle formed by the outer wheels. starts with a positive integer T, that denotes the number of test cases. Each test case is described by the two real numbers D and N in the same line. These numbers are always given with two digits after the decimal point. T 1000; 3 D 10; 1 < N 10 For each test case, print the case number, followed by the circumference of the outer tracks (in feet), with exactly three digits after the decimal point. Sample Sample Case 1: Case 2: Case 3:

3 Problema B (Valladolid 10250) The Other Two Trees You have a quadrilateral shaped land whose opposite fences are of equal length. You have four neighbors whose lands are exactly adjacent to your four fences, that means you have a common fence with all of them. For example if you have a fence of length d in one side, this fence of length d is also the fence of the adjacent neighbor on that side. The adjacent neighbors have no fence in common among themselves and their lands also don t intersect. The main difference between their land and your land is that their lands are all square shaped. All your neighbors have a tree at the center of their lands. Given the Cartesian coordinates of trees of two opposite neighbors, you will have to find the Cartesian coordinates of the other two trees. The input file contains several lines of input. Each line contains four floating point or integer numbers x1, y1, x2, y2, where (x1, y1), (x2, y2) are the coordinates of the trees of two opposite neighbors. is terminated by end of file. For each line of input produce one line of output which contains the line Impossible. without the quotes, if you cannot determine the coordinates of the other two trees. Otherwise, print four floating point numbers separated by a single space with ten digits after the decimal pointax1, ay1, ax2, ay2, where (ax1, ay1) and (ax2, ay2) are the coordinates of the other two trees. The output will be checked with special judge program, so don t worry about the ordering of the points or small precision errors. The sample output will make it clear. Sample Sample

4 Problema C (Valladolid 10286) Trouble with a Pentagon You are asked to place the largest possible square inside a regular pentagon (whose internal angles are same and all the sides are same in length). You are given the information that one vertex of the square will be coincident with a vertex of the square as shown in the figure below. You will have to find the length of a side of the square when a side of the regular pentagon is given. Fig: Square in a pentagon. The input file contains several lines of input. Each line contains a floating point number F (0<=F<=100000) which indicates the length of a side of the pentagon. is terminated by end of file. For each line of input produce one line of output containing a floating point number with ten digits after the decimal point. This number indicates the largest possible side of a square that fits in the pentagon. This output will be judged with a special correction program, so don t worry about small precision errors. Sample Sample

5 Problema D (Valladolid 10355) Superman Superman, with his incredible power, can fly faster than rockets! He can even pierce the Great Wall if it is in his path, and this doesn't affect his speed. But he is facing an unbearable problem in large cities now a days. Some regions of these cities are covered with polluted air. When flying through these regions, he can hardly breathe and his speed reduces significantly. He wants to find out whether he could pass through such regions by finding out the length of his path through these regions. Superman knows that each regions of polluted air have the shape of a sphere. He also knows where the polluted regions are located. But he doesn't know how to calculate the path length inside a sphere. So, he requests you to do that for him. There are multiple datasets. is terminated by EOF. Each dataset consists of the followings (All numbers are integers < 21 in absolute value): City name (consisting of 1 to 8 alphanumeric characters) in the first line. Starting and ending points' coordinates (x 1, y1, z1, x2, y2, z2) of Superman's path (separated by space(s)). He always flies in a straight line. Number (between 1 and 10 inclusive) of polluted regions in the third line. Center and radius (x, y, z, r) of each region (separated by space(s)), one line per region. No two regions intersect each other. For each dataset, print the city name in a line followed by the percentage of his path inside polluted regions. The result should be correct to 2 places after the decimal point. Sample Dhaka Rio Sample Dhaka Rio 86.60

6 Problema E (Valladolid 12851) The tinker's puzzlle There is an old nursery rhyme that says: I agreed with a tinker whose name was Doo-little to make for my aunt a fat-bottomed kettle. Twelve inches exactly the depth of the same, and twenty-fve gallons of beer to contain. The inches across at the top would show just twice the width, as measured below. So tell me that width, across at the top for auntie now wants a lid from the shop. Can you indicate the diameter of the required lid to ft on the kettle, which is twelve inches deep, and will hold just twenty-five gallons? Given the depth of the kettle, and the volume it can hold, calculate its diameter at the top which is twice the diameter at the bottom. The depth is given in inches, while the volume is given in "beer gallons", which you should assume to be equivalent to 282 cubic inches. starts with a positive integer T, that denotes the number of test cases. Each test case contains two integers: D and V which denote the depth and the volume of the kettle, respectively. T 1000; 1 D 50; 1 V 100. For each test case, print the case number, followed by the diameter at the top of the kettle, in inches. Print this as a real number rounded to exactly three digits after the decimal point. Sample Sample Case 1: Case 2:

7 Problema F (Valladolid 10991) Region From above figure, it is clear that C1, C2 and C3 circles are touching each other. Consider, C1 circle have R1 radius. C2 circle have R2 radius. C3 circle have R3 radius. Write a program that will calculate the area of shaded region G The first line will contain an integer k (1 k 1000) which is the number of cases to solve. Each of the following k Lines will contain threefloating point number R1 (1 R1 1000), R2 (1 R2 1000) and R3 (1 R3 1000). For each line of input, generate one line of output containing the area of G rounded to six decimal digits after the decimal point. Floating-point errors will be ignored by special judge program. Sample for Sample

8 Problema G (Valladolid 11152) Colourful Flowers "Roses are red, violets are blue..." Millionaire Mr Smith is well-known -- not for his wealth, but for his odd sense of "art"... Mr Smith has got a circular garden. On the boundary he picks three points and gets a triangle. He then finds the largest circle in that triangular region. So he gets something like this Mr Smith then plants yellow sunflowers, blue violets and red roses in the way shown in the figure. (Nice combination, eh? :-) Given the lengths of the three sides of the triangle, you are to find the areas of the regions with each kind of flowers respectively. and Each line of input contains three integers a, b, c, the lengths of the three sides of the triangular region, with 0 < a b c For each case, your program should output the areas of the regions with sunflowers, with violets and with roses respectively. Print your answers correct to 4 decimal places. Sample Sample

9 Problema H (Valladolid 11646) Atlhetics Track London Olympics is approaching very shortly in just 3 years. Three years might not sound as that small a time to say just, but it is indeed for those who have to organize the competition. There are so many things to do preparing the venues, building the Olympic village for accommodating athletes and officials, improving the transportation of the entire city as the venues are located all over the city and also there will be great number of tourists / spectators during the Olympics. One of the most important tasks is to build the stadium. You are appointed as a programmer to help things out in certain matters more specifically in designing and building the athletics tracks. After some study, you find out that athletics tracks have a general shape of a rectangle with two sliced circles on two ends. Now the turf that is placed inside this rectangle is prepared elsewhere and comes in different shapes different length to width ratios. You know one thing for certain your track should have a perimeter of 400 meters. That s the standard length for athletics tracks. You are supplied with the design parameter length to width ratio. You are also told that the sliced circles will be such that they are part of the same circle. You have to find the length and width of the rectangle. There will be at most 1000 test cases. Each test case will be given in one line. It will contain ratio of the length and width of the rectangle in the format a : b. Here, a and b will be integers and both will be between 1 and 1000 (inclusive). For each test case, output a line in the following format Case n: L W where n is the case no (starting from 1) and L and W are length and width of the rectangle (in meters) respectively. You can output as many digits as you want after the decimal point. will be verified by a validator for 1E-5 precision. Sample 3 : 2 5 : 4 for Sample Case 1: Case 2:

10 Problema I (Valladolid 11834) Elevator The FCC (Factory of Cylinders of Carbon) manufactures various types of cylinders of carbon. FCC is installed on the tenth floor of a building, and uses the several building's elevators to transport the cylinders. For security, the cylinders must be transported in the upright position, and since they are heavy, at most two cylinders can be transported in a single elevator ride. The elevators have the shape of a parallelepiped and their height is always greater than the height of the cylinders. To minimize the number of elevator trips to transport the cylinders, the FCC wants, whenever possible, to put two cylinders in the elevator. The figure below illustrates, schematically (top view) a case where this is possible (a), and a case where this is not possible (b): As there is a very large amount of elevators and types of cylinders, FCC hired you to write a program that, given the dimensions of the elevator and of the two cylinders, determines whether it is possible to put the two cylinders in the elevator. The input contains several test cases. The first and only line of each test case contains four integers L, C, R 1 and R 2, separated by blanks, indicating the width ( 1 L 100) and the length ( 1 C 100) of the elevator and the radii of the cylinders ( 1 R 1, R 2 100). The last test case is followed by a line containing four zeros separated by blanks. For each test case your program should print a single line with a single character, `S' if you can put the two cylinders in the elevator and `N' otherwise. Sample Sample S N N S

11 Problema J (Valladolid 12704) Little Masters Bangladesh whitewashed New Zealand in the three-match one day international series defeating the visitors by four wickets in the last and final match in Narayanganj. The Tigers scored 309 runs in 49.2 overs for the loss of six wickets at the Khan Shaheb Osman Ali Stadium in Fatullah.The most remarkable was the performance from the batsman of tiger side. Mominul, Nasir, Naeem, Mushfiq all showed tremendous batting performance. People call them little masters. They are clever enough to find a quick boundary. Here we have to do a little task for our busy little masters. We have to find out the length of the shortest and longest boundary distance from the batsman. We know the radius of the circular stadium and the position of the batsman. Center of the stadium is always the origin (0, 0). Boundary means the perimeter of the circular field. starts with an integer T ( 100), denoting the number of test cases. Each case starts with a line containing three integers x, y, r (0 x; y; r 1000). (x; y) denotes the coordinate of the batsman. And r denotes the radius of the stadium. You can safely assume that coordinate of the batsman will not be out of the stadium. For each case, print the shortest and longest boundary distance. Show exactly 2 digits after decimal point, properly rounded. See the samples for exact formatting. Sample Sample