In a billiard table with horizontal side a inches and vertical side b inches, a ball is launched from the middle of the table. After s > 0 seconds the ball returns to the point from which it was launched, after having made m bounces off the vertical sides and n bounces off the horizontal sides of the table. Find the launching angle A (measured from the horizontal), which will be between 0 and 90 degrees inclusive, and the initial velocity of the ball.
Assume that the collisions with a side are elastic (no energy loss), and thus the velocity component of the ball parallel to each side remains unchanged. Also, assume the ball has a radius of zero. Remember that, unlike pool tables, billiard tables have no pockets.
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You have been hired by several clients of a factory that manufactures brass bricks. Brass is an alloy of copper and zinc; each brick weighs 1000 grams, and the copper content of a brick can range from 1 to 999 grams. (Note that brass with less than 55% or more than 62% of copper is practically useless; however, this is irrelevant for this question) The factory manufactures, through various processes, different types of brick, each of which has a different copper concentration and price. It distributes a catalog of these types to its customers.
Your clients desire to buy a certain number (M) of bricks, which for, uh, religious reasons must be of different types. They will be melted together, and the resultant mixture must have a concentration of at least CMin and at most CMax grams of copper per kilogram. Their goal is to pick the M types of brick so that the mixture has the correct concentration and the price of the collection is minimized. You must figure out how to do this. M, CMin, and CMax will vary depending on the client.
]]>The first part of input consists of a line containing a number N (1 <= N <= 200), the number of brick types, and then Nlines containing the copper concentration (between 1 and 999) and price (in cents) of each brick type. No brick costs more than 10 dollars.
The second part consists of a line containing a number C (1 <= C <= 100), the number of clients you are serving, followed byC lines containing M (1 <= M <= 20), CMin (1 <= CMin <= 999), and CMax (1 <= CMax <= 999) for each client.
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Canada has a multi-party system of government. Each candidate is generally associated with a party, and the party whose candidates win the most ridings generally forms the government. Some candidates run as independents, meaning they are not associated with any party. Your job is to count the votes for a particular riding and to determine the party with which the winning candidate is associated.
]]>The first line of input contains a positive integer n satisfying 2 <= n <= 20, the number of candidates in the riding. npairs of lines follow: the first line in each pair is the name of the candidate, up to 80 characters; the second line is the name of the party, up to 80 characters, or the word "independent" if the candidate has no party. No candidate name is repeated and no party name is repeated in the input. No lines contain leading or trailing blanks.
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You have been blindfolded and deposited someplace in a maze. You have no idea where you are. You do know, however, that the maze is laid out on a grid, and that each grid location is either blocked or free. In fact, you have memorized a map of the maze. Also, your magnetic personality allows you to always sense which direction is north.
In this maze, you have four possible moves: north, south, east, and west. Your task is to find the shortest sequence of moves that will guarantee your escape, regardless of your initial placement in the maze. You have "escaped" whenever you reach a square on an outside edge of the grid (and if you start there, then you've already escaped). Further moves are irrelevant once you have escaped. If you try to walk into a wall, you will simply stay in the same spot.
You may assume that it is possible to escape from every unblocked position in the maze.
]]>Input consists of a positive integer n <= 8, followed by n lines giving the rows of an n by n grid. This grid describes the maze you are trapped in. Written on the screen, north is up. Blocked locations are denoted by the character "O" (that's an uppercase "o"), while unblocked locations are indicated by the character ".".
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You have a drawer that is full of two kinds of socks: red and black. You know that there are at least 2 socks, and not more than 50000. However, you do not know how many there actually are, nor do you know how many are red, or how many are black. (Your mother does the laundry!)
You have noticed, though, that when you reach into the drawer each morning and choose two socks to wear (in pitch darkness, so you cannot distinguish red from black), the probability that you pick two red socks is exactly p/q, where 0 < q and 0 <= p <= q.
From this, can you determine how many socks of each colour are in your drawer? There may be multiple solutions - if so, pick the solution with the fewest total number of socks.
]]>Input consists of multiple problems, each on a separate line. Each problem consists of the integers p and q separated by a single space. Note that p and q will both fit into an unsigned long integer.
Input is terminated by a line consisting of two zeroes.
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