| # | Problem | Pass Rate (passed user / total user) |
|---|---|---|
| 1544 | 23 Out of 5 [01] |
|
| 1552 | Twin Primes [1] |
|
| 1576 | Domino Effect [01] |
|
| 1588 | Fans and Gems [01] |
|
Description
Your task is to write a program that can decide whether you can find an arithmetic expression consisting of five given numbers ai (1 ≤ i ≤ 5) that will yield the value 23.
For this problem we will only consider arithmetic expressions of the following from:
where 
:{1,2,3,4,5} -> {1,2,3,4,5} is a bijective function and 
{+,-,*} (1 ≤ i ≤ 4)
Input
The Input consists of 5-Tupels of positive Integers, each between 1 and 50.
Input is terminated by a line containing five zero's. This line should not be processed.
Output
For each 5-Tupel print "Possible" (without quotes) if their exists an arithmetic expression (as described above) that yields 23. Otherwise print "Impossible".
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Description
Twin primes are pairs of primes of the form (p, p+2). The term "twin prime" was coined by Paul Stäckel (1892-1919). The first few twin primes are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43). In this problem you are asked to find out the S-th twin prime pair where S is an integer that will be given in the input.
Input
The input will contain less than 10001 lines of input. Each line contains an integers S (1 ≤ S ≤ 100000), which is the serial number of a twin prime pair. Input file is terminated by end of file.
Output
For each line of input you will have to produce one line of output which contains the S-th twin prime pair. The pair is printed in the form (p1,
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Did you know that you can use domino bones for other things besides playing Dominoes? Take a number of dominoes and build a row by standing them on end with only a small distance in between. If you do it right, you can tip the first domino and cause all others to fall down in succession (this is where the phrase ``domino effect'' comes from).
While this is somewhat pointless with only a few dominoes, some people went to the opposite extreme in the early Eighties. Using millions of dominoes of different colors and materials to fill whole halls with elaborate patterns of falling dominoes, they created (short-lived) pieces of art. In these constructions, usually not only one but several rows of dominoes were falling at the same time. As you can imagine, timing is an essential factor here.
It is now your task to write a program that, given such a system of rows formed by dominoes, computes when and where the last domino falls. The system consists of several ``key dominoes'' connected by rows of simple dominoes. When a key domino falls, all rows connected to the domino will also start falling (except for the ones that have already fallen). When the falling rows reach other key dominoes that have not fallen yet, these other key dominoes will fall as well and set off the rows connected to them. Domino rows may start collapsing at either end. It is even possible that a row is collapsing on both ends, in which case the last domino falling in that row is somewhere between its key dominoes. You can assume that rows fall at a uniform rate.
Input
The input file contains descriptions of T domino systems (T ≤ 30). The first line of each description contains two integers: the number n of key dominoes (1 ≦ n < 500) and the number m of rows between them. The key dominoes are numbered from 1 to n. There is at most one row between any pair of key dominoes and the domino graph is connected, i.e. there is at least one way to get from a domino to any other domino by following a series of domino rows.
The following m lines each contain three integers a, b, and l, stating that there is a row between key dominoes a and b that takes l seconds to fall down from end to end.
Each system is started by tipping over key domino number 1.
The file ends with an empty system (with n = m = 0), which should not be processed.
Output
For each case output a line stating the number of the case (`System #1', `System #2', etc.). Then output a line containing the time when the last domino falls, exact to one digit to the right of the decimal point, and the location of the last domino falling, which is either at a key domino or between two key dominoes. If the last domino is between key domino A and key domino B, you should output the smaller one first and then the larger one. For example, if A = 5, B = 3, and the falling time of last domino is 3.0, you should output "The last domino falls after 3.0 seconds, between key dominoes 3 and 5.". Adhere to the format shown in the output sample. It is guaranteed that only one such output exists. Output a blank line after each system.
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Description
Tomy's fond of a game called 'Fans and Gems' (also known as Gravnic). In the game, he can use fans to collect gems, but he's satisfied with his play only if all the gems are collected with minimal number of steps. The game is played as following:
There are three kinds of gems, one colored red, one colored green and one colored blue. There are walls in the space, as you see. There are also virtual fans everywhere in the game, but you cannot see them. What you can do each time is to select a DIRECTION to which the fans should blow. There are only four directions possible: UP, DOWN, LEFT and RIGHT. Then, the fans will work, pushing all the gems to fly to the selected direction at the same speed, until they cannot move further(blocked by the wall, other gems or a flyer). Then, if there are some gems touching some same-colored gem(touching means adjacent in one of the four directions), they disappear simultaneously. Note that the fans are still working, so some gems may go on moving in that direction after some gems disappeared. The fans stop working when all the gems cannot move any more, and none of them should disappear. There may be some flyers that can be moved by the fans, but they can NEVER disappear.
You are to write a program that finds the minimal number of operations to make all the gems disappear.
Input
The input file begins with an integer T, indicating the number of test cases. (1 ≤ T ≤ 15) Each test case begins with two integers N, M, indicating the height and width of the map. (1 ≤ N ≤ 12, 1 ≤ M ≤ 20) In the following N lines, each line contains M characters describing the map. There is one line after each map, ignore them. Spaces denotes empty square, '#' denotes a wall, '1' denotes a red gem, '2' denotes a green gem, '3' denotes a blue gem, and '@' denotes a flyer. It's guaranteed that the four sides of the map are all walls. There is at least one gem in the map, and no two same-colored gems will touch each other at the beginning of the game.
Output
You should print a single line for each case. If there is a solution, write the shortest operation sequence in a string. The ith character must be from the set {'U','D','L','R'}, describing ith operation. The four characters represent UP, DOWM, LEFT, RIGHT respectively. If there are more than one solution, choose the lexicographical smallest one, if there are no solution, output -1 on the line. When a solution exists, you need only 18 or fewer steps to carry it out.