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  Concept of Multiple input programs and their problems

Multiple input programs:

The Multiple input programs are an invention of online judge. The online judge frequently employs the problems and data that were first represented in live contests. Most of the solutions to problems presented in live contests take a solitary set of data, give the output for it, and finish. This doesn’t imply that the judges will provide merely a single set of data. The judges really give multiple files as input one after the other and compare the corresponding output files with the judge output. Though, the Valladolid online judge provides only one file as input. It inserts all judge inputs into a single file and at the top of that file; it also writes how many sets of inputs are there. A blank line now divides each set of data. Therefore the structure of input file for multiple input programs becomes:

Integer N     //representing the number of sets of input
--blank line---
input set 1 //As explained in the problem statement
--blank line---
input set 2 //As explained in the problem statement
--blank line---
input set 3 //As explained in the problem statement
--blank line---
.
.
.
--blank line---
input set n  //As explained in the problem statement
--end of file--

Note that there must be no blank subsequent to the last set of data. The structure of output file for multiple input programs becomes:

Output for set 1 //As explained in the problem statement
--Blank line---
Output for set 2 //As explained in the problem statement
--Blank line---
Output for set 3 //As explained in the problem statement
--Blank line---
.
.
.
--blank line---
Output for set n //As explained in the problem statement
--end of file--

The USU online judge doesn’t contain multiple input programs such as Valladolid. It prefers to offer multiple files as input and sets a time limit for each and every set of input. 

Problems of multiple input programs:

There are various issues which you should consider in a different way for multiple input programs. Even when the input specification states that the input finishes with the end of file (EOF), each and every set of input is really terminated by a blank line, apart from for the last one, which is terminated by the end of file. As well, be careful regarding the initialization of variables. When they are not correctly initialized, your program might work for a single set of data however give accurate output for multiple sets of data. All the global variables are initialized to their equivalent zeros.

This is the most fundamental problem solving method. Utilizing the fact that computer is really very fast.

Complete search develops the brute force, straight-forward, try-them-all technique of finding the answer. This technique must almost always be the first algorithm or solution you consider. When this works in time and space constraints, then do it: it is simple to code and generally easy to debug. This signifies you will encompass more time to work on all the hard problems, where brute force does not work quickly sufficient.

Party Lamps:

You are provided N lamps and four switches. The primary switch toggles all lamps, the second even lamps, the third odd lamps, and last switch toggles lamps 1,4,7,10,...

Given number of lamps, N, the number of button presses made up to (10,000), and the state of few of lamps (example: lamp 7 is off), output all the probable states the lamps could be in.

Naively, for each and every button press, you have to try 4 possibilities, for a total of 4^10000 (around 10^6020), that signifies there is no way you could do complete search (that is, this particular algorithm would exploit the recursion).

Noticing that the order of button presses doesn’t matter gets this number down to around 10000^4 (around 10^16), still too big to totally search (however certainly closer by a factor of over 10^6000).

Though, pressing a button twice is similar as pressing the button no times, thus you all really have to check pressing each button either 0 or 1 times. That is only 2^4 = 16 possibilities, certainly a number of iterations solvable in the time limit.

The Clocks:

A group of nine clocks resides in a 3 x 3 grid; each is set to 12:00, 3:00, 6:00, or 9:00. Your aim is to manipulate them all to read 12:00. Unluckily, the only way you can manipulate the clocks is by one of nine distinct types of move, each one of which rotates a certain sub-set of the clocks 90 degrees clockwise. Find the shortest series of moves that returns all the clocks to 12:00.

The apparent thing to do is a recursive solution that checks to see if there is a solution of 1 move, 2 moves, and so on until it finds a solution. This would take 9^k time, here k is the number of moves. As k might be fairly big, this is not going to execute with reasonable time constraints.

Note that the order of moves doesn’t matter. This decreases the time down to k^9 that isn't sufficient of an enhancement.

Though, since doing each move 4 times is similar as doing it no times, you know that no move will be completed more than 3 times. Therefore, there are only 49 possibilities that are only 262,072, that, given the rule of thumb for run-time of more than 10,000,000 operations in a second, must work in time. The brute-force solution, given this insight, is perfectly enough.

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