Divide and conquer

Problem code: F6

All submissions for this problem are available.

The Chef has one long loaf of bread. Let us say, of length 1. He wants to cut it into as many little loaves as he can. But he wants to adhere to the following rule: At any moment, the length of the longest loaf which he possesses may not be larger than the length of shortest one, times some constant factor. Every time, he is only allowed to cut exactly one loaf into two shorter ones.

Input

One floating-point number, 1 k 1.999, meaning the stated constant factor.

Output

First, you should output one number n, the maximal achievable number of loaves for the given value of the constant factor. Then, you should output any proof that this number of loaves is in fact achievable: n-1 descriptions of cutting, using the following notation. At each step, you print two numbers: first, the index of the loaf that you want to cut into two parts; second, the length of the newly created loaf (cut off from the original one). It is assumed that the starting loaf has index 0. Each newly created loaf will be given the lowest possible free integer index (so, at the ith step this will be i). Each time, the size of size of the original loaf will be decreased by the size of the newly created loaf.

Example

Input:
1.5
Output:
4
0 0.4
0 0.3
1 0.2
Date: 2009-07-10
Time limit: 1s
Source limit: 50000
Languages: C C99 strict C++ PAS gpc PAS fpc JAVA NICE JAR C# C#2 NEM ST ASM D FORT ADA BASH PERL PYTH RUBY LUA ICON PIKE PHP SCM guile SCM qobi LISP sbcl LISP clisp SCALA HASK CAML CLPS PRLG WSPC BF ICK TEXT


Comments

triplem @ 15 Aug 2009 01:59 PM

My solution which was accepted in the contest is no longer accepted here - did something change?

admin 2 @ 15 Aug 2009 06:15 PM

@Stephen Try now, it should work.

triplem @ 15 Aug 2009 06:52 PM

Cool, thanks.

what is the things other

krishanu @ 14 Jan 2010 01:47 AM

what is the things other than

int main() &  return NULL at end,I have to attach for GNU compiler??

i didn't get what the output

krish00back @ 17 Feb 2010 07:01 PM

i didn't get what the output is?????

not actually the o/p but the

krish00back @ 17 Feb 2010 07:02 PM

not actually the o/p but the proof???

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