24 hour archive: Problem
1811  Weird Numbers 1811  Weird Numbers 1811  Weird Numbers
Statistics  Sub: 99  AC: 47  AC%: 47,47  Score: 2,44 
Created by  2006/2007 ACMICPC Central Europe Regional Contest 
Added by  ymondelo20 (20120422) 
Limits 
Total Time: 2000 MS
Memory: 62 MB  Output: 64 MB  Size:
29 KB

Enabled languages  
Available in 
Description
Binary numbers form the principal
basis of computer science. Most of you have heard of other systems, such
as ternary, octal, or hexadecimal. You probably know how to use these
systems and how to convert numbers between them. But did you know that
the system base (radix) could also be negative;jsessionid=8CAAF5699E07053AD4197E8AA5ED08FE? One assistant professor
at the Czech Technical University has recently met negabinary numbers and other systems with a negative base. Will you help him to convert numbers to and from these systems?
A number N written in the system with a positive base R will always appear as a string of digits between 0 and R  1, inclusive. A digit at the position P (positions are counted from right to left and starting with zero) represents a value of R^P. This means the value of the digit is multiplied by R^P and values of all positions are summed together. For example, if we use the octal system (radix R = 8), a number written as 17024 has the following value:
With a negative radix R, the principle remains the same: each digit will have a value of (R)^P. For example, a negaoctal (radix R = 8) number 17024 counts as:
One
big advantage of systems with a negative base is that we do not need a
minus sign to express negative numbers. A couple of examples for the negabinary system (R = 2):
You may notice that the negabinary
representation of any integer number is unique, if no “leading zeros”
are allowed. The only number that can start with the digit “0”, is the
zero itself.
A number N written in the system with a positive base R will always appear as a string of digits between 0 and R  1, inclusive. A digit at the position P (positions are counted from right to left and starting with zero) represents a value of R^P. This means the value of the digit is multiplied by R^P and values of all positions are summed together. For example, if we use the octal system (radix R = 8), a number written as 17024 has the following value:
Binary numbers form the principal
basis of computer science. Most of you have heard of other systems, such
as ternary, octal, or hexadecimal. You probably know how to use these
systems and how to convert numbers between them. But did you know that
the system base (radix) could also be negative;jsessionid=8CAAF5699E07053AD4197E8AA5ED08FE? One assistant professor
at the Czech Technical University has recently met negabinary numbers and other systems with a negative base. Will you help him to convert numbers to and from these systems?
A number N written in the system with a positive base R will always appear as a string of digits between 0 and R  1, inclusive. A digit at the position P (positions are counted from right to left and starting with zero) represents a value of R^P. This means the value of the digit is multiplied by R^P and values of all positions are summed together. For example, if we use the octal system (radix R = 8), a number written as 17024 has the following value:
With a negative radix R, the principle remains the same: each digit will have a value of (R)^P. For example, a negaoctal (radix R = 8) number 17024 counts as:
One
big advantage of systems with a negative base is that we do not need a
minus sign to express negative numbers. A couple of examples for the negabinary system (R = 2):
You may notice that the negabinary
representation of any integer number is unique, if no “leading zeros”
are allowed. The only number that can start with the digit “0”, is the
zero itself.
A number N written in the system with a positive base R will always appear as a string of digits between 0 and R  1, inclusive. A digit at the position P (positions are counted from right to left and starting with zero) represents a value of R^P. This means the value of the digit is multiplied by R^P and values of all positions are summed together. For example, if we use the octal system (radix R = 8), a number written as 17024 has the following value:
Binary numbers form the principal
basis of computer science. Most of you have heard of other systems, such
as ternary, octal, or hexadecimal. You probably know how to use these
systems and how to convert numbers between them. But did you know that
the system base (radix) could also be negative;jsessionid=8CAAF5699E07053AD4197E8AA5ED08FE? One assistant professor
at the Czech Technical University has recently met negabinary numbers and other systems with a negative base. Will you help him to convert numbers to and from these systems?
A number N written in the system with a positive base R will always appear as a string of digits between 0 and R  1, inclusive. A digit at the position P (positions are counted from right to left and starting with zero) represents a value of R^P. This means the value of the digit is multiplied by R^P and values of all positions are summed together. For example, if we use the octal system (radix R = 8), a number written as 17024 has the following value:
With a negative radix R, the principle remains the same: each digit will have a value of (R)^P. For example, a negaoctal (radix R = 8) number 17024 counts as:
One
big advantage of systems with a negative base is that we do not need a
minus sign to express negative numbers. A couple of examples for the negabinary system (R = 2):
You may notice that the negabinary
representation of any integer number is unique, if no “leading zeros”
are allowed. The only number that can start with the digit “0”, is the
zero itself.
A number N written in the system with a positive base R will always appear as a string of digits between 0 and R  1, inclusive. A digit at the position P (positions are counted from right to left and starting with zero) represents a value of R^P. This means the value of the digit is multiplied by R^P and values of all positions are summed together. For example, if we use the octal system (radix R = 8), a number written as 17024 has the following value:
Input specification
The input will contain several
conversions, each of them specified on one line. A conversion from the
decimal system to some negativebase system will start with a lowercase
word “to” followed by a minus sign (with no space before it), the
requested base (radix) R, one space, and a decimal number N.
A conversion to the decimal system will start with a lowercase word “from”, followed by a minus sign, radix R, one space, and a number written in the system with a base of R. The input will be terminated by a line containing a lowercase word “end”. All numbers will satisfy the following conditions: 2 <= R <= 10, 10^6 <= N <= 10^6.
;jsessionid=8CAAF5699E07053AD4197E8AA5ED08FE
A conversion to the decimal system will start with a lowercase word “from”, followed by a minus sign, radix R, one space, and a number written in the system with a base of R. The input will be terminated by a line containing a lowercase word “end”. All numbers will satisfy the following conditions: 2 <= R <= 10, 10^6 <= N <= 10^6.
The input will contain several
conversions, each of them specified on one line. A conversion from the
decimal system to some negativebase system will start with a lowercase
word “to” followed by a minus sign (with no space before it), the
requested base (radix) R, one space, and a decimal number N.
A conversion to the decimal system will start with a lowercase word “from”, followed by a minus sign, radix R, one space, and a number written in the system with a base of R. The input will be terminated by a line containing a lowercase word “end”. All numbers will satisfy the following conditions: 2 <= R <= 10, 10^6 <= N <= 10^6.
;jsessionid=8CAAF5699E07053AD4197E8AA5ED08FE
A conversion to the decimal system will start with a lowercase word “from”, followed by a minus sign, radix R, one space, and a number written in the system with a base of R. The input will be terminated by a line containing a lowercase word “end”. All numbers will satisfy the following conditions: 2 <= R <= 10, 10^6 <= N <= 10^6.
The input will contain several
conversions, each of them specified on one line. A conversion from the
decimal system to some negativebase system will start with a lowercase
word “to” followed by a minus sign (with no space before it), the
requested base (radix) R, one space, and a decimal number N.
A conversion to the decimal system will start with a lowercase word “from”, followed by a minus sign, radix R, one space, and a number written in the system with a base of R. The input will be terminated by a line containing a lowercase word “end”. All numbers will satisfy the following conditions: 2 <= R <= 10, 10^6 <= N <= 10^6.
;jsessionid=8CAAF5699E07053AD4197E8AA5ED08FE
A conversion to the decimal system will start with a lowercase word “from”, followed by a minus sign, radix R, one space, and a number written in the system with a base of R. The input will be terminated by a line containing a lowercase word “end”. All numbers will satisfy the following conditions: 2 <= R <= 10, 10^6 <= N <= 10^6.
Output specification
For each conversion, print one number
on a separate line. If the input used a decimal format, output the same
number written in the system with a base R. If the input contained such
a number, output its decimal value. Both input and output numbers must
not contain any leading zeros. The minus sign “” may only be present
with negative numbers written in the decimal system. Any nonnegative
number or a number written in a negativebase system must not start with
it.
;jsessionid=8CAAF5699E07053AD4197E8AA5ED08FE
For each conversion, print one number
on a separate line. If the input used a decimal format, output the same
number written in the system with a base R. If the input contained such
a number, output its decimal value. Both input and output numbers must
not contain any leading zeros. The minus sign “” may only be present
with negative numbers written in the decimal system. Any nonnegative
number or a number written in a negativebase system must not start with
it.
;jsessionid=8CAAF5699E07053AD4197E8AA5ED08FE
The input will contain several
conversions, each of them specified on one line. A conversion from the
decimal system to some negativebase system will start with a lowercase
word “to” followed by a minus sign (with no space before it), the
requested base (radix) R, one space, and a decimal number N.
A conversion to the decimal system will start with a lowercase word “from”, followed by a minus sign, radix R, one space, and a number written in the system with a base of R. The input will be terminated by a line containing a lowercase word “end”. All numbers will satisfy the following conditions: 2 <= R <= 10, 10^6 <= N <= 10^6.
;jsessionid=8CAAF5699E07053AD4197E8AA5ED08FE
A conversion to the decimal system will start with a lowercase word “from”, followed by a minus sign, radix R, one space, and a number written in the system with a base of R. The input will be terminated by a line containing a lowercase word “end”. All numbers will satisfy the following conditions: 2 <= R <= 10, 10^6 <= N <= 10^6.
Sample input
to2 10
from2 1010
to10 10
to10 10
from10 10
end
Sample output
11110
10
190
10
10
Hint(s)
http://coj.uci.cu/24h/
http://coj.uci.cu/24h/
http://coj.uci.cu/24h/