Dept. of Computer Science and Engineering, Czech Technical University in Prague
Faculty of Mathematics and Physics, Charles University in Prague
Faculty of Electrical Engineering and Computer Science, Technical University of Ostrava
Faculty of Informatics and Information Technologies, Slovak University of Technology
Faculty of Informatics, Masaryk University
Faculty of Management Science and Informatics, University of Zilina
CTU Open Contest 2008
Government Help
help.c, help.C,, help.p
Two major banks in our country are knee-deep in troubles. We will call them “Bank A" and
“Bank B" — hopefully you understand we absolutely cannot tell you their real names. It might
ruin them.
As a logical consequence of their troubles, government comes to rescue them, preparing a set
of financial “packages" that will be distributed between these two banks. However, there is
one important condition: the packages will be given to the banks one by one and we need to
minimize the di.erence between the amount given to both banks in any particular moment.
Otherwise, one of the banks would gain a big advantage over the other.
For example, imagine that we have four packages with the values of 100 000, 110 000, 120 000,
and 150 000. If we give the first package to the Bank A, then the second one to the Bank B,
the third one to the Bank B, and the fourth package to the Bank A, the di.erence between
the help provided to the banks will be +100 000 after the first package, -10 000 after the second
one, -130 000 after the third one, and +20 000 after the last package. The maximal di.erence is
therefore 130 000.
There is a better solution, with the maximal di.erence of 100 000 only: first, give 100 000 to the
Bank A, then 120 000 to the Bank B, then 110 000 to the Bank A, and then 150 000 to the Bank
Input Specification
The input contains multiple sets of financial packages. Each set begins with a line containing
a single positive integer N: the number of financial packages (1 . N . 50 000). The second line
is a set of N positive integers separated by a space, all of them between 100 000 and 199 999
inclusive. These numbers specify the amount of money in individual packages. Packages can be
assigned in any order, the order of numbers on the second line is therefore not important.
The last set will be followed by a line containing single zero.
Output Specification
For each set of financial packages, output one line containing the order of assignments of packages
to the banks, such as the maximal di.erence is as low as possible. If there are more possible
solutions, you may print any of them.
Assignments must be separated by a space, each assignment consists of one number (the package
size), one dash character (“-"), and an uppercase letter (“A"or“B") specifying the bank.
Sample Input
100000 110000 120000 150000
100000 100000 100000
Output for Sample Input
100000-A 120000-B 110000-A 150000-B
100000-B 100000-A 100000-A