X Olympiad in Informatics 2002/2003

Problem: PrintedCircuit Boards

Author: Marcin Kubica

The firm of Bytel starts to produce seriesparallel electronic
circuits. Each such a circuit consists of electronic units, connections
between them, and two power connections. A seriesparallel circuit may
consist of:
 a single unit
 several smaller seriesparallel circuits connected in series
 two branching units connecting in parallel several smaller
seriesparallel circuits.
The circuits are assembled on twosided printedcircuit boards. The
problem is to determine which connections should run on the top and
which on the bottom side of the board. For technical reasons as
many connections as possible should run on the bottom side but to each
unit at least one must come from the top side of the board.
Task
Write a program which:
 reads the description of a seriesparallel circuit,
 computes the minimal number of connections that must run on the
top side of the board,
 writes the result.
Input
From the standard input one should read the description of a
seriesparallel circuit. The description is in a recursive form:
 if the first line of the description contains a capital letter
S and a positive integer n (2 <= n <=
10000) separated from each other by a single space, then the circuit
being described consists of n smaller circuits connected in
series; they are described in the successive lines,
 if the first line of the description contains a capital
letter R and a positive integer n (2 <= n
<= 10000) separated from each other by a single space, then the
circuit being described consists of n smaller circuits
connected in parallel (by means of two branching units); they are
described in the successive lines,
 a line containing only one capital letter X
describes a circuit consisting of a single unit only.
The
total number of letters X occurring in the description of a
circuit does not exceed 10000000, and the recursive depth of the
description does not exceed 500.
Output
Your program should write to the standard output. In the first line
there should be one integer equal to the minimal number of connections
that must run on the top side of the board.
Example
For the following input data:
R 3
S 2
X
R 2
S 2
X
X
S 2
X
X
S 3
X
X
X
R 2
X
X
the correct answer is in the following output:
8

Scheme of the seriesparallel circuit for the data from the
example. Solid lines indicate the connections running on the top side
of the board.
