Problem B: Smeech
Professor Octastichs has invented a new programming language, Smeech.
An expression in Smeech may be a positive or negative integer, or
may be of the form
(p e1 e2)
where p is a real number between 0 and 1 (inclusive) and
e1 and e2 are Smeech expressions.
The value represented by a Smeech expression is as follows:
- An integer represents itself
- With probability p, (p e1 e2) represents
x+y where x is the value of e1 and y is the value of e2;
otherwise it represents x-y.
Given a Smeech expression, what is its expected value?
Input consists of several Smeech expressions, one per line, followed by a
line containing (). For each expression, output its expected value to
two decimal places.
Sample Input
7
(.5 3 9)
()
Output for Sample Input
7.00
3.00
Gordon V. Cormack
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