1. (24 pts) Translate the following expression into (a) postfix and (b) prefix notation:
(b + sqrt(b×b − 4×a×c))/(2×a)
(26 pts) Some languages (e.g., Algol 68) do not employ short-circuit evaluation for Boolean expressions. However, in such languages an if…then…else construct (which only evaluates the arm that is needed) can be used as an expression that returns a value. Show how to use if…then…else to achieve the effect of short-circuit evaluation for A and B and for A or B.
(24 pts) Consider a midtest loop, here written in C, that processes all lines in the input until a blank line is found:
for ( ; ; )
{
line = read_line();
if (all_blanks(line)) break; process_line(line);
}
Show how you might accomplish the same task in C using a (a) while and (b) do loop, if break instructions were not available.
(26 pts) Write a tail-recursive function in Scheme to compute n factorial (n! = 1×2×…×n). You will probably want to define a “helper” function, as discussed in the textbook.
(Extra Credit - 10 pts) Give an example in C in which an in-line subroutine may be significantly faster than a functionally equivalent macro. Give another example in which the macro is likely to be faster. Hint: think about applicative versus normal-order evaluation of arguments.
