Problem 1.

In your favorite language write a tail-call recursive function. You might need a helper

function. (can be written in Java even though Java doesn't support that feature. If you

need an example check Christoph's notes)

n

i

i =1

Problem 2.

Provide a pseudo code alternative to the following loop that utilizes a GOTO statement

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Algorithm 1 Mah special LOOP

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v1. assume v1 is initialized and positive

v2 <-- 0

LOOP:

if v1 = v2 then

Statement

v2 <-- v2 + 1

else

GoTo OUT:

end if

GoTo LOOP:

OUT:

Problem 3.

Write a recursive function that computes the following expression L= {aⁿ bⁿ, n >= 0}

Problem 4.

Provide an alternative to the following function that utilizes a GOTO statement instead of a WHILE loop

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Algorithm 2 Mah other special LOOP

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v1. assume v1 is initialized and positive

while v1 > 0 do

Statement

v1<-- v1 - 1

end while

Problem 5.

Translate the following function from prefixed to infix notation

(< ( (mod a b)(+ c d)) (* e f))