Question

Consider the following pseudocode function.
function Crunch(x is in R)
if x ≥ 100 then
return x/100
else
return x + Crunch(10 · x)
(a) Compute Crunch(5).
Crunch(5) =

Answer 1

@e.mccormick

Answer 2

(b) What happens if you try to compute Crunch(−23)? What does this suggest about an appropriate precondition for this function?

Answer 3

crunch(5)
since x is not >= 100
return x + Crunch(10 · x)
= 5+crunch(10*5) = 5+crunch(50)
crunch 50 will return 50+crunch(50*10)
so we have 5+50+crunch(500)
crunch 500 will return 500/100 = 5
so crunch(5) returns 5+50+5 = 60

Answer 4

I think

Answer 5

Crunch(−23)
will always crunch a number <= 100 so it will go in infinite loop, thus x needs to be positive

Answer 6

Consider the following pseudocode function.
function Crunch(x is in R)
if x ≥ 100 then
return x/100
else
return x + Crunch(10 · x)
(a) Compute Crunch(5).
Crunch(5) =