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) Compute Crunch(117).

Discrete math

Consider the following pseudocode function. function Crunch$$\displaystyle{\left({x}\ {i}{s}\in{R}\right)}{\quad\text{if}\quad}{x}≥{100}$$ then return x/100 else return $$x + Crunch(10 \cdot x)$$ Compute Crunch(117).

2021-01-01

Given
Crunch (x is in R)
if $$\displaystyle{x}\Rightarrow{100}$$ then
returen $$\displaystyle\frac{{x}}{{100}}$$
else return $$x+$$Crunch $$\displaystyle{\left({10}\cdot{x}\right)}$$
We need to compute Crunch(117)
$$x=117$$
Since 117 is at least 100, we need to execute the then-statement "return $$\displaystyle\frac{{x}}{{100}}$$" and thus we need to divide the input $$x=117$$ by 100:
$$\displaystyle\frac{{x}}{{100}}=\frac{{117}}{{100}}={1.17}$$
Thus Crunch $$(117)=1.17$$