# SICP Solutions

### Section - Procedures and the Processes They Generate

#### Exercise 1.15

We can see that the procedure keeps on dividing the angle, $\alpha$ by $3$ until it becomes less than $0.1$. Clearly at max number of times the division is required is ${log}_3 {\alpha}$.

Thus the time complexity is ${ log }_3 { \alpha }$.

Also since the procedure is recursive process and the maximum depth it reaches is ${ log }_3 { \alpha }$, the space complexity is also ${ log }_3 { \alpha }$.

To find number of steps for $12.15$, we can see: $12.15/3 = 4.05$,
$4.05/3 = 1.35$,
$1.35/3 = 0.45$,
$0.45/3 = 0.15$,
$0.15/3 = 0.05$.

Thus we have to divide $5$ times. Thus $p$ is called $5$ times.