Chapter 4, Problem 4R

Explanation of Solution

Recursion trace of “Power” algorithm to compute “p(2,9)”:

• The power is calculated using the following function,

$\text{p}\left(\text{x,n}\right)\text{=}\{\begin{array}{c}\text{1 if n=0}\\ \text{x}\text{.p}{\left(\text{x,}\frac{\left(\text{n}-\text{1}\right)}{\text{2}}\right)}^{\text{2}}\\ \text{p}{\left(\text{x,}\frac{\text{n}}{\text{2}}\right)}^{\text{2}}\text{ if n>0 is even}\\ \end{array}\text{if n>0 is odd}$

• In “p(2,9)”, the value of “x” is “2” and the value of “n” is “9”.
• Here, the value “9” is odd.
• Hence the formula to compute “p(2,9)” is as follows,

$\text{p}\left(\text{x,n}\right)=\text{x}$