Draw the recursion trace of the Power algorithm (Code Fragment 4.4, which computes the power function p(x,n)) for computing p(2,9).

Data from in Fragment 4.4

Computing the power function using linear recursion.
To analyze the running time of the algorithm, we observe that each recursive call of function Power(x,n) divides the exponent, n, by two. Thus, there are O(logn) recursive calls, not O(n). That is, by using linear recursion and the squaring technique, we reduce the running time for the computation of the power function from O(n) to O(logn), which is a big improvement.