Textbook Problem

For each of the algorithm segments in 6—19, assume that n is a positive integer. (a) Compute the actual number of elementary operations (additions, subtractions, multiplications, divisions, and comparisons) that are performed when the algorithm segment is executed. For simplicity, however, count only comparisons that occur within if then statements; ignore those implied by for-next loops. (b) Use the theorem on polynomial orders to find an order for the algorithm segment.

15. for $i:=1$ to $n-1$ $\begin{array}{l}p:=1\\ q:=1\end{array}$ for $j:=i+1$ to n $\begin{array}{l}p:=p\cdot c\left[j\right]\\ q:=q\cdot {\left(c\left[j\right]\right)}^2\end{array}$ next j $r:=p+q$next i