Question $3.$

$[20$ marks$]$

Write the pseudocode of an efficient algorithm to compute the value of $F(x,y,n)$

below. The algorithm should have its worst$-$case running time in O$-$notation as tight as

possible. Marks will be deducted if the algorithm is not efficient enough in terms of

running time. In this problem, we do not care about space cost.

Then, analyze the worst$-$case running time of your algorithm in O$-$notation in terms of

$n.$

$F(x,y,n)={\displaystyle \underset{a=1}{\overset{n}{}}}{x}^a\frac{2}{y^{n-a}}$