The following algorithm takes an unsorted list of positive integers, along with two integers x and y$.$ It returns the largest number, z$,$ in the list such that either z$^$x$=$y or z$^$y$=$x is true. It returns $0$ if no such z exists. The algorithm assumes that the list size, n$,$ is a power of $2$ with n$\backslash$ge$\{\}1.($An underscore is for a subscript. A caret is for an exponent. If these need multiple characters, they are enclosed in curly braces.$)$