(15 pts] For a given array of distinct real numbers A, a local minimum is a value in the array that is strictly smaller than its immediate neighboring element(s) (all entries have two such neighboring elements, except the first and last which only have one). Note that any array will have at least one local minimum, since the global minimum must also be a local minimum. Devise an algorithm that will find the location index) of a local minimum in an array of length n with elog n) comparisons, and make sure you justify why your algorithm is correct