Consider a set S of n points in the plane and assume the convex layers of S have been computed and are available in array based representations. Assume the layers are numbered L1, L2, ..., Lk, from the outer layer to the innermost layer (that is, L is the convex hull of S). Given a point a, describe an efficient algorithm to find the innermost layer that contains a or report no layer contains a (that is, a is outside the convex hull of S). Note: your grade will depend on the time complexity of the algorithm, that is an O(n) time algorithm will get a better grade than an O(na) time algorithm. Consider a set S of n points in the plane and assume the convex layers of S have been computed and are available in array based representations. Assume the layers are numbered L1, L2, ..., Lk, from the outer layer to the innermost layer (that is, L is the convex hull of S). Given a point a, describe an efficient algorithm to find the innermost layer that contains a or report no layer contains a (that is, a is outside the convex hull of S). Note: your grade will depend on the time complexity of the algorithm, that is an O(n) time algorithm will get a better grade than an O(na) time algorithm