Recursion

This week we spent a considerable amount of time on recursion, and implementing recursive algorithms.  Basically, recursion means that a function can call itself within its definition.  While this provides a way to solve a complicated problem in a simple and elegant way, one must be very cautious when executing a recursive algorithm.   To elaborate, a recursive algorithm must always have a base case (terminating condition), otherwise you will have an infinite recursion, and end up with a runtime error (although other errors could possibly occur).

Prior to this class, my only previous encounter with recursion was with determinants.  To explain, the determinant of an n*n matrix is computed from the determinants of several (n-1)*(n-1) matrices, and the determinants of these (n-1)*(n-1) matrices may then be computed from the determinants of (n-2)*(n-2) matrices, etc.  In this case, the 2*2 matrix serves as the base case, as it can easily be computed.  This procedure is often referred to as Laplacian Expansion.