Let’s look at each one of these laws in more detail and see how it was used in the list_sum algorithm. First, a base case is the condition that allows the algorithm to stop recursing. A base case is typically a problem that is small enough to solve directly. In the list_sum algorithm the base case is a list of length 1.
To obey the second law, we must arrange for a change of state that moves the algorithm toward the base case. A change of state means that some data that the algorithm is using is modified. Usually the data that represents our problem gets smaller in some way. In the list_sum algorithm our primary data structure is a list, so we must focus our state-changing efforts on the list. Since the base case is a list of length 1, a natural progression toward the base case is to shorten the list. This is exactly what happens on line 5 of Listing 4.3.2 when we call list_sum with a shorter list.
The final law is that the algorithm must call itself. This is the very definition of recursion. Recursion is a confusing concept to many beginning programmers. As a novice programmer, you have learned that functions are good because you can take a large problem and break it up into smaller problems. The smaller problems can be solved by writing a function to solve each problem. When we talk about recursion it may seem that we are talking ourselves in circles. We have a problem to solve with a function, but that function solves the problem by calling itself! But the logic is not circular at all; the logic of recursion is an elegant expression of solving a problem by breaking it down into a smaller and easier problems.
In the remainder of this chapter we will look at more examples of recursion. In each case we will focus on designing a solution to a problem by using the three laws of recursion.
Q-2: Suppose you are going to write a recusive function to calculate the factorial of a number. fact(n) returns n * n-1 * n-2 * … Where the factorial of zero is defined to be 1. What would be the most appropriate base case?
