Example 10.4.1

Consider a rather simple function to determine if an integer X is prime or not. Y is a helper variable that is used as the devisor. When calling the function initially, Y = X - 1

We see that Prime has two base cases and one recursive call.

Example 10.4.2

Here is a function that has multiple recursive calls. Given an int array named arr, function isSubsetSum determines whether some of the values in arr add up to sum. For example, given the number 3, 8, 1, 7, and -3, with sum = 4, the result is true because the values 3 and 1 sum to 4. If sum = 6, then the result will be true because the \(8 + 1 + -3 = 6\). On the other hand, if sum = 2 then the result is false there is no combination of the five numbers that adds up to 2. In this code, variable n is the number of values that we look at. We don't want to just use arr.length because the recursive calls need to limit their work to part of the array.

This example has two base cases and two recursive calls.

Example 10.4.3

Here is a function that has multiple base cases and multiple recursive calls. Function paths counts the number of different ways to reach a given basketball score. Recall that in Basketball, it is possible to get points in increments of 1, 2, or 3. So if n = 3, then paths will return 4, since there are four different ways to accumulate 3 points: \(1+1+1, 1+2, 2+1,\) and 3.

This function has three base cases and three recursive calls.