A Practical Introduction to Data Structures and Algorithm Analysis

130 Chap. 4 Lists, Stacks, and Queuester 1 is made, requiring that the stack store the calling address (say β 3 ) and currentvalue (which is 2).At this point, we have reached the base case for fact, and so the recursionbegins to unwind. Each return from fact involves popping the stored value forn from the stack, along with the return address from the function call. The returnvalue for fact is multiplied by the restored value for n, and the result is returned.Because an activation record must be created and placed onto the stack foreach subroutine call, making subroutine calls is a relatively expensive operation.While recursion is often used to make implementation easy and clear, sometimesyou might want to eliminate the overhead imposed by the recursive function calls.In some cases, such as the factorial function of Section 2.5, recursion can easily bereplaced by iteration.Example 4.2 As a simple example of replacing recursion with a stack,consider the following non-recursive version of the factorial function.static long fact(int n) { // Compute n!// To fit n! in a long variable, require n < 21assert (n >= 0) && (n 1) S.push(n--);long result = 1;while (S.length() > 0)result = result * S.pop();return result;}Here, we simply push successively smaller values of n onto the stack untilthe base case is reached, then repeatedly pop off the stored values andmultiply them into the result.In practice, an iterative form of the factorial function would be both simplerand faster than the version shown in Example 4.2. Unfortunately, it is not alwayspossible to replace recursion with iteration. Recursion, or some imitation of it, isnecessary when implementing algorithms that require multiple branching such asin the Towers of Hanoi algorithm, or when traversing a binary tree. The Mergesortand Quicksort algorithms of Chapter 7 are also examples in which recursion isrequired. Fortunately, it is always possible to imitate recursion with a stack. Let usnow turn to a non-recursive version of the Towers of Hanoi function, which cannotbe done iteratively.