Data Structures and Algorithm Analysis - Computer Science at ...

Sec. 4.2 Stacks 123you 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./** @return n! */static long fact(int 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.An iterative form of the factorial function is both simpler and faster than theversion shown in Example 4.2. But it is not always possible to replace recursionwith iteration. Recursion, or some imitation of it, is necessary when implementingalgorithms that require multiple branching such as in the Towers of Hanoi algorithm,or when traversing a binary tree. The Mergesort and Quicksort algorithmsof Chapter 7 are also examples in which recursion is required. Fortunately, it is alwayspossible to imitate recursion with a stack. Let us now turn to a non-recursiveversion of the Towers of Hanoi function, which cannot be done iteratively.Example 4.3 The TOH function shown in Figure 2.2 makes two recursivecalls: one to move n − 1 rings off the bottom ring, and another to movethese n − 1 rings back to the goal pole. We can eliminate the recursion byusing a stack to store a representation of the three operations that TOH mustperform: two recursive calls and a move operation. To do so, we must firstcome up with a representation of the various operations, implemented as aclass whose objects will be stored on the stack.Figure 4.23 shows such a class. We first define an enumerated typecalled TOHop, with two values MOVE and TOH, to indicate calls to themove function and recursive calls to TOH, respectively. Class TOHobjstores five values: an operation field (indicating either a move or a newTOH operation), the number of rings, and the three poles. Note that the