A Practical Introduction to Data Structures and Algorithm Analysis

132 Chap. 4 Lists, Stacks, and Queuesstatic void TOH(int n, Pole start,Pole goal, Pole temp) {// Make a stack just big enoughStack S = new AStack(2*n+1);S.push(new TOHobj(operation.TOH, n,start, goal, temp));while (S.length() > 0) {TOHobj it = S.pop(); // Get next taskif (it.op == operation.MOVE) // Do a movemove(it.start, it.goal);else if (it.num > 0) { // Imitate TOH recursive// solution (in reverse)S.push(new TOHobj(operation.TOH, it.num-1,it.temp, it.goal, it.start));S.push(new TOHobj(operation.MOVE, it.start,it.goal)); // A move to doS.push(new TOHobj(operation.TOH, it.num-1,it.start, it.temp, it.goal));}}}We first define an enumerated type called TOHop, with two valuesMOVE and TOH, to indicate calls to the move function and recursive callsto TOH, respectively. Note that an array-based stack is used, because weknow that the stack will need to store exactly 2n + 1 elements. The newversion of TOH begins by placing on the stack a description of the initialproblem of n rings. The rest of the function is simply a while loop thatpops the stack and executes the appropriate operation. In the case of a TOHoperation (for n > 0), we store on the stack representations for the threeoperations executed by the recursive version. However, these operationsmust be placed on the stack in reverse order, so that they will be popped offin the correct order.Some “naturally recursive” applications lend themselves to efficient implementationwith a stack, because the amount of information needed to describe a subproblemis small. For example, Section 7.5 discusses a stack-based implementationfor Quicksort.4.3 QueuesLike the stack, the queue is a list-like structure that provides restricted access toits elements. Queue elements may only be inserted at the back (called an enqueue