For a given integer n>1, the smallest integer d>1 that divides n is a prime factor. We can find the prime factorization of n if we find d and then replace n by the quotient of n divided by d, repeathing this until n becomes 1. Write a program that queries the user for a value for n, determines the prime factorization of n in this manner, but displays the prime factors in descending oder. For example for n = 3960 your program should produce:

11 * 5 * 3 * 3 * 2 * 2 * 2

You must use Nyhoff's Stack class (attached); you can not use the STL stack class.

/*-- Stack.cpp------------------------------------------------------------- This file implements Stack member functions. --------------------------------------------------------------------------*/ #include  using namespace std; #include "Stack.h" //--- Definition of Stack constructor Stack::Stack() : myTop(-1) {} //--- Definition of empty() bool Stack::empty() const { return (myTop == -1); } //--- Definition of push() void Stack::push(const StackElement & value) { if (myTop < STACK_CAPACITY - 1) //Preserve stack invariant { ++myTop; myArray[myTop] = value; } else { cerr << "*** Stack full -- can't add new value *** " "Must increase value of STACK_CAPACITY in Stack.h "; //exit(1); } } //--- Definition of display() void Stack::display(ostream & out) const { for (int i = myTop; i >= 0; i--) out << myArray[i] << endl; } //--- Definition of top() StackElement Stack::top() const { if ( !empty() ) return (myArray[myTop]); else { cerr << "*** Stack is empty -- returning garbage value *** "; StackElement garbage; return garbage; } } //--- Definition of pop() void Stack::pop() { if ( !empty() ) myTop--; else cerr << "*** Stack is empty -- can't remove a value *** "; } 

/*-- Stack.h --------------------------------------------------------------- This header file defines a Stack data type. Basic operations: constructor: Constructs an empty stack empty: Checks if a stack is empty push: Modifies a stack by adding a value at the top top: Retrieves the top stack value; leaves stack unchanged pop: Modifies stack by removing the value at the top display: Displays all the stack elements Class Invariant: 1. The stack elements (if any) are stored in positions 0, 1, . . ., myTop of myArray. 2. -1 <= myTop < STACK_CAPACITY --------------------------------------------------------------------------*/ #include  #ifndef STACK #define STACK const int STACK_CAPACITY = 128; typedef int StackElement; class Stack { public: /***** Function Members *****/ /***** Constructor *****/ Stack(); /*------------------------------------------------------------------------ Construct a Stack object. Precondition: None. Postcondition: An empty Stack object has been constructed (myTop is initialized to -1 and myArray is an array with STACK_CAPACITY elements of type StackElement). -----------------------------------------------------------------------*/ bool empty() const; /*------------------------------------------------------------------------ Check if stack is empty. Precondition: None Postcondition: Returns true if stack is empty and false otherwise. -----------------------------------------------------------------------*/ void push(const StackElement & value); /*------------------------------------------------------------------------ Add a value to a stack. Precondition: value is to be added to this stack Postcondition: value is added at top of stack provided there is space; otherwise, a stack-full message is displayed and execution is terminated. -----------------------------------------------------------------------*/ void display(ostream & out) const; /*------------------------------------------------------------------------ Display values stored in the stack. Precondition: ostream out is open. Postcondition: Stack's contents, from top down, have been output to out. -----------------------------------------------------------------------*/ StackElement top() const; /*------------------------------------------------------------------------ Retrieve value at top of stack (if any). Precondition: Stack is nonempty Postcondition: Value at top of stack is returned, unless the stack is empty; in that case, an error message is displayed and a "garbage value" is returned. -----------------------------------------------------------------------*/ void pop(); /*------------------------------------------------------------------------ Remove value at top of stack (if any). Precondition: Stack is nonempty. Postcondition: Value at top of stack has been removed, unless the stack is empty; in that case, an error message is displayed and execution allowed to proceed. -----------------------------------------------------------------------*/ private: /***** Data Members *****/ StackElement myArray[STACK_CAPACITY]; int myTop; }; // end of class declaration #endif