Question

Write code to complete PrintFactorial()'s recursive case. Sample output if userVal is 5:5! = 5 * 4 * 3 * 2 * 1 = 120

Answer 1

Answer:

Here is the C++ program:

#include <iostream>  //to use input output functions

using namespace std;   //to access objects like cin cout

void PrintFactorial(int factCounter, int factValue){  // method definition

  int nextCounter = 0;  // initialize value of nextCounter by 0

  int nextValue = 0;   // initialize value of nextValue by 0

  if (factCounter == 0) { //base case 1: 0! = 1          

     cout << "1" << endl;    }  //displays 1 in the output

  else if (factCounter == 1) {  //base case 2: 1! = 1  

     cout << factCounter << " = " << factValue << endl;    } //displays 1 in result    

  else {  //recursive case                          

     cout << factCounter << " * ";

     nextCounter = factCounter - 1;  //decrements factCounter by 1

     nextValue = nextCounter * factValue;  // multiplies values of nextCounter and factValue and assigns the result to nextValue

PrintFactorial( nextCounter,  nextValue);    } }  //recursively calls PrintFactorial method to compute the factorial

int main() {  //start of main function

  int userVal = 0;   //initialize the userVal variable to 0

  userVal = 5;  //assigns 5 to the userVal variable

  cout << userVal << "! = ";  //prints the userVal with ! =

  PrintFactorial(userVal, userVal); } //calls PrintFactorial method to compute the factorial of userVal i.e. 5

Explanation:

I will explain the logic of the program with an example.

The value of variable userVal is 5  

This is passed to the method PrintFactorial()

1st step:

void PrintFactorial(int factCounter, int factValue) becomes:  

PrintFactorial(5, 5)

PrintFactorial method has two base conditions which do not hold because the factCounter is 5 here which is neither 1 nor 0 so the program control moves to the recursive part.  

cout << factCounter << " * ";

In recursive part, the above statement prints the value of factCounter  followed by an asterisk on the output screen. So this prints:

5 *

nextCounter = factCounter - 1;

This statement decrements the value of factCounter by 1 and assigns it to nextCounter as:

nextCounter = 5 - 1;

nextCounter = 4

nextValue = nextCounter * factValue;  multiplies the value of nextCounter by factValue and stores result in nextValue . So

nextValue = 4 * 5  

nextValue = 20

PrintFactorial( nextCounter,  nextValue);  this statement calls the PrintFactorial() recursively to perform the above steps again until the base condition is reached. This statement becomes:  

PrintFactorial(4,20)

2nd step:

PrintFactorial method has two base conditions which do not hold because the factCounter is 4 here which is neither 1 nor 0 so the program control moves to the recursive part.  

cout << factCounter << " * ";

In recursive part, the above statement prints the value of factCounter  followed by an asterisk on the output screen. So this prints:

5* 4 *

nextCounter = factCounter - 1;

This statement decrements the value of factCounter by 1 and assigns it to nextCounter as:

nextCounter = 4 - 1;

nextCounter = 3

nextValue = nextCounter * factValue;  multiplies the value of nextCounter by factValue and stores result in nextValue . So

nextValue = 3 * 20

nextValue = 60

PrintFactorial( nextCounter,  nextValue);   This statement becomes:  

PrintFactorial(3,60)

3rd step:

PrintFactorial method has two base conditions which do not hold because the factCounter is 3 here which is neither 1 nor 0 so the program control moves to the recursive part.  

cout << factCounter << " * ";

In recursive part, the above statement prints the value of factCounter  followed by an asterisk on the output screen. So this prints:

5* 4 * 3 *

nextCounter = factCounter - 1;

This statement decrements the value of factCounter by 1 and assigns it to nextCounter as:

nextCounter = 3 - 1;

nextCounter = 2

nextValue = nextCounter * factValue;  multiplies the value of nextCounter by factValue and stores result in nextValue . So

nextValue = 2 * 60

nextValue = 120

PrintFactorial( nextCounter,  nextValue);  This statement becomes:  

PrintFactorial(2,120)

4th step:

PrintFactorial method has two base conditions which do not hold because the factCounter is 2 here which is neither 1 nor 0 so the program control moves to the recursive part.  

cout << factCounter << " * ";

In recursive part, the above statement prints the value of factCounter  followed by an asterisk on the output screen. So this prints:

5* 4 * 3 * 2 *

nextCounter = factCounter - 1;

This statement decrements the value of factCounter by 1 and assigns it to nextCounter as:

nextCounter = 2 - 1;

nextCounter = 1

nextValue = nextCounter * factValue;  multiplies the value of nextCounter by factValue and stores result in nextValue . So

nextValue = 1 * 120

nextValue = 120

PrintFactorial( nextCounter,  nextValue);  This statement becomes:  

PrintFactorial(1,120)

Now the base case 2 evaluates to true because nextCounter is 1

cout << factCounter << " = " << factValue  statement prints the value of factCounter i.e. 1 followed by an equal sign = followed by value of factValue i..e 120

So the output of the above program with userVal = 5 is:  

5! = 5 * 4 * 3 * 2 * 1 = 120