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

Answer 2

Recursion functions are functions whose execution is controlled from within the function

The PrintFactorial()'s recursive case

The code segment written in Python, where comments are used to explain each action is as follows:

#This defines the function

def PrintFactorial(n):

#if n is 1, this returns the value of n

  if n == 1:

      return n

#If otherwise

  else:

#This calculates the factorial, recursively

      return n*PrintFactorial(n-1)

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