Question

include 4 using std::cout; 5 using std::cin; 6 using st… # What does the following program do? 1 // Exercise 6.50: ex06_50.cpp 2 // What does this program do? 3 #include 4 using std::cout; 5 using std::cin; 6 using std::endl; 7 8 int mystery( int, int ); // function prototype 9 10 int main() 11 { 12 int x, y; 13 14 cout << "Enter two integers: "; 15 cin >> x >> y; 16 cout << "The result is " << mystery( x, y ) << endl; 17 18 return 0; // indicates successful termination 19 } // end main 20 21 // Parameter b must be a positive integer to prevent infinite recursion 22 int mystery( int a, int b ) 23 { 24 if ( b == 1 ) // base case 25 return a; 26 else // recursion step 27 return a + mystery( a, b - 1 ); 28 } // end function mystery

Short answer

The program multiplies two integers using recursion.

Step-by-step solution

Understanding the main function

The program begins execution in the `main()` function. It first declares two integer variables, `x` and `y`. Then, it prompts the user with the message "Enter two integers:" and reads two integer values from the user input into the variables `x` and `y`.

Invoking the mystery function

After obtaining user input for `x` and `y`, the program calls the `mystery` function with `x` and `y` as arguments. It then prints out the result prefixed with the message "The result is".

Analyzing the mystery function

The `mystery` function is defined to take two integer parameters, `a` and `b`. It performs a recursive operation. If `b` equals 1, it returns `a` as the base case. Otherwise, it returns `a` plus the result of calling `mystery(a, b - 1)`. This continues until `b` equals 1.

Understanding the recursive process

The `mystery` function calculates the product of `a` and `b` using the addition operation repetitively. It essentially computes `a` multiplied by `b` by adding `a` to itself `b` times, illustrating a simple form of multiplying without using the multiplication operator.

Concluding the function's operation

The final result of this recursive process is returned to the `main()` function where it is printed. The `mystery` function effectively computes the multiplication of the two integers entered by the user.

Key concepts

Function Recursion

Recursion in programming can feel a bit like magic at first. It's when a function calls itself in order to solve a problem. This concept might seem tricky but is incredibly powerful once understood. In our example, the program focuses on the `mystery` function using recursion.

• Recursive Process: The fundamental idea here is to break down a problem into smaller, more manageable pieces, tackling each one with the repetition of calling the same function. This function is then expected to handle these pieces until reaching an endpoint, known as the base case.
• Base Case: In recursion, identifying a base case is crucial. It's the condition where the function stops calling itself, preventing what could otherwise become an infinite loop. For our mystery function, the base case is when `b` equals 1.

The combination of these aspects forms the backbone of a recursive solution. Understanding them makes handling recursive functions much clearer.

Recursive Function

A recursive function is a specific type of function designed to call itself within its own definition. This self-referential behavior allows it to solve complex problems by breaking them down into simpler sub-problems, repeatedly. Let's dive into what makes recursive functions special using the `mystery` function from the exercise.

• Recursive Definition: The `mystery` function is defined recursively. It first checks if the input `b` is 1, in which case it simply returns `a`. Otherwise, it performs the recursive step by calling itself with a reduced value of `b`, effectively combining the current value with a simpler version of the same problem.
• Parameters Importance: Here, the parameters `a` and `b` control how many times the function is called. The parameter `b` decreases with each recursive call, guiding the function towards the base case and ensuring it eventually terminates.

Recursive functions, once understood, reveal an elegant approach to problem-solving, allowing programmers to express solutions succinctly.

Multiplication through Addition

The mystery function in this program demonstrates a clever technique of achieving multiplication through repeated addition. Rather than using the multiplication operator, the function makes use of addition to yield the same result.

• Concept: Multiplication through addition involves adding a number to itself repeatedly. In mathematical terms, multiplying `a` by `b` is equivalent to adding `a` to itself `b` times.
• In Action: In the `mystery` function, the recursive calls effectively accumulate the total by incrementally adding `a` until `b` becomes 1. Each recursive call represents another addition of `a`, illustrating multiplication via repeated addition.

This demonstrates that programming affords multiple methods to achieve the same goal, offering insights into various strategies and problem-solving approaches.