Question

What does the following code do? 1 public int mystery( int a, int b ) 2 { 3 if ( b == 1 ) 4 return a; 5 else 6 return a + mystery( a, b - 1 ); 7 } // end method mystery

Short answer

The code multiplies `a` by `b` using recursion.

Step-by-step solution

Understand the Method Signature

The method is named `mystery` and it takes two integer parameters, `a` and `b`. It returns an integer value.

Examine the Base Case

The method has an `if` statement that checks if `b` is equal to 1. If true, it returns `a`. This is the base case of the recursion, terminating further recursive calls when `b` reaches 1.

Analyze the Recursive Case

If `b` is not equal to 1, the method returns `a` plus the result of a recursive call to itself with the same `a` and `b` decremented by 1 (`mystery(a, b - 1)`). This suggests repeated addition.

Derive the Functionality

The function calculates the multiplication of `a` and `b` by recursively adding `a` to itself `b` times. Each call reduces `b` by 1 until it reaches the base case.

Key concepts

Base Case

In recursive functions, it's crucial to have a base case. The base case acts like a stopping point and prevents the function from calling itself indefinitely.
In the `mystery` function, the base case is found in the line where the condition checks if `b` is equal to 1. If this condition is met, the function simply returns `a`.

• This means that when `b` is 1, we stop the recursive calls.
• It provides a clear point where the recursion ends, ensuring the process doesn't continue infinitely.

Understanding and correctly implementing a base case is essential for any recursive function to work properly without causing an error or stack overflow.

Recursive Case

The recursive case is where the function calls itself with modified parameters. It progresses the function towards the base case.
In the `mystery` function, if `b` is not equal to 1, the function enters the recursive case. Here, it calculates `a + mystery(a, b - 1)`. This line:

• Decrements `b` by 1 in each recursive call, ensuring we eventually reach the base case.
• Adds `a` to the result of the recursive function call `mystery(a, b - 1)`.

The recursive case thus helps in building up the final answer step-by-step through multiple recursive calls, reducing `b` by one at each step until it hits 1.

Multiplication through Recursion

While the code might look mysterious at first with its recursive pattern, what it accomplishes is actually a simple yet elegant task: multiplication through recursion.
By leveraging these repeated recursive steps, the function achieves multiplication by essentially adding the number `a` to itself `b` times, which is what multiplication signifies.

• If `b` is 3 and `a` is 4, the process would look like: 4 (from `b`=1) + 4 + 4, giving 12, which is 4 \( \times \) 3.
• Each call contributes to a partial sum, neatly combining all instances of `a` and yielding the product of `a` and `b` as the final result.
• Thus, through the magic of recursion, it implements repeated addition, producing the effect of multiplication without using the `*` operator directly.

This approach demonstrates the power of recursion in solving seemingly complex tasks using simple repetitive processes.