Question

What does the following program do? 1 // Exercise 15.12 Solution: MysteryClass.java 2 3 public class MysteryClass 4 { 5 public int mystery( int array2[], int size ) 6 { 7 if ( size == 1 ) 8 return array2[ 0 ]; 9 else 10 return array2[ size - 1 ] + mystery( array2, size - 1 ); 11 } // end method mystery 12 } // end class MysteryClass 1 // Exercise 15.12 Solution: MysteryTest.java 2 3 public class MysteryTest 4 { 5 public static void main( String args[] ) 6 { 7 MysteryClass mysteryObject = new MysteryClass(); 8 9 int array[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }; 10 11 int result = mysteryObject.mystery( array, array.length ); 12 13 System.out.printf( "Result is: %d\n", result ); 14 } // end method main 15 } // end class MysteryTest

Short answer

The program calculates and prints the sum of all elements in the array, which is 55.

Step-by-step solution

Understanding the Base Case

The method `mystery` checks if the size of the array equals 1. If true, it returns the first element of the array, `array2[0]`. This is the base case for the recursive function, which stops the recursion.

Analyzing the Recursive Case

If the size is not 1, the method returns the last element of the current sub-array `array2[size - 1]` added to the result of a recursive call to `mystery` with the size decremented by 1. This operation continues until it hits the base case.

Recognizing Pattern in Recursion

In each recursive call, the method adds the elements one by one from the end towards the beginning of the array until all elements are summed up. This recursive pattern effectively calculates the sum of all elements in the array.

Running the Test

In the `MysteryTest` class, the `main` method creates an instance of `MysteryClass` and initializes an integer array with elements from 1 to 10. It calls the `mystery` method with this array and its length, expecting the sum of the array's elements.

Calculating the Output

The array elements from 1 to 10 are summed, resulting in \(1 + 2 + 3 + \, ... \, + 10 = 55\). The program prints "Result is: 55" as the output.

Key concepts

Recursive Function

Recursion is a concept in programming where a function calls itself to solve a problem. In the context of Java, a recursive function repeatedly invokes itself, processing smaller portions of the original problem, until a certain condition, known as the base case, is satisfied to halt further calls.

The key benefits of using recursion include simplicity in solving problems that have a repetitive structure, like tree traversal, factorial calculations, and the exercise at hand—summing array elements. Recursion is often compared to iteration. Both can achieve similar outcomes, but recursion can sometimes result in shorter and potentially more expressive code.

However, it's important to consider the stack memory usage caused by recursive calls. Each call consumes stack space, leading to potential issues like "stack overflow" if the recursion depth is too high. As such, understanding and structuring recursive functions effectively is crucial.

Base Case

The base case is the stopping criterion in recursion. It determines when the recursive calls should end. In the `MysteryClass` example, the base case is when the size of the array is 1.

When defining a recursive function, it's crucial to specify this condition clearly, as it prevents the function from calling itself indefinitely, which could lead to errors or program crashes. Without a well-defined base case, recursion would lack termination, making the function unsustainable in execution.

In the provided exercise, the base case triggers when the function encounters an array of size 1. It then returns the first and only element of the array, ensuring that no further recursive calls occur. This well-defined base case ensures that every recursive path finds closure, allowing the solution to proceed back up the recursive chain correctly.

Array Sum

The task of summing elements in an array can be naturally approached through recursion. The `mystery` function in the `MysteryClass` example is essentially a recursive function that sums elements of an array.

• It starts by checking whether the array's size is 1. If so, it returns the single element, serving as the base result.
• If not, it takes the last element of the array slice provided and adds it to the sum of the previous elements computed through a recursive call.

This approach ensures that elements are added in reverse order, from the last to the first, but ultimately achieves the sum of all numbers in the array of any given size.

The recursion moves towards the base case by reducing the size of the array in each call. Once reaching the base case, it adjoins the accumulated sums as it returns through the recursive calls, producing the final result thenceforth.

MysteryClass Example

The exercise provided involves the `MysteryClass`, within which the `mystery` method is implemented. This example sums the elements of a pre-specified integer array using recursion.

Upon initialization of an array with elements from 1 to 10 in the `MysteryTest` class, the main method invokes the `mystery` function with this array and its length. Each recursive call reduces the problem size by shrinking the array's size passed to the function by 1, until it meets the base case.

• The initial call targets summing up all elements in the array.
• This leads to subsequent steps where portions of the array are progressively summed up until the whole array is summed.

Ultimately, the process reveals the total sum, 55 in the given instance, demonstrating the strength and efficiency of recursion within this seemingly straightforward use case. Even though the method is called "mystery," the logic behind it unfolds as a sum calculator, unraveling the method's intentions seamlessly upon execution.