Question

Consider a definition of mystery():

a.mystery(0,N) = N
b.mystery(P,Q) = mystery(P-1, Q+1)
According to this definition, what is mystery(2,4)?

Answer 1

To calculate mystery(2,4), apply the recursive relationship twice, first getting mystery(1,5), then mystery(0,6), finally resulting in the value 6.

Step-by-step explanation:

The function mystery() defined in the question uses a recursive relationship to transform two numbers. When the function mystery(2,4) is called, we can apply the recursive step twice according to the definition provided.

1. mystery(2,4) becomes mystery(1, 4+1) or mystery(1,5).
2. Applying the step again, mystery(1,5) becomes mystery(0, 5+1) or mystery(0,6).

Now, according to the base case of the function, we see that mystery(0,N) equates to N. Therefore, mystery(2,4) simplifies to 6.

In summary, the iterative process involves decreasing the first argument by 1 and increasing the second argument by 1 until the first argument reaches zero, at which point the second argument is the result of the function.