Question

I was solving practice questions from a book when I stumbled upon this one :

*Describe a recursive algorithm that will check if an array A of
integers contains an integer A[i] that is the sum of two integers
that appear earlier in A, that is, such that

 A[i] = A[j] +A[k] for j,k < i.

*

I have been thinking about this for a few hours but haven’t been able to come up with a good recursive algorithm.

Answer 1

A recursive solution without any loops (pseudocode):

bool check (A, i, j, k)
    if (A[j] + A[k] == A[i])
        return true
    else
        if      (k + 1 < j)      return check (A, i, j, k + 1)
        else if (j + 1 < i)      return check (A, i, j + 1, 0)
        else if (i + 1 < A.size) return check (A, i + 1, 1, 0)
        else                     return false

The recursive function is called with check(A, 2, 1, 0). To highlight the main part of the algorithm it does not check if the array initially has more than two elements.