The max product of consecutive elements in an array

Question

I was asked this algorithm question during my onsite interview. Since I was not asked to sign NDA, I post it here for an answer.

Given an array of REAL

Answer 1

Ignoring negative numbers for the moment...

Let A[i..j] mean A[i]*A[i+1]*...*A[j]

The problem is to find max(A[i..j])

Notice that A[i..j] = A[0..j] / A[0..i-1]

So if we calculate A[0..x] for all x.

We can then determine max(A[i..j]) = max(A[0..x]) / min(A[0..y])