Naive Solution: Maximum Pairwise Product

Naive algorithm

A naive way to solve the Maximum Pairwise Product Problem is to go through all possible pairs of the input elements $A[1...n] = [a_1,...,a_n]$ and to find a pair of distinct elements with the largest product, as given in the following pseudocode.

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 $MaxPairwiseProductNaive(A[1 . . . n])$:
  $product \leftarrow 0$
  for $i$ from $1$ to $n$:
       for $j$ from $1$ to $n$:
              if $i\neq j$:
                     if $product < A[i] \cdot A[j]$:
                            $product \leftarrow A[i] \cdot A[j]$
 return $product$

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This code can be optimized and made more compact as follows:

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 $MaxPairwiseProductNaive(A[1 . . . n])$:
  $product \leftarrow 0$
  for $i$ from $1$ to $n$:
       for $j$ from $i+1$ to $n$:
              $product \leftarrow max(product, A[i] \cdot A[j])$
 return $product$

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