Memoization of Simple Arithmetic for loop

Question

While reading another interesting post regarding for loop optimization, I noticed one of the commentors suggested using memoization technique.

I dug around a bit to learn more and found several examples of how to memoize functions such as factorial or fibonacci sequence just to name two.

I can follow these and understand the general idea but I'm struggling with how this can be applied to a simple arithmetic operation such as the one in the original post:

for (j=0; j < ARRAY_SIZE; j++) {
    sum += array[j];
}

What would be the portion that has already been calculated?

Is it possible or was the commentor incorrect on their assumption that it could apply here?

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Just interested in learning memoization techniques in this post, I know there are other methods such as unrolling, that provide significant optimization.

Answer 1

That for-loop can't be memoized in itself. Memoization is applicable when you can store previously solved subproblems and use them to calculate bigger subproblems/problems. It's therefore closely related to functions that can be solved by recursion since this also means that a problem is split into subproblems. (See also: Dynamic programming).