Does this algorithm have a name?

Question

Does this algorithm have a name? I've listed three examples of it below. I'm wanting to document some code that uses this algorithm, and I don't know what to call it. My version is way more complicated but it is fundamentally this.

Example 1:

var maxValue = Int32.MinValue;
foreach (var value in new [] {2, 3, 4, 4, -3, 1, 7})
{
    if (value > maxValue)
        maxValue = value;
}

Example 2:

var minValue = Int32.MaxValue;
foreach (var value in new [] {7, 6, 5, 4, 3, 2, 20, 42})
{
    if (value < maxValue)
        minValue = value;
}

Example 3:

var mostPrimeFactors = 0;
var valueWithMostPrimeFactors = 0
foreach (var value in new [] {2, 4, 6, 8, 12, 60, 360})
{
    var primeFactorCount = GetPrimeFactors(value).Count;
    if (primeFactorCount > mostPrimeFactors)
    {
        mostPrimeFactors = primeFactorCount
        mostPrimeFactors = value;
    }
}

Answer 1

As @FrankHileman says, maxima and minima seem to be the operations being performed by these algorithms.

However, maxima and minima are mathematical continuous functions rather than things that reduce a discrete set of values to a single value.

As applied to an array or sequence, these particular algorithms are each a type of fold, which operates over the series of values and provides a smaller (single) output.

Some languages offer a fold operation that takes

• a data set (the array or sequence),
• a function (e.g. that captures the min or max algorithm in terms of a single comparison, i.e. rather than in terms of the full list/array/sequence), and
• an initial value (first of the list), and

that returns a single value.

Fold will invoke the reducing function on each element (perhaps recursively) and will eventually return a single value as the final result.

---

See also MapReduce, a capability for doing map & fold/reduce, distributed across multiple computing nodes.

Answer 2

In your examples, the common characteristic is iteration through a sequence to find a member matching a particular characteristic.

So, the general class of algorithms you might be looking for is just a sequential search (aka linear search). It's the general form of algorithms that, "sequentially checks each element of the list for the target value until a match is found or until all the elements have been searched."

In your case, the characteristics you're matching on happen to be mathematical, but the comparisons aren't part of the algorithm. They're your match-criteria. The algorithmic aspect of all three examples is the iteration.

Answer 3

To expand on what @Erik_Eidt said, maxima and minima fall into the category of percentiles. They just happen to be the largest and smallest percentiles. It can be useful to find other percentiles such as the median or mode.

For example, in image processing finding the median color of an area of pixels can be used to smooth out image noise while preserving object edges.