Add mode function

[delphidabbler]

The following Mode function applies to countable sets. It obeys the rule that if all items in a sequence of values are unique then there is no mode. The following function returns an empty array in that case. If sequence in mono-modal an array of one element containing the mode is returned, while if sequence is multi-modal, an array containing all the modes is returned.

This function illustrates the case for a sequence of Integer values. Overloads for other ordinal types are obvious.

function ModeN(const A: array of Integer): TArray<Integer>;
begin
  if Length(A) = 0 then
    raise EArgumentException.Create('Array is empty');
  var MaxCount: Cardinal := 0;
  var Counts := TDictionary<Integer,Cardinal>.Create;
  try
    for var X in A do
    begin
      var C: Cardinal;
      if not Counts.TryGetValue(X, C) then
        C := 0;
      Inc(C);
      Counts.AddOrSetValue(X, C);
      if MaxCount < C then
        MaxCount := C;
    end;
    // equivalent test?: if MaxCount = 1 then
    if Length(A) = Counts.Count then 
    begin
      // All numbers are unique => no mode
      SetLength(Result, 0);
      Exit;
    end;
    var Results := TList<Integer>.Create;
    try
      for KV in Counts do
      begin
        if KV.Value = MaxCount then
          Results.Add(KV.Key);
      end;
      Result := Results.ToArray;
    finally
      Results.Free;
    end;
  finally
    Counts.Free;
  end;
end;

This issue was extracted from issue #16

[delphidabbler]

It obeys the rule that if all items in a sequence of values are unique then there is no mode. The following function returns an empty array in that case.

There is no consistency in the documentation about how to handle the situation where every element occurs equally often, so the decision has been taken to returns an array of all the unique values of a given array.

For example:

Mode([1,2,3,4]) => [1,2,3,4]
Mode([1,1,2,2,3,3,4,4] => [1,2,3,4]
Mode([2,2,2,2]) => [2]
Mode([0,1,3,3,2,2]) => [2,3]

It has also been decided to require an array of at least two elements.

[delphidabbler]

There is no consistency in the documentation about how to handle the situation where every element occurs equally often, so the decision has been taken to returns an array of all the unique values of a given array.

This is the same as the approach taken by the Calculator Soup online calculator.

[delphidabbler]

Also adding:

• ModeAlt - As Mode but returns [] when there is no mode.
• ModeCount - Returns the number of modes in an array.
• HasMode - Returns True if an array of integers has a mode, False if not.
• CountOccurences - Helper function that counts the number of occurrences of each unique integer in an array.