用于检测和分解算术或几何序列的算法

问：

如果一个序列是纯算术或纯几何，它很容易被检测。(1,3,5,7,9...)(3,9,27,81...)

“混合”算术/几何序列怎么样？

e.g. 2 3 5 6 7 9 10 14
it contain 3 arithmetic sequences (3 6 9), (3 5 7 9) and (2 6 10 14) in it.

e.g. 2 3 4 8 9 16 27 32 81
it contain 2 geometric sequences (2 4 8 16 32) and (3 9 27 81) in it.

e.g. 2 3 4 5 8 9 16 32
it contain 1 geometric sequence (2 4 8 16 32) and 2 arithmetic sequences (2 3 4 5) (3 5 7 9) in it.

（假设序列应包含 2 个以上的元素）

有没有算法可以检测（分析）上述混合序列并对其进行分解？即检测并列出其中的所有序列？（假设原始序列包含整数）<= 20

谢谢。

问候

林志峰

基于 Abhinav Mathur 算法的代码，可能需要更多的调试，所有结果都是 -1 ;<

            #include <Array.au3>
    
    Func GetSequences(ByRef $arr)
        Local $arithmetic_seq[1], $geometric_seq[1]
        Local $n = UBound($arr)
    
        For $i = 0 To $n - 3
            For $j = $i + 1 To $n - 2
                Local $arithmetic = $arr[$i] & "|" & $arr[$j]
                Local $geometric = $arr[$i] & "|" & $arr[$j]
                Local $d = $arr[$j] - $arr[$i]
                Local $r = $arr[$j] / $arr[$i]
    
                $ArithTmp=$arr[$j]
                $GeoTmp=$arr[$j]
                For $k = $j + 1 To $n - 1
                    If ($arr[$k] - $ArithTmp) = $d Then
                        $arithmetic &= "|" & $arr[$k]
                        $ArithTmp=$arr[$k]
                    EndIf
    
                    If $arr[$k] / $GeoTmp = $r Then
                        $geometric &= "|" & $arr[$k]
                        $GeoTmp=$arr[$k]
                    EndIf
                Next
    
                If StringReplace($arithmetic, "|", "") <> $arr[$i] & $arr[$j] And StringLen($arithmetic) > 2 Then
                    _ArrayAdd($arithmetic_seq, StringSplit($arithmetic, "|", 2))
                EndIf
    
                If StringReplace($geometric, "|", "") <> $arr[$i] & $arr[$j] And StringLen($geometric) > 2 Then
                    _ArrayAdd($geometric_seq, StringSplit($geometric, "|", 2))
                EndIf
            Next
        Next
    
        ConsoleWrite("Sequences for " & _ArrayToString($arr) & @CRLF)
        ConsoleWrite("Arithmetic: " & @CRLF)
        _ArrayDisplay($arithmetic_seq)
    
        ; Clear the arithmetic sequence for the next iteration
        _ArrayDelete($arithmetic_seq, 1)
    
        ConsoleWrite("Geometric: " & @CRLF)
        _ArrayDisplay($geometric_seq)
    
        ; Clear the geometric sequence for the next iteration
        _ArrayDelete($geometric_seq, 1)
    EndFunc
    
    Local $sequence1[9] = [2, 3, 5, 6, 7, 8, 9, 10, 14]
    Local $sequence2[9] = [2, 3, 4, 8, 9, 16, 27, 32, 81]
    Local $sequence3[9] = [2, 3, 4, 5, 7, 8, 9, 16, 32]
    
    Local $sequences[3] = [$sequence1, $sequence2, $sequence3]
    
    For $i = 0 To UBound($sequences) - 1
        GetSequences($sequences[$i])
    Next