Data commit

Task/Determinant-and-permanent/VBA/determinant-and-permanent.vba

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+Option Base 1
+Private Function minor(a As Variant, x As Integer, y As Integer) As Variant
+    Dim l As Integer: l = UBound(a) - 1
+    Dim result() As Double
+    If l > 0 Then ReDim result(l, l)
+    For i = 1 To l
+        For j = 1 To l
+            result(i, j) = a(i - (i >= x), j - (j >= y))
+        Next j
+    Next i
+    minor = result
+End Function
+
+Private Function det(a As Variant)
+    If IsArray(a) Then
+        If UBound(a) = 1 Then
+            On Error GoTo err
+            det = a(1, 1)
+            Exit Function
+        End If
+    Else
+        det = a
+        Exit Function
+    End If
+    Dim sgn_ As Integer: sgn_ = 1
+    Dim res As Integer: res = 0
+    Dim i As Integer
+    For i = 1 To UBound(a)
+        res = res + sgn_ * a(1, i) * det(minor(a, 1, i))
+        sgn_ = sgn_ * -1
+    Next i
+    det = res
+    Exit Function
+err:
+    det = a(1)
+End Function
+
+Private Function perm(a As Variant) As Double
+    If IsArray(a) Then
+        If UBound(a) = 1 Then
+            On Error GoTo err
+            perm = a(1, 1)
+            Exit Function
+        End If
+    Else
+        perm = a
+        Exit Function
+    End If
+    Dim res As Double
+    Dim i As Integer
+    For i = 1 To UBound(a)
+        res = res + a(1, i) * perm(minor(a, 1, i))
+    Next i
+    perm = res
+    Exit Function
+err:
+    perm = a(1)
+End Function
+
+Public Sub main()
+    Dim tests(13) As Variant
+    tests(1) = [{1,  2; 3,  4}]
+    '--Determinant: -2, permanent: 10
+    tests(2) = [{2, 9, 4; 7, 5, 3; 6, 1, 8}]
+    '--Determinant: -360, permanent: 900
+    tests(3) = [{ 1,  2,  3,  4; 4,  5,  6,  7; 7,  8,  9, 10; 10, 11, 12, 13}]
+    '--Determinant: 0, permanent: 29556
+    tests(4) = [{ 0,  1,  2,  3,  4; 5,  6,  7,  8,  9; 10, 11, 12, 13, 14; 15, 16, 17, 18, 19; 20, 21, 22, 23, 24}]
+    '--Determinant: 0, permanent: 6778800
+    tests(5) = [{5}]
+    '--Determinant: 5, permanent: 5
+    tests(6) = [{1,0,0; 0,1,0; 0,0,1}]
+    '--Determinant: 1, permanent: 1
+    tests(7) = [{0,0,1; 0,1,0; 1,0,0}]
+    '--Determinant: -1, Permanent: 1
+    tests(8) = [{4,3; 2,5}]
+    '--Determinant: 14, Permanent: 26
+    tests(9) = [{2,5; 4,3}]
+    '--Determinant: -14, Permanent: 26
+    tests(10) = [{4,4; 2,2}]
+    '--Determinant: 0, Permanent: 16
+    tests(11) = [{7,    2,      -2,     4; 4,    4,      1,      7; 11,   -8,     9,      10; 10,   5,      12,     13}]
+    '--det:  -4319   permanent:      10723
+    tests(12) = [{-2,   2,      -3; -1,   1,      3; 2 ,   0,      -1}]
+    '--det:  18      permanent:      10
+    tests(13) = 13
+    Debug.Print "Determinant", "Builtin det", "Permanent"
+    For i = 1 To 12
+        Debug.Print det(tests(i)), WorksheetFunction.MDeterm(tests(i)), perm(tests(i))
+    Next i
+    Debug.Print det(tests(13)), "error", perm(tests(13))
+End Sub