零基础学算法->最大公约数(GCD)和最小公倍数(LCM)

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欧几里德算法

'Use Euclid Method
'Calculate GCD and LCM
'https://zh.wikipedia.org/wiki/%E6%9C%80%E5%B0%8F%E5%85%AC%E5%80%8D%E6%95%B8

Sub Euclid_Method()
Dim a&, b&
Dim nGCD&, nLCM

With Sheet4
a = .Cells(4, 3).Value
b = .Cells(5, 3).Value
nGCD = Euclid_GCD_Iter(a, b)
nLCM = Euclid_LCM_Iter(a, b)
.Cells(6, 3) = nGCD
.Cells(7, 3) = nLCM

End With
Debug.Print Timer
End Sub

'Iterate
'x>y
Function Euclid_GCD_Iter(a, b)
Dim r&
If a > b Then x = a: y = b Else x = b: y = a  'Make x>y
r = x Mod y              'remainder
    Do While r           'Loop till r>0
        x = y
        y = r
        r = x Mod y
        Debug.Print x, y
    Loop
   Euclid_GCD_Iter = y    'Return GCD
End Function

Function Euclid_LCM_Iter(x, y)
Dim t
t = Euclid_GCD_Iter(x, y)       'Get the GCD
Euclid_LCM_Iter = (x * y) / t   'LCM=(a*b)/GCD
End Function

Stein算法

'Use Stein Method
'Calculate GCD and LCM
'******************************************
'https://baike.baidu.com/item/%E6%9C%80%E5%A4%A7%E5%85%AC%E7%BA%A6%E6%95%B0/869308?fr=aladdin
'Stein Algorithm:
'
'Set A1=A;B1=B;C1=1
'1 if An=0,Bn*Cn is GCD, Exit Program
'2 if Bn=0, An*Cn is GCD, Exit Program
'3 if An and Bn is Even; An+1=An/2,Bn+1=Bn/2,Cn+1=Cn/2
'4 If An is Even, Bn is not Even; An+1=An/2,Bn+1=Bn,Cn+1=Cn
'5 If Bn is Even, An is not Even; An+1=An,Bn+1=Bn/2,Cn+1=Cn
'6 if Either An or Bn is Even; An+1=|An-Bn|,Bn+1=Min(An,Bn),Cn+1=Cn
'7 n+1, go to Step 1
'******************************************
Sub Stein_Method()
Dim a&, b&
Dim nGCD&, nLCM

With Sheet5
a = .Cells(4, 3).Value
b = .Cells(5, 3).Value
nGCD = Stein_GCD_Recur(a, b)
nLCM = Stein_LCM(a, b)
.Cells(6, 3) = nGCD
.Cells(7, 3) = nLCM

End With
Debug.Print Timer
End Sub

'Iterate
'x>y
Function Stein_GCD_Recur(a, b)
Dim c&
If a > b Then x = a: y = b Else x = b: y = a  'Make x>y
If y = 0 Then Stein_GCD_Recur = x: Exit Function
If x Mod 2 = 0 And y Mod 2 = 0 Then
    Stein_GCD_Recur = 2 * Stein_GCD_Recur(x / 2, y / 2)    'An and Bn is Even
ElseIf x Mod 2 = 0 Then
    Stein_GCD_Recur = Stein_GCD_Recur(x / 2, y)            'An is Even
ElseIf y Mod 2 = 0 Then
    Stein_GCD_Recur = Stein_GCD_Recur(x, y / 2)            'Bn is Even
Else
    Stein_GCD_Recur = Stein_GCD_Recur((x + y) / 2, (x - y) / 2)   'An or Bn is NOT Even
End If
End Function

Function Stein_LCM(x, y)
Dim t
t = Stein_GCD_Recur(x, y)     'Get the GCD
Stein_LCM = (x * y) / t       'LCM=(a*b)/GCD
End Function

 

转载于:https://my.oschina.net/tedzheng/blog/3001276