非递归实现不重复序列的全排列（三）

?笔者曾利用进制转换实现不重复序列全排列（http://blog.csdn.net/northwolves/archive/2004/07/21/47400.aspx），但从0 循环到n^(n-1)-1,效率实在不高，经过仔细分析，发现一个另人激动的规律，详情见下表：

?

A

?

BA

CBA

DCBA

CDBA

CBDA

CBAD

BCA

DBCA

BDCA

BCDA

BCAD

BAC

DBAC

BDAC

BADC

BACD

AB

CAB

DCAB

CDAB

CADB

CABD

ACB

DACB

ADCB

ACDB

ACBD

ABC

DABC

ADBC

ABDC

ABCD

从上面表格可以看出，对于“ABCD”，假如先放好A（只有一种放法），再放B时，可以有BA，AB两种放法；再放C时，则针对BA，AB 各有3种放法（BA前，BA中，BA后），再放D时，各有4种放法。所以第一个元素排好后，第2个元素的位置可以用0，1 表示，第3个元素的位置可以用0，1 ，2表示，第n个元素的位置可以用0，1 ,2,3,...n-1表示，因而使用混合进制（笔者起的名字）可以实现数组元素的全排列。

代码如下：

Sub pailie3(ParamArray x())
Dim starttime As Single, endtime As Single
Dim i As Integer, j As Integer, Num As Long, n As Integer
Dim ALL As New Collection, TEMP1 As Long, TEMP2 As Long
n = UBound(x) + 1 '元素个数
starttime = Timer '开始计时
Num = 1
For i = 1 To n
Num = Num * i? '递归计算n！
Next
For i = 1 To Num
Set ALL = Nothing '初始化集合all
ALL.Add x(0)
TEMP1 = i
For j = 2 To n
TEMP2 = TEMP1 Mod j
TEMP1 = TEMP1 / j
If TEMP2 = 0 Then
ALL.Add x(j - 1) 'temp2为 0则放在最后
Else
ALL.Add x(j - 1), , BEFORE:=TEMP2 'temp2不为 0 则置于第temp2个元素前
End If
Next
For j = 1 To n
Debug.Print ALL(j) & " "; '输出
Next
Debug.Print
Next
endtime = Timer
Debug.Print "共 " & Num & " 种排列！用时 " & endtime - starttime & " 秒！"
End Sub

Private Sub Command1_Click()
pailie3 "a", "b", "c", "d", "e", "f", "g"
End Sub

?

由于集合属于VARIANT类型，运算速度慢，换成数组进行同样的转换，发现确实快了很多：

Sub pailie4(ParamArray x())
Dim starttime As Single, endtime As Single
Dim i As Integer, j As Integer, k As Integer, Num As Long, n As Integer
Dim ALL(), TEMP1 As Long, TEMP2 As Long
n = UBound(x) + 1 '元素个数

starttime = Timer '开始计时
Num = 1
For i = 1 To n
Num = Num * i? '递归计算n！
Next
For i = 1 To Num
ReDim ALL(1 To n) '初始化数组all
ALL(1) = x(0)
TEMP1 = i
For j = 2 To n
TEMP2 = TEMP1 Mod j
TEMP1 = TEMP1 / j
If TEMP2 = 0 Then
ALL(j) = x(j - 1) 'temp2为 0则放在最后
Else
For k = j To TEMP2 + 1 Step -1
ALL(k) = ALL(k - 1)? ' temp2之后的元素后移一位
Next
ALL(TEMP2) = x(j - 1) 'temp2不为 0 则置于第temp2个元素前
End If
Next
Debug.Print Join(ALL, " ")? '输出
Next
endtime = Timer
Debug.Print "共 " & Num & " 种排列！用时 " & endtime - starttime & " 秒！"
End Sub
Private Sub Command1_Click()
pailie4 "a", "b", "c", "d", "e", "f", "g"
End Sub

如果用COPYMEMORY进行数组的移动，速度应该更快，大家有兴趣不妨一试。