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。
