快速组合数C（N，K）=N*（N-1）*（N-2）*...*(N-K+1)/1*2*3*...*K 的求法：
Function ZDGYS(ByVal x As Long, ByVal y As Long) As Long 'GET Greatest Common Divisor最大公约数
Dim TEMP As Long
If x > y Then TEMP = x: x = y: y = TEMP 'LET X < Y
Do
TEMP = y Mod x
If TEMP = 0 Then ZDGYS = x: Exit Function
y = x
x = TEMP
Loop
End Function
Sub CALC(ByVal N As Long, ByVal K As Long, Optional ByRef CNK As String) '计算C（N，K），赋值给CNK
Dim XYS() As Integer, x() As Integer, y() As Integer, result() As String, i As Long, j As Long, T As Long, TEMP As Long, stimer As Double
If N < 0 Or N < K Then Exit Sub
stimer = Timer
If K = N Or K = 1 Then CNK = N: GoTo R '特殊情况
If N > 0 And K = 0 Then CNK = 1: GoTo R '特殊情况
If K > N - K Then K = N - K '减少计算量
Dim NN() As Long, NK() As Long
ReDim NN(1 To K)
ReDim NK(1 To K)
For i = 1 To K
NN(i) = N + 1 - i ' N*(N-1)*(N-2)*....*(N+1-K)
NK(i) = i ' 1*2*3*...*K
Next
For i = K To 1 Step -1
For j = 1 To K
TEMP = ZDGYS(NK(j), NN(i)) '最大公约数
If TEMP > 1 Then '消除分子分母
NN(i) = NN(i) / TEMP
NK(j) = NK(j) / TEMP
End If
Next
Next
ReDim x(1)
ReDim XYS(1)
x(1) = 1 '初始化数组
XYS(1) = 1
T = 1
Do While Not T > K
TEMP = Len(CStr(NN(T)))
ReDim y(1 To TEMP)
For i = 1 To TEMP
y(i) = Val(Mid(NN(T), TEMP + 1 - i, 1))
Next
ReDim XYS(1 To UBound(x) + UBound(y))
For i = 1 To UBound(x)
For j = 1 To UBound(y)
XYS(i + j - 1) = XYS(i + j - 1) + x(i) * y(j) '模拟乘法运算
Next
Next
For i = 1 To UBound(x) + UBound(y) - 1 '进位
TEMP = XYS(i) \ 10
XYS(i) = XYS(i) Mod 10
XYS(i + 1) = XYS(i + 1) + TEMP
Next
T = T + 1
x = XYS
If x(UBound(x)) = 0 Then ReDim Preserve x(1 To UBound(x) - 1) '第一位为零则去掉之
Loop
ReDim result(1 To UBound(x)) '逐位赋值
For i = 1 To UBound(x)
result(i) = x(UBound(x) + 1 - i)
Next
CNK = Join(result, "") '最后结果
R:
Debug.Print "C(" & N & "," & K & ")=" & CNK & vbCrLf & "用时 "; Timer - stimer & " 秒, 结果大约为 " & Val(Left(CNK, 3)) / 100 & "* 10^" & Len(CNK) - 1
Erase x() '释放
Erase y()
Erase XYS()
Erase result()
Erase NN()
Erase NK()
End Sub
Private Sub Command1_Click()
CALC 1500000000, 1000
End Sub
C(1500000000,1000)=30652804367164696580061245618584644612627630767867968160482287207505578854118075767413733341865113545827821943234215925381601476838491502713562101051308121811886256344264074095500443454498544782873527381232953591608839778443126863125303594776637408010065945137971003022970106087272779912095118673993148835415545404803408210359936057541641298321398866367630909780954427950260602677841356572015384593028076391922880188863454695625613158555189739103273043693186054292522757402389201949262458783982625369769215639665513120651343627077305247225448215405511745177315577297307995592278944000912129608635572003811892730638646576505559665098287067901804492021447447275828527448463319437263974332506979369648426322521012083011115417734792185803613847776098673007574058102010392545564626748974852860654213922561671313738154819315936146389699558632939168101222776477404052002491162770708016843923192174292119830692530203631071406591557820008413480936874626325481432195805380233658534174129959183937867662826991079111
338507834850334729288527369247878587832565479208744508778338876845312482987364108498465104568456246126301664867675212989415452257963231582428804132453530623562038287815118381775031194128075371634249125005163175363459748867914155909874673736671257895290315504998299550045865237426434834900678181142251825976824066859247763393966728415101293183767884565520685140354199404573267540148178613083039288640368764932196092260612808432688740318168177149884264936965681432808552602506769960231167314402042115391322928445848804527619718942273029739119754679079466440615744683934345683854846607341007539932315717364854225714347670890166770915776776243078592968724832489687527728645194872553456998869305207865806227228240462763947538604009461323117527793289745018918680050158833377256878342226038335968075073066708948751926064101932688708070972742976746669773522500626362218897275189840528789502160913361730351366579932326949751303046239529917281431024867799141200833929055039117446235095261319287039924501955885408786864766666179804050
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6608908558954975144280515042437103513526943923346637991231240111666845924976878803784724718010351062368178879274540425781148703984672314559414795767769357321073222899722903734370283198049596503724417629404981774693732136715506926958567040649893166041510601704826598030208663351081485700207580107291827140144496139095464493330834978911758605670606624144954404663833872654567200762263525195723339349006395584852284826376552648716276636192737185771244752744819887086709751962025613217186000000
用时 9.03125 秒, 结果大约为 3.06* 10^6608
