阶乘
在数学中，正整数的阶乘（英语：factorial）是所有小于及等于该数的正整数的积，计为n!
例如5的阶乘为5!，其值=120; 5!=5x4x3x2x1=120用递归计算阶乘
一般数字的阶乘可以用递归的方法进行计算。
以下用递归计算1~12阶乘值；阶乘的值是以指数进行增长。
Sub Factorial_Main()Dim num%, m%Dim FactorNum&With Sheet9For num = 1 To 12 m = 5 + num 'if num>13 program will overflow FactorNum = Factorial_Recursion(num) .Cells(m, 1) = num .Cells(m, 2) = FactorNumNext numEnd WithDebug.Print TimerEnd Sub'Factorial by Recursion MethodFunction Factorial_Recursion(ByVal n)If n <= 1 Then Factorial_Recursion = 1 Exit FunctionElse Factorial_Recursion = n * Factorial_Recursion(n - 1)End IfEnd Function
大数阶乘
一般阶乘的值都比较大，这时递归的方法不可行。此时需要用数组保存阶乘结果来进行计算。
思路：
1. 当前值乘以数组中的值 2. 将结果保存到数组中 3. 判断每个元素是否需要进位 4. 使用一个数组来保存阶乘每一位结果
以下是1~100的阶乘
具体代码如下：
'log10:https://baike.baidu.com/item/%E5%AF%B9%E6%95%B0%E5%87%BD%E6%95%B0/6013318?fr=aladdin'Calculate the CarryFunction Carry_Bit(ByRef Bit, ByVal Pos)Dim i&Dim CarryCarry = 0 'InitialFor i = 1 To Pos 'Check 1~Pos whether need carry bit Bit(i) = Bit(i) + Carry 'Current value+Carry value If Bit(i) <= 9 Then '<9 no need carray bit Carry = 0 ElseIf Bit(i) > 9 And i < Pos Then '>9 but9 And i >= Pos Then '>9 and highest digit Do While Bit(i) > 9 Carry = Int(Bit(i) / 10) 'Save carry Bit(i) = Bit(i) Mod 10 'one digit i = i + 1 Bit(i) = Carry 'Save the carry Loop End IfNext iCarry_Bit = Bit 'Return the ArrayEnd Function'Calculate multiple number factor'Loop mSub Factorial_BigNumber_Multiple()Dim numDim Digit, sumDim i, jDim Fact()Dim Count, Str$Dim m, nWith Sheet10For m = 10 To 43 sum = 0: Digit = 0 num = .Cells(m, 10).Value 'Input Value For i = 1 To num 'Calculate Result digit sum = Log10(i) + sum Next i Digit = Int(sum) + 1 'Length of Data ReDim Fact(1 To Digit) 'Allocate Array For i = 1 To Digit 'Initial Array Fact(i) = 0 Next i Fact(1) = 1 'Setup 1st digit For i = 1 To num 'Loop fact num Pos = Highest_Digit(Fact, Digit) 'Record highest digit For j = 1 To Pos Fact(j) = Fact(j) * i 'fact(n-1)xN Next j Fact = Carry_Bit(Fact, Pos) 'process carry bit Next i Pos = Highest_Digit(Fact, Digit) 'Record highest digit' m = 10 n = 12 'Initial i = Pos Str = "'" Count = 0 Do While i <= Pos And i >= 1 Count = Count + 1 Str = Str & Fact(i) If Count Mod 5 = 0 Then .Cells(m, n) = Str Str = "'" n = n + 1 End If If i = 1 And Str <> "" Then .Cells(m, n) = Str i = i - 1 Loop .Cells(m, 11) = CountNext mEnd WithDebug.Print TimerEnd Sub'Find Hightest digitFunction Highest_Digit(Arr, n)Dim iFor i = n To 1 Step -1 If Arr(i) <> 0 Then Highest_Digit = i Exit Function End IfNext iEnd Function'Function for Log10Function Log10(ByVal x) As DoubleDim nLog10nLog10 = Log(x) / Log(10)Log10 = nLog10End Function