散分。 - 调试易

散分。

请用代码将字符串"2x(3-4x)+5(8+3x+8x^2)=(x^2+2)5x-3x^2(2x-7)"
变为字符串"6x-8x^2+40+15x+40x^2=5x^3+10x-6x^3+21x^2"
其中^表示乘方,也就是去括号.
顶贴有分.

解决方案 »

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这个可以参考微软 Microsoft Student 2009 里面学生计算器的做法。
包括表达式化简，解方程，函数作图等等。大概看了下 .NET写的，没有混淆
Dim a, b, c, d, e, x As String
Dim f As Integer
a = "2x(3-4x)+5(8+3x+8x^2)"
f = InStr(1, a, "+")
b = Left(a, f - 1)  'b=2x(3-4x)
c = Mid(a, f + 1, 12) 'c=5(8+3x+8x^2)
Debug.Print c
d = Mid(b, 4, 1)      'd=3
f = Val(d) * Val(Mid(b, 1, 1))
e = f & "x"          'e=6x
f = Val(Mid(b, 1, 1)) * Val(Mid(b, 6, 1))
e = e & "-" & f & "x ^ 2" & "+"  'e=6x-8x^2+
a = Mid(c, 3, 1)
b = Mid(c, 1, 1)
f = Val(a) * Val(b)
e = e & f & "+"
a = Mid(c, 5, 1)
f = Val(a) * Val(b)
e = e & f & "x" & "+"
a = Mid(c, 8, 1)
f = Val(a) * Val(b)
e = e & f & "x^2"
Debug.Print eDim a, b, c, d, e, x As String
Dim f As Integer
a = "2x(3-4x)+5(8+3x+8x^2)"
f = InStr(1, a, "+")
b = Left(a, f - 1)  'b=2x(3-4x)
c = Mid(a, f + 1, 12) 'c=5(8+3x+8x^2)
Debug.Print c
d = Mid(b, 4, 1)      'd=3
f = Val(d) * Val(Mid(b, 1, 1))
e = f & "x"          'e=6x
f = Val(Mid(b, 1, 1)) * Val(Mid(b, 6, 1))
e = e & "-" & f & "x ^ 2" & "+"  'e=6x-8x^2+
a = Mid(c, 3, 1)
b = Mid(c, 1, 1)
f = Val(a) * Val(b)
e = e & f & "+"
a = Mid(c, 5, 1)
f = Val(a) * Val(b)
e = e & f & "x" & "+"
a = Mid(c, 8, 1)
f = Val(a) * Val(b)
e = e & f & "x^2"
Debug.Print e
真是无聊了，呵呵
s = "2x(3-4x)+5(8+3x+8x^2)=(x^2+2)5x-3x^2(2x-7)"
s = "6x-8x^2+40+15x+40x^2=5x^3+10x-6x^3+21x^2"
变好了，
'Remove parentheses in a math expression
Private Function RemParen(ByVal strInput As String) As String
    Dim strResult As String
    Dim strIn As String '括号里的表达式'
    Dim strOut As String '括号外的表达式'
    Dim strtmp() As String, i As Long '用于分割'
    Dim lngStartPos As Long, lngEndPos As Long, lngRightParen As Long, lngLeftParen As Long
    Dim strEndSign As String '每段括号后最近的加号或等号'

    '把减号替换成+-以便分割
    strInput = Replace(strInput, "-", "+-")

    lngStartPos = 1
    '逐括号分段处理'
    Do
        '*****取得括号内部分和括号外部分'
        lngRightParen = InStr(lngStartPos, strInput, ")")
        lngLeftParen = InStr(lngStartPos, strInput, "(")
        strIn = Mid(strInput, lngLeftParen + 1, lngRightParen - lngLeftParen - 1)
        If lngLeftParen = lngStartPos Then
        '括号部分在前：(x^2+2)5x这种形式的'
            lngEndPos = FindEndSign(lngRightParen, strInput, strEndSign)
            strOut = Mid(strInput, lngRightParen + 1, lngEndPos - lngRightParen - 1)
        Else
        '括号部分在后: 2x(3-4x)这种形式的'
            strOut = Mid(strInput, lngStartPos, lngLeftParen - lngStartPos)
            lngEndPos = lngRightParen + 1
            strEndSign = Mid(strInput, lngEndPos, 1)
        End If
'        Debug.Print strIn, strOut, strEndSign

        '*****把括号内部分和括号外部分相乘'
        strtmp = Split(strIn, "+")
        For i = 0 To UBound(strtmp)
            strResult = strResult & MplyStr(strOut, strtmp(i)) & "+"
        Next i

        '*****把最后一个字符弄对'
        strResult = Left(strResult, Len(strResult) - 1) & strEndSign
        lngStartPos = lngEndPos + 1
        If strEndSign = "" Then Exit Do
    Loop

    strResult = Replace(strResult, "+-", "-")
    RemParen = strResult

'    Debug.Print strInput
'    Debug.Print strResult
End Function
'从str1的lngStartPos开始找到其后最近的加号或等号'
'返回值是找到的等号或加号的位置，找不到则返回str1的长度加1'
'找到的等号或加号存在ByRef参数strEndSign里返回，找不到则返回""'
Private Function FindEndSign(ByVal lngStartPos As Long, ByVal str1 As String, _
        ByRef strEndSign As String) As Long
    Dim lngAdd As Long, lngEqual As Long

    lngAdd = InStr(lngStartPos, str1, "+")
    lngEqual = InStr(lngStartPos, str1, "=")

    If lngAdd = 0 Then lngAdd = 10000
    If lngEqual = 0 Then lngEqual = 10000    If lngAdd < lngEqual Then
        strEndSign = "+"
        FindEndSign = lngAdd
    Else
        strEndSign = "="
        FindEndSign = lngEqual
    End If

    If FindEndSign = 10000 Then
        strEndSign = ""
        FindEndSign = Len(str1) + 1
    End If
End Function'把str1和str2所表示的表达式"相乘"，并把相乘的结果输出'
'注意：str1，str2都只能是含有0个或1个变量的单项式！变量只能是x!
'可处理的最复杂情况是：MplyStr("3x^2", "-2x") = "-6x^3"
Private Function MplyStr(str1 As String, str2 As String) As String
    Dim strResult As String
    Dim i As Long, j As Long
    Dim str1suf As String, str2suf As String '后缀'

    AnaStr str1, i, str1suf
    AnaStr str2, j, str2suf

    If str1suf <> "" And str2suf <> "" Then
        strResult = (i * j) & "x^" & (GetPower(str1suf) + GetPower(str2suf))
    Else
        strResult = (i * j) & str1suf & str2suf
    End If
    MplyStr = strResult
End Function'分析str1，拆分它的数字部分和变量部分'
'数字部分返回到ByRef参数lng1里；变量部分返回到ByRef参数str1suf里'
'比如 str1="-x^2", lng1 = -1, str1suf = "x^2"
Private Sub AnaStr(ByVal str1 As String, ByRef lng1 As Long, ByRef str1suf As String)
    Dim strtmp() As String

    On Error GoTo AnaStr_ErrHandler
    str1suf = ""
    strtmp = Split(str1, "x")
    strtmp(0) = Replace(strtmp(0), "+-", "-")
    If strtmp(0) = "" Then
        lng1 = 1
    ElseIf strtmp(0) = "-" Then
        lng1 = -1
    Else
        lng1 = strtmp(0)
    End If
    str1suf = "x" & strtmp(1)
    Exit Sub

AnaStr_ErrHandler:
    If Err.Number = 9 Then
    'Subscript out of range
    '没有x
        Resume Next
    Else
        Stop
        Resume
    End If
End Sub
'从带幂的字符串得到对应的幂次
'GetPower("x^2") = 2, GetPower("x") = 1
Private Function GetPower(strPower As String) As Long
    If strPower = "x" Then
        GetPower = 1
    Else
        GetPower = Right(strPower, Len(strPower) - 2)
    End If
End Function测试函数：
Public Sub test_RemParen()
    Debug.Assert RemParen("2x(3-4x)+5(8+3x+8x^2)=(x^2+2)5x-3x^2(2x-7)") = "6x-8x^2+40+15x+40x^2=5x^3+10x-6x^3+21x^2"
    Debug.Assert RemParen("2x(3-4x)") = "6x-8x^2"
    Debug.Assert RemParen("5(8+3x+8x^2)") = "40+15x+40x^2"
    Debug.Assert RemParen("(x^2+2)5x") = "5x^3+10x"
    Debug.Assert RemParen("-3x^2(2x-7)") = "-6x^3+21x^2"
End SubPublic Sub Test_MplyStr()
    Debug.Assert MplyStr("2", "3") = "6"
    Debug.Assert MplyStr("2", "-4x") = "-8x"
    Debug.Assert MplyStr("5", "8x^2") = "40x^2"
    Debug.Assert MplyStr("5x", "2") = "10x"
    Debug.Assert MplyStr("3x^2", "7") = "21x^2"
    Debug.Assert MplyStr("3x^2", "2x") = "6x^3"
    Debug.Assert MplyStr("5x", "x^2") = "5x^3"
End SubPublic Sub test_AnaStr()
    Dim lng1 As Long
    Dim str1suf As String

    AnaStr "2", lng1, str1suf
    Debug.Assert lng1 = 2
    Debug.Assert str1suf = ""

    AnaStr "-7", lng1, str1suf
    Debug.Assert lng1 = -7
    Debug.Assert str1suf = ""

    AnaStr "x", lng1, str1suf
    Debug.Assert lng1 = 1
    Debug.Assert str1suf = "x"

    AnaStr "-x", lng1, str1suf
    Debug.Assert lng1 = -1
    Debug.Assert str1suf = "x"

    AnaStr "2x", lng1, str1suf
    Debug.Assert lng1 = 2
    Debug.Assert str1suf = "x"    AnaStr "-2x", lng1, str1suf
    Debug.Assert lng1 = -2
    Debug.Assert str1suf = "x"    AnaStr "-2x^2", lng1, str1suf
    Debug.Assert lng1 = -2
    Debug.Assert str1suf = "x^2"

    AnaStr "x^2", lng1, str1suf
    Debug.Assert lng1 = 1
    Debug.Assert str1suf = "x^2"    AnaStr "-x^2", lng1, str1suf
    Debug.Assert lng1 = -1
    Debug.Assert str1suf = "x^2"End Sub