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多元一次方程往往采用循环求解。笔者在与网友们讨论一个问题（http://expert.csdn.net/Expert/topic/2607/2607772.xml?temp=.7494928）过程中，琢磨出一种算法，采用递归进行多元一次方程的求解。并将解分为整数解和 非负整数解两种情况，请大家指教。
Private Sub Command1_Click() ''''演示求X1+X2+X3+X4+X5=10整数解
Text1.Text = ""
Dim answer As String
answer = GETRESULT(5, 10, True) ''''赋值
Dim temp
temp = Split(answer, vbCrLf)
For i = 0 To UBound(temp)
temp(i) = "解" & i + 1 & "：" & vbTab & temp(i) '''' add index
Next
answer = Join(temp, vbCrLf)
Text1.Text = "方程 X1+X2+X3+X4+X5=10 共有 " & UBound(temp) + 1 & " 个整数解：" & vbCrLf & answer ''''show all answer in textbox
End Sub
Private Sub Command2_Click() ''''演示求X1+X2+X3+X4+X5=10非负整数解
Text1.Text = ""
Dim answer As String
answer = GETRESULT(5, 10, False) ''''赋值
Dim temp
temp = Split(answer, vbCrLf)
For i = 0 To UBound(temp)
temp(i) = "解" & i + 1 & "：" & vbTab & temp(i) ''''add index
Next
answer = Join(temp, vbCrLf)
Text1.Text = "方程 X1+X2+X3+X4+X5=10 共有 " & UBound(Split(answer, vbCrLf)) + 1 & " 个非零整数解：" & vbCrLf & answer ''''show all answer in textbox
End Sub
Private Sub Command3_Click() ''''演示无解情况
Text1.Text = ""
Dim answer As String
answer = GETRESULT(5, 3, False)
Dim temp
temp = Split(answer, vbCrLf)
For i = 0 To UBound(temp)
temp(i) = "解" & i + 1 & "：" & vbTab & temp(i)
Next
answer = Join(temp, vbCrLf)
Text1.Text = "方程 X1+X2+X3+X4+X5=3 共有 " & UBound(Split(answer, vbCrLf)) + 1 & " 个非零整数解：" & vbCrLf & answer
End Sub
''''求解函数
Function GETRESULT(ByVal n As Integer, ByVal SUM As Integer, Optional allowzero As Boolean = True) As String
Dim temp() As String, i As Long
If n = 2 Then ''''二元方程
If allowzero = True Then
ReDim temp(SUM)
For i = 0 To SUM '''' allow zero
temp(i) = "X1=" & i & ",X2=" & SUM - i
Next
GETRESULT = Join(temp, vbCrLf)
Erase temp
Else
ReDim temp(1 To SUM - 1) ''''forbid zero
For i = 1 To SUM - 1
temp(i) = "X1=" & i & ",X2=" & SUM - i
Next
GETRESULT = Join(temp, vbCrLf)
Erase temp
End If
End If
If n > 2 Then
If allowzero = True Then
ReDim temp(SUM)
For i = SUM To 0 Step -1 '''' allow zero
temp(i) = Replace(GETRESULT(n - 1, i, True), vbCrLf, ",X" & n & "=" & SUM - i & vbCrLf) & ",X" & n & "=" & SUM - i
Next
GETRESULT = Join(temp, vbCrLf)
Erase temp
Else
If SUM < n Then MsgBox "无解！": Exit Function ''''无解情况
ReDim temp(1 To SUM - n + 1) ''''not allow zero
For i = 1 To SUM - n + 1
temp(i) = Replace(GETRESULT(n - 1, SUM - i, False), vbCrLf, ",X" & n & "=" & i & vbCrLf) & ",X" & n & "=" & i ''''递归
Next
GETRESULT = Join(temp, vbCrLf)
Erase temp
End If
End If
End Function
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