据说属微软公司的面试题.
原题目描述：
已知两个数字为1~30的，甲知道两数只和，乙知道两数之积，甲问乙：“你知道是
那两个数吗？”乙说：“不知道”。乙问甲：“你知道是那两个数吗？”甲说：“也
不知道”。于是，乙说 ：“那我知道了”随后甲也说：“那我也知道了”这两个数是'什么？
以下用VB。NET实现：
Dim NUM, SUM, PRODUCT As Int32
Dim Product1()() As Int32
Dim i, m, n, Sum1(3)() As Int32
Private Sub MyMain()
Product1 = Nothing
NUM = CInt(Me.TextBox1.Text)
GetSum1()
GetProduct1()
For m = 1 To NUM
For n = m To NUM
If SumOnly(m, n) Or ProductOnly(m, n) Then GoTo NextItem '不好意思用了个ＧＯＴＯ
SUM = m + n
PRODUCT = m * n
'甲的和产生的积中最多有（n -2）个是唯一积
If SUMtoPRODUCT_N_2(SUM) < 2 Then GoTo NextItem
'乙的积产生的和中有且只有一个满足1、不是唯一和 2、和产生的积中最多有（n -2）个是唯一积
'并且其余的和均满足 1、不是唯一和 2、有n－1个唯一积
If PROCUCTtoSUM(PRODUCT) Then
MsgBox(m.ToString() & " " & n.ToString())
End If
NextItem: Next
Next
End Sub
Private Sub GetSum1()
'产生唯一和并保存在数组中
ReDim Sum1(0)(1)
Sum1(0)(0) = 1
Sum1(0)(1) = 1
ReDim Sum1(1)(1)
Sum1(1)(0) = 1
Sum1(1)(1) = 2
ReDim Sum1(2)(1)
Sum1(2)(0) = NUM - 1
Sum1(2)(1) = NUM
ReDim Sum1(3)(1)
Sum1(3)(0) = NUM
Sum1(3)(1) = NUM
End Sub
Private Function SumOnly(ByVal N1 As Int32, ByVal N2 As Int32) As Boolean
'判断是否为唯一和
Dim i As Int32
For i = 0 To 3
If N1 = Sum1(i)(0) AndAlso N2 = Sum1(i)(1) Then Return True
Next
Return False
End Function
Private Sub GetProduct1()
'产生唯一积并保存在数组中
Dim tmp(NUM * NUM)() As Int32
For m = 1 To NUM '????????????????
For n = m To NUM '??????????????
Dim meme() As Int32 = tmp(m * n)
If meme Is Nothing Then
ReDim meme(2)
Else
ReDim Preserve meme(meme.Length + 1)
End If
meme(meme.Length - 1) = m
meme(meme.Length - 2) = n
meme(0) += 1
tmp(m * n) = meme
meme = Nothing
Next
Next
For i = 1 To NUM * NUM
If Not tmp(i) Is Nothing AndAlso tmp(i)(0) = 1 Then
For m = 1 To tmp(i).GetUpperBound(0) Step 2
If Product1 Is Nothing Then
ReDim Product1(0)
ReDim Product1(0)(1)
Else
ReDim Preserve Product1(Product1.Length)
ReDim Product1(Product1.Length - 1)(1)
End If
Product1(Product1.Length - 1)(0) = tmp(i)(m)
Product1(Product1.Length - 1)(1) = tmp(i)(m + 1)
Next
End If
Next
End Sub
Private Function ProductOnly(ByVal N1 As Int32, ByVal N2 As Int32) As Boolean
'判断是否为唯一积
Dim i As Int32
For i = 0 To Product1.GetUpperBound(0)
If N1 = Product1(i)(1) AndAlso N2 = Product1(i)(0) Then Return True
If N1 = Product1(i)(0) AndAlso N2 = Product1(i)(1) Then Return True
Next
Return False
End Function
Private Function SUMtoPRODUCT_N_2(ByVal SUM As Int32) As Int32
'甲的和产生的积中最多有（n -2）个是唯一积
Dim n As Int32 = CInt(SUM / 2 - 0.2)
Dim i, m As Int32
For i = 1 To n
If ProductOnly(i, SUM - i) Then m += 1
Next
Return n - m
End Function
Private Function PROCUCTtoSUM(ByVal PRODUCT As Int32) As Boolean
'乙的积产生的和中有且只有一个满足1、不是唯一和 2、和产生的积中最多有（n -2）个是唯一积
'并且其余的和均满足 1、不是唯一和 2、有n－1个唯一积
Dim tmp()(), i, m, n As Int32
'1、分解积看能产生多少个和
For i = 1 To CInt(Math.Sqrt(PRODUCT) - 0.4)
If PRODUCT Mod i = 0 Then
If tmp Is Nothing Then
ReDim tmp(0)
ReDim tmp(0)(2)
Else
ReDim Preserve tmp(tmp.Length)
ReDim Preserve tmp(tmp.Length - 1)(2)
End If
tmp(tmp.Length - 1)(2) = PRODUCT / i
tmp(tmp.Length - 1)(1) = i
If Not SumOnly(tmp(tmp.Length - 1)(1), tmp(tmp.Length - 1)(2)) And SUMtoPRODUCT_N_2(i + PRODUCT / i) >= 2 Then
'和不为唯一和，且和产生的积中支多有n－2个是唯一积
tmp(tmp.Length - 1)(0) = 1
End If
If SumOnly(tmp(tmp.Length - 1)(1), tmp(tmp.Length - 1)(2)) Then
'唯一和
tmp(tmp.Length - 1)(0) = 3
End If
If Not SumOnly(tmp(tmp.Length - 1)(1), tmp(tmp.Length - 1)(2)) And SUMtoPRODUCT_N_2(i + PRODUCT / i) = 1 Then
'不是唯一和，但是有n－1个唯一积
tmp(tmp.Length - 1)(0) = 2
End If
End If
Next
Dim count As Int32 = 0
For i = 0 To tmp.Length - 1
If tmp(i)(0) = 0 Then Return False
If tmp(i)(0) = 1 Then count += 1
Next
If count <> 1 Then Return False
Return True
End Function
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