一道算法题，求解求解！！！

[123工艺品]

  '给定数组arr，arr中所有的值都为正整数且不重复。每个值代表一种面值的货币，
    '每种面值的货币可以使用任意张，再给定一个aim，代表要找的钱数，求组成aim的最少货币数。
    '如果无解，请返回-1. 数据范围：数组大小满足 0 <= n <=10000 ，
    '数组中每个数字都满足 0 < val <=10000，0 <= aim <=100000
    '要求：时间复杂度 O(n×aim) ，空间复杂度 O(aim)。
    '[5,2,3],20    结果为4
 我的方法：

 Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
        Dim str As String = InputBox("输入数组及要找的钱数(大于零小于10000)" + vbCrLf + "例如：[5,2,3],20", "输入")
        Dim arrSi As Integer = 0, arrEi As Integer = 0, aim As Integer = 0, myarr() As Integer, mynum As Integer = 0
        Dim arrstr As String = String.Empty, s As String = String.Empty, cf As Boolean = False
        If str <> String.Empty Then '输入不为空’
            Dim strL As Integer = Len(Str)
            If strL >= 5 Then '输入长度>=5’
                Dim zn As Integer = 0, yn As Integer = 0
                For i As Integer = 1 To strL - 1  '字符“[”出现次数及位置
                    If str.Substring(i - 1, 1) = "[" Then
                        zn += 1
                        arrSi = i - 1
                    End If
                    If str.Substring(i - 1, 1) = "]" Then '字符“]”出现次数及位置
                        yn += 1
                        arrEi = i - 1
                    End If
                Next
                If zn = 1 And arrSi = 0 And yn = 1 Then  '字符"["出现1次位置为0，字符" ] "出现1次
                    If str.Substring(arrEi + 1, 1) = "," Then  '字符"]"后为","
                        arrstr += str.Substring(arrSi + 1, arrEi - arrSi - 1)
                        Dim a() As String = arrstr.Split(",").ToArray()
                        ReDim myarr(a.Length - 1)
                        For i As Integer = 0 To a.Length - 1 '得到数组（integer）
                            Dim ka As Integer = 0
                            Try
                                ka = CInt(a(i))
                            Catch ex As Exception
                            End Try
                            If ka <= 10000 And ka > 0 Then '数组超过限制
                                myarr(i) = ka
                            Else
                                mynum = -1
                            End If
                        Next

                    Else
                        mynum = -1
                        s = "输入错误"
                    End If
                    Try
                        aim = CInt(str.Substring(arrEi + 2))  '得到钱数
                    Catch ex As Exception
                        aim = 0
                    End Try
                    If aim > 0 And aim <= 100000 Then '钱数在范围内
                        Array.Sort(myarr) '数组排序（从小到大）
                        If myarr.Length >= 2 Then '数组是否有重复
                            For i As Integer = 0 To myarr.Length - 2
                                If myarr(i) = myarr(i + 1) Then
                                    cf = True
                                End If
                            Next
                        End If
                        s += "不同面值的货币:" + arrstr + vbCrLf + "钱数：" + aim.ToString
                        If cf Then
                            mynum = -1
                        Else  '数组不重复
                            For i = myarr.Length - 1 To 0 Step -1
                                If aim < myarr(i) Then
                                Else
                                    mynum += CInt(aim \ myarr(i))
                                    aim = aim Mod myarr(i)
                                    If aim < myarr(0) And aim > 0 Then
                                        aim += myarr(i)
                                        mynum -= 1
                                    End If
                                End If
                            Next
                            If aim > 0 Then mynum = -1 '如果零钱数大于零，无解
                        End If
                    Else
                        mynum = -1
                        s = "输入错误"
                    End If
                Else
                    mynum = -1
                    s = "输入错误"
                End If
            Else
                mynum = -1
                s = "输入错误"
            End If
            MsgBox(s + vbCrLf + "最少货币数:" + mynum.ToString, vbOKOnly, "零钱兑换")
        Else
            MsgBox("没有输入！", vbOKOnly, "零钱兑换 ")
        End If

    End Sub

以上红色为主要算法，但有些解不出来。例如[5,12,3],21

求正解~！