Find the least number of coins required that can make any change from 1 to 99 cents

Question

Recently I challenged my co-worker to write an algorithm to solve this problem:

Find the least number of coins required that can make any change from

Answer 1

A vb version

Public Class Form1

    Private Sub Button1_Click(ByVal sender As System.Object, _
                              ByVal e As System.EventArgs) Handles Button1.Click
        For saleAMT As Decimal = 0.01D To 0.99D Step 0.01D
            Dim foo As New CashDrawer(0, 0, 0)
            Dim chg As List(Of Money) = foo.MakeChange(saleAMT, 1D)
            Dim t As Decimal = 1 - saleAMT
            Debug.WriteLine(t.ToString("C2"))
            For Each c As Money In chg
                Debug.WriteLine(String.Format("{0} of {1}", c.Count.ToString("N0"), c.moneyValue.ToString("C2")))
            Next
        Next
    End Sub

    Class CashDrawer

        Private _drawer As List(Of Money)

        Public Sub New(Optional ByVal QTYtwoD As Integer = -1, _
                       Optional ByVal QTYoneD As Integer = -1, _
                       Optional ByVal QTYfifty As Integer = -1, _
                       Optional ByVal QTYquarters As Integer = -1, _
                       Optional ByVal QTYdimes As Integer = -1, _
                       Optional ByVal QTYnickels As Integer = -1, _
                       Optional ByVal QTYpennies As Integer = -1)
            _drawer = New List(Of Money)
            _drawer.Add(New Money(2D, QTYtwoD))
            _drawer.Add(New Money(1D, QTYoneD))
            _drawer.Add(New Money(0.5D, QTYfifty))
            _drawer.Add(New Money(0.25D, QTYquarters))
            _drawer.Add(New Money(0.1D, QTYdimes))
            _drawer.Add(New Money(0.05D, QTYnickels))
            _drawer.Add(New Money(0.01D, QTYpennies))
        End Sub

        Public Function MakeChange(ByVal SaleAmt As Decimal, _
                                   ByVal amountTendered As Decimal) As List(Of Money)
            Dim change As Decimal = amountTendered - SaleAmt
            Dim rv As New List(Of Money)
            For Each c As Money In Me._drawer
                change -= (c.NumberOf(change) * c.moneyValue)
                If c.Count > 0 Then
                    rv.Add(c)
                End If
            Next
            If change <> 0D Then Throw New ArithmeticException
            Return rv
        End Function
    End Class

    Class Money
        '-1 equals unlimited qty
        Private _qty As Decimal 'quantity in drawer
        Private _value As Decimal 'value money
        Private _count As Decimal = 0D

        Public Sub New(ByVal theValue As Decimal, _
                       ByVal theQTY As Decimal)
            Me._value = theValue
            Me._qty = theQTY
        End Sub

        ReadOnly Property moneyValue As Decimal
            Get
                Return Me._value
            End Get
        End Property

        Public Function NumberOf(ByVal theAmount As Decimal) As Decimal
            If (Me._qty > 0 OrElse Me._qty = -1) AndAlso Me._value <= theAmount Then
                Dim ct As Decimal = Math.Floor(theAmount / Me._value)
                If Me._qty <> -1D Then 'qty?
                    'limited qty
                    If ct > Me._qty Then 'enough 
                        'no
                        Me._count = Me._qty
                        Me._qty = 0D
                    Else
                        'yes
                        Me._count = ct
                        Me._qty -= ct
                    End If
                Else
                    'unlimited qty
                    Me._count = ct
                End If
            End If
            Return Me._count
        End Function

        ReadOnly Property Count As Decimal
            Get
                Return Me._count
            End Get
        End Property
    End Class
End Class