Task: Sum to 100







Python: from itertools import product, islice


def expr(p):
    return "{}1{}2{}3{}4{}5{}6{}7{}8{}9".format(*p)


def gen_expr():
    op = ['+', '-', '']
    return [expr(p) for p in product(op, repeat=9) if p[0] != '+']


def all_exprs():
    values = {}
    for expr in gen_expr():
        val = eval(expr)
        if val not in values:
            values[val] = 1
        else:
            values[val] += 1
    return values


def sum_to(val):
    for s in filter(lambda x: x[0] == val, map(lambda x: (eval(x), x), gen_expr())):
        print(s)


def max_solve():
    print("Sum {} has the maximum number of solutions: {}".
          format(*max(all_exprs().items(), key=lambda x: x[1])))


def min_solve():
    values = all_exprs()
    for i in range(123456789):
        if i not in values:
            print("Lowest positive sum that can't be expressed: {}".format(i))
            return


def highest_sums(n=10):
    sums = map(lambda x: x[0],
               islice(sorted(all_exprs().items(), key=lambda x: x[0], reverse=True), n))
    print("Highest Sums: {}".format(list(sums)))


sum_to(100)
max_solve()
min_solve()
highest_sums()


VB: 
Function plusOne(iAry() As Integer, spot As Integer) As Integer
    Dim spotLim As Integer = If(spot = 0, 1, 2) 
    If iAry(spot) = spotLim Then 
        If spot = 0 Then Return -1 
        iAry(spot) = 0 
        Return plusOne(iAry, spot - 1) 
    Else
        iAry(spot) += 1 
    End If
    Return spot
End Function


Function generate(iAry() As Integer, terms As String) As String
    Dim operations As String() = {"", "-", "+"} 
    generate = ""
    For i As Integer = 0 To iAry.Count - 1
        generate &= operations(iAry(i)) & Mid(terms, i + 1, 1).ToString()
    Next
End Function


Function eval(sequence As String) As Integer
    eval = 0
    Dim term As Integer = 0, operation As Integer = 1
    For Each ch As Char In sequence
        Select Case ch
            Case "-", "+" 
                eval += If(operation = 0, -term, term) : term = 0 
                operation = If(ch = "-", 0, 1) 
            Case Else 
                term = term * 10 + Val(ch)
        End Select
    Next
    eval += If(operation = 0, -term, term) 
End Function


Sub reSort(ByRef first As List(Of Integer), ByRef second As List(Of Integer))
    Dim lou As New List(Of ULong) 
    For i As Integer = 0 To first.Count - 1
        lou.Add((CULng(first(i)) << 32) + second(i)) 
    Next
    lou.Sort()
    For k As Integer = 0 To first.Count - 1
        first(k) = lou(k) >> 32 
        second(k) = lou(k) And &H7FFFFFFF 
    Next
End Sub



Function firstMiss(loi As List(Of Integer))
    Dim low As Integer = 0, high As Integer = loi.Count - 1, middle = (low + high) \ 2
    Do
        If loi(middle) = middle Then low = middle + 1 Else high = middle - 1
        middle = (low + high) \ 2
    Loop Until high <= low
    Return middle + If(loi(middle) = middle, 1, 0)
End Function



Sub Solve100(Optional terms As String = "123456789",
             Optional targSum As Integer = 100,
             Optional highNums As Integer = 10)
    Dim lastDig As Integer = Len(terms) - 1 
    Dim iAry() As Integer = New Integer(lastDig) {} 
    Dim seq As String 
    Dim sVal As Integer 
    Dim sCnt As Integer = 1 
    Dim res As New List(Of Integer) 
    Dim tally As New List(Of Integer) 
    Console.WriteLine("List of solutions that evaluate to 100:")
    Do 
        seq = generate(iAry, terms) 
        sVal = eval(seq) 
        If sVal >= 0 Then 
            If res.Contains(sVal) Then tally(res.IndexOf(sVal)) += 1 _
                                  Else res.Add(sVal) : tally.Add(1)
            If sVal = targSum Then _
                Console.WriteLine(" {0,2} {1}", sCnt, seq) : sCnt += 1
        End If
    Loop Until plusOne(iAry, lastDig) < 0
    reSort(tally, res) 
    Console.WriteLine("The sum that has the the most solutions is {0}, (at {1}).",
                      res.Last, tally.Last)
    reSort(res, tally) 
    Console.WriteLine("The lowest positive sum that can
                      firstMiss(res))
    Console.WriteLine("The ten highest numbers that can be expressed are:")
    res.Reverse() 
    sCnt = 0 
    For Each item As Integer In res.Take(highNums)
        Console.Write("{0, -11}", item)
        sCnt = (sCnt + 1) Mod 5 : If sCnt = 0 Then Console.WriteLine()
    Next
End Sub

Sub Main()
    Solve100() 
End Sub