How to generate all combinations of partitioning a string in VB.Net - vb.net

Question

Given a string, how do you generate all partitions of it (shown as smaller strings separated by commas)?
Also, what is the total number of partitions for a string of length n?
The following will give the result, but is not good on long strings.
String: CODE
C,O,D,E
C,O,DE
C,OD,E
C,ODE
CO,D,E
CO,DE
COD,E
String: PEACE
P,E,A,C,E
P,E,A,CE
P,E,AC,E
P,E,ACE
P,EA,C,E
P,EA,CE
P,EAC,E
PE,A,C,E
PE,A,CE
PE,AC,E
PE,ACE
PEA,C,E
PEA,CE
Sub getAllComb()
oriStr = TextBox1.Text
Dim tmp = ""
Dim k = 0
For i = 0 To oriStr.Length
For j = 1 To 3
'tmp = Mid(oriStr, i, j)
Try
tmp1(k) = oriStr.Substring(i, j)
k = k + 1
'tmp = oriStr.Substring(i, j)
'Debug.Print(tmp)
Catch ex As Exception
'Debug.Print("Error>>>>" + ex.Message)
Exit For
End Try
Next
Next
tmp = ""
For i = 0 To k
Debug.Print(i.ToString + "<i " + tmp1(i))
tmp = tmp & tmp1(i) & vbCrLf
Next
'MessageBox.Show(tmp)
Dim tmpAll1 = ""
tmpAll1 = addFunclen4(k)
MessageBox.Show(tmpAll1)
Debug.Print(tmpAll1)
TextBox1.Text = oriStr & vbCrLf & vbCrLf & tmpAll1
End Sub
Function addFunclen4(k As Integer) As String
Dim retVal = ""
Dim tmp = ""
Dim tmpAll = ""
Dim tmpStr = ""
Dim tmpAll1 = ""
For i = 0 To k
For i1 = 0 To k
For i2 = 0 To k
For i3 = 0 To k
For i4 = 0 To k
tmp = Form1.tmp1(i) + Form1.tmp1(i1) + Form1.tmp1(i2) + Form1.tmp1(i3) + Form1.tmp1(i4)
If Form1.tmp1(i) <> "" Then
If tmp = Form1.oriStr Then
tmpStr = Form1.tmp1(i) + "," + Form1.tmp1(i1) + "," + Form1.tmp1(i2) + "," + Form1.tmp1(i3) + "," + Form1.tmp1(i4)
Do While tmpStr.Contains(",,") = True
tmpStr = Replace(tmpStr, ",,", ",")
Loop
If Mid(tmpStr, tmpStr.Length, 1) = "," Then
tmpStr = Mid(tmpStr, 1, tmpStr.Length - 1)
End If
If tmpAll1.Contains(tmpStr) = False Then
tmpAll1 = tmpAll1 + tmpStr + vbCrLf
End If
End If
End If
Next
Next
Next
Next
Next
retVal = tmpAll1
Return retVal
End Function

Answer 1

I reckon [2^(n-1) - 1] in total:
(n-1) positions to put a comma, 2 "states" (comma or not comma), -1 for the trivial case with no commas.
A simpler algorithm would be to iterate through the number of cases and use the binary representation to determine whether to put a comma in each position.
For example (simple form with TextBox, Button and ListBox):
Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
ListBox1.Items.Clear()
Dim s As String = TextBox1.Text
If s.Length < 2 Then
MessageBox.Show("Enter a longer string")
Return
End If
For i = 1 To Math.Pow(2, s.Length - 1) - 1
Dim result As String = s(0)
For j = 1 To s.Length - 1
result = result & CommaOrNot(i, j) & s(j)
Next
ListBox1.Items.Add(result)
Next
End Sub
Private Function CommaOrNot(i As Integer, j As Integer) As String
If (i And Math.Pow(2, j - 1)) = Math.Pow(2, j - 1) Then
Return ","
Else
Return ""
End If
End Function

Answer 2

I really liked Fruitbat's approach. Here's an alternate version using a slightly different mechanism for the representation of the binary number and how to determine if the comma should be included or not:
Public Class Form1
Private combinations As List(Of String)
Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
Dim s As String = TextBox1.Text
If s.Length < 2 Then
MessageBox.Show("Enter a longer string")
Exit Sub
End If
Button1.Enabled = False
ListBox1.DataSource = Nothing
ListBox1.Items.Clear()
ListBox1.Items.Add("Generating combinations...")
BackgroundWorker1.RunWorkerAsync(s)
End Sub
Private Sub BackgroundWorker1_DoWork(sender As Object, e As System.ComponentModel.DoWorkEventArgs) Handles BackgroundWorker1.DoWork
Dim s As String = e.Argument
Dim combinations As New List(Of String)
Dim binary() As Char
Dim values() As Char = s.ToCharArray
Dim max As Integer = Convert.ToInt32(New String("1", s.Length - 1), 2)
Dim sb As New System.Text.StringBuilder
For i As Integer = 0 To max
sb.Clear()
binary = Convert.ToString(i, 2).PadLeft(values.Length, "0").ToCharArray
For j As Integer = 0 To values.Length - 1
sb.Append(If(binary(j) = "0", "", ","))
sb.Append(values(j))
Next
combinations.Add(sb.ToString)
Next
e.Result = combinations
End Sub
Private Sub BackgroundWorker1_RunWorkerCompleted(sender As Object, e As System.ComponentModel.RunWorkerCompletedEventArgs) Handles BackgroundWorker1.RunWorkerCompleted
combinations = e.Result
ListBox1.Items.Clear()
ListBox1.Items.Add("Generating combinations...Done!")
ListBox1.Items.Add("Adding Results...one moment please!")
Application.DoEvents()
ListBox1.DataSource = Nothing
ListBox1.DataSource = combinations
Button1.Enabled = True
MessageBox.Show("Done!")
End Sub
End Class