Solve hanging lantern problem

Solve hanging lantern problem
You are encouraged to solve this task according to the task description, using any language you may know.

There are some groups of lantern hanging on the ceil. Each group contais one or more lanterns. Each time you can fetch one lantern. Now you need to get all these lanterns down, but you can only fetch the one in the bottom of the group. The qustion is how many ways are there to do this.

For example, there are some lanterns hanging like this:
🏮 🏮 🏮

   🏮 🏮
      🏮

Number these lanterns:
1 2 4

  3 5
    6

You can take like this: [6,3,5,2,4,1] or [3,1,6,5,2,4]
But not: [6,3,2,4,5,1] because at that time 5 is under 4.

There are 60 ways to take them down.

---

Task

Input:
First an integer (n): the number of groups.
Then n integers: the number of lanterns each group has.
Output:
An integer: the number of sequences.

For example, the input of the example above could be:
3

1

2

3

And the output is:
60

---

Optional task

Output all the sequences using this format:
[a,b,c,…]

[b,a,c,…]

……

Python

Recursive version

<lang python> def getLantern(arr):

   res = 0
   for i in range(0, n):
       if arr[i] != 0:
           arr[i] -= 1
           res += getLantern(arr)
           arr[i] += 1
   if res == 0:
       res = 1
   return res

a = [] n = int(input()) for i in range(0, n):

   a.append(int(input()))

print(getLantern(a)) </lang>

VBA

See Visual Basic

Visual Basic

Works with: Visual Basic version 6

Main code

<lang vb> Dim n As Integer, c As Integer Dim a() As Integer

Private Sub Command1_Click()

   Dim res As Integer
   If c < n Then Label3.Caption = "Please input completely.": Exit Sub
   res = getLantern(a())
   Label3.Caption = "Result：" + Str(res)

End Sub

Private Sub Text1_Change()

   If Val(Text1.Text) <> 0 Then
       n = Val(Text1.Text)
       ReDim a(1 To n) As Integer
   End If

End Sub

Private Sub Text2_KeyPress(KeyAscii As Integer)

   If KeyAscii = Asc(vbCr) Then
       If Val(Text2.Text) = 0 Then Exit Sub
       c = c + 1
       If c > n Then Exit Sub
       a(c) = Val(Text2.Text)
       List1.AddItem Str(a(c))
       Text2.Text = ""
   End If

End Sub

Function getLantern(arr() As Integer) As Integer

   Dim res As Integer
   For i = 1 To n
       If arr(i) <> 0 Then
           arr(i) = arr(i) - 1
           res = res + getLantern(arr())
           arr(i) = arr(i) + 1
       End If
   Next i
   If res = 0 Then res = 1
   getLantern = res

End Function</lang>

Form code

<lang vb> VERSION 5.00 Begin VB.Form Form1

  Caption         =   "Get Lantern"
  ClientHeight    =   4410
  ClientLeft      =   120
  ClientTop       =   465
  ClientWidth     =   6150
  LinkTopic       =   "Form1"
  ScaleHeight     =   4410
  ScaleWidth      =   6150
  StartUpPosition =   3  
  Begin VB.CommandButton Command1 
     Caption         =   "Start"
     Height          =   495
     Left            =   2040
     TabIndex        =   5
     Top             =   3000
     Width           =   1935
  End
  Begin VB.ListBox List1 
     Height          =   1320
     Left            =   360
     TabIndex        =   4
     Top             =   1440
     Width           =   5175
  End
  Begin VB.TextBox Text2 
     Height          =   855
     Left            =   3360
     TabIndex        =   1
     Top             =   480
     Width           =   2175
  End
  Begin VB.TextBox Text1 
     Height          =   855
     Left            =   360
     TabIndex        =   0
     Top             =   480
     Width           =   2175
  End
  Begin VB.Label Label3 
     Height          =   495
     Left            =   2040
     TabIndex        =   6
     Top             =   3720
     Width           =   2295
  End
  Begin VB.Label Label2 
     Caption         =   "Number Each"
     Height          =   375
     Left            =   3960
     TabIndex        =   3
     Top             =   120
     Width           =   1695
  End
  Begin VB.Label Label1 
     Caption         =   "Total"
     Height          =   255
     Left            =   960
     TabIndex        =   2
     Top             =   120
     Width           =   1455
  End

End Attribute VB_Name = "Form1" Attribute VB_GlobalNameSpace = False Attribute VB_Creatable = False Attribute VB_PredeclaredId = True Attribute VB_Exposed = False</lang>