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Index Exercise 3: Recursive functions (Difficult)
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 1      About Futurama
 1.1        Version information
 1.2        Getting Started
 1.2.1          Futurama Website
 1.2.1.1            Behavior of Futurama regarding TimeOuts, Login and Logoff
 1.2.1.2            Replacing an existing Futurama Session
 1.2.2          Futurama Webservice
 1.2.2.1            warmUpDocuments
 1.2.3          Futurama Export
 1.3        Overview - Futurama Modules
 1.3.1          Overview - Futurama Accounts
 1.3.2          Overview - Futurama Server
 1.3.3          Overview - Futurama Monitor
 1.3.4          Overview - Futurama Insight
 1.3.5          Overview - Futurama Console
 1.3.6          Overview - Futurama Webservice
 1.4        Loadbalancing Futurama applications
 1.4.1          Getting the most out of Futurama Web using the Load-Balancer
 1.4.2          Application Request Routing
 1.5        Text management and Multi-language
 2      Installation – Configuration – Testing
 2.1        Installation - Futurama Website Edition
 2.1.1          Installation Futurama HTML
 2.1.2          Installation Futurama Monitor
 2.1.3          Installation Futurama Insight
 2.1.4          Installation Futurama Accounts
 2.1.5          Installation SAML2LoadBalancer
 2.2        Installation - Futurama Export Edition
 2.2.1          Installation Futurama Console
 2.2.2          Installation Futurama Server
 2.3        Installation - Futurama Webservice Edition
 2.3.1          Installation Futurama Webservice
 2.4        Installation Futurama Editor
 2.5        Configuration
 2.5.1          Configuration - Cache
 2.5.2          Configuration - Calculation
 2.5.3          Configuration - Debug
 2.5.4          Configuration - File manager
 2.5.5          Configuration - Fileproviders
 2.5.6          Configuration - Format
 2.5.7          Configuration - History
 2.5.8          Configuration - Identity Provider
 2.5.9          Configuration - Log
 2.5.10           Configuration - Mail
 2.5.11           Configuration - Mapping
 2.5.12           Configuration - Monitor
 2.5.13           Configuration - PlugIns
 2.5.14           Configuration - Rendering
 2.5.15           Configuration - ScenarioRecording
 2.5.16           Configuration - Security
 2.5.17           Configuration - Server
 2.5.18           Configuration - Vision
 2.5.19           Configuration - WebAPI
 2.6        Logging
 2.7        Troubleshooting
 2.8        Security - hardening
 3      Updating and file compatibility
 3.1        Updating Futurama - Compatibility behavior
 3.2        Converting Futurama documents
 3.3        12819 - DataTable file updates
 3.4        12889 - DataTable file updates
 3.5        Conversion web.config to .NET Framework 4
 3.6        Deprecated conversion formulas
 4      Futurama Editor - How to
 4.1        At first glance
 4.2        Developing in the Futurama Editor
 4.2.1          Working with objects
 4.2.2          Evaluating objects
 4.2.3          Finding objects
 4.3        Transferring objects
 4.4        Testing objects
 4.5        Validating objects
 4.6        Troubleshooting objects
 4.7        Advanced/special functionality
 4.8        Checking the layout of objects
 5      Futurama - Formulas
 5.1        Futurama Formulas - Date and time
 5.1.1          Date
 5.1.2          Day
 5.1.3          Days360
 5.1.4          Days360Excel
 5.1.5          DaysInMonth
 5.1.6          DaysInPeriod
 5.1.7          Min
 5.1.8          Max
 5.1.9          Month
 5.1.10           Now
 5.1.11           WeekDay
 5.1.12           Year
 5.2        Futurama Formulas - Math
 5.2.1          Abs
 5.2.2          Add
 5.2.3          Divide
 5.2.4          Floor
 5.2.5          Ln
 5.2.6          Log
 5.2.7          Log10
 5.2.8          Mod
 5.2.9          Multiply
 5.2.10           Pi
 5.2.11           Power
 5.2.12           Rand
 5.2.13           Round
 5.2.14           RoundDown
 5.2.15           RoundUp
 5.2.16           SquareRoot
 5.2.17           Subtract
 5.3        Futurama Formulas - Statistical
 5.3.1          AverageDeviation
 5.3.2          Beta
 5.3.3          Binomial
 5.3.4          Covariance
 5.3.5          Factorial
 5.3.6          Gamma
 5.3.7          GeometricMean
 5.3.8          Lognormal
 5.3.9          Max
 5.3.10           Median
 5.3.11           Min
 5.3.12           Normal
 5.3.13           StandardDeviation
 5.3.14           Uniform
 5.3.15           Variance
 5.4        Futurama Formulas - Text
 5.4.1          CalculateBase64Hashcode
 5.4.2          CalculateXmlHashcode
 5.4.3          Concatenate
 5.4.4          ConcatenateBase64
 5.4.5          ContainsText
 5.4.6          Convert.CSV.2.XML
 5.4.7          ConvertFromBase64
 5.4.8          ConvertToBase64
 5.4.9          ConvertXml
 5.4.10           DecodeURL
 5.4.11           DecryptXml
 5.4.12           EncodeURL
 5.4.13           EncryptXml
 5.4.14           Find
 5.4.15           HashBase64EncodedFile
 5.4.16           HashBase64EncodedFileWithBase64
 5.4.17           HashText
 5.4.18           HashTextWithBase64
 5.4.19           Left
 5.4.20           Len
 5.4.21           Linefeed
 5.4.22           Lower
 5.4.23           Mid
 5.4.24           Proper
 5.4.25           ReadConfigKey
 5.4.26           ReadDirectoryNames
 5.4.27           ReadFile
 5.4.28           ReadFileAsBase64
 5.4.29           ReadFileNames
 5.4.30           ReadFileWithEncoding
 5.4.31           ReadXPathScalar
 5.4.32           ReadXPathVector
 5.4.33           Repeat
 5.4.34           Right
 5.4.35           Substitute
 5.4.36           Trim
 5.4.37           TrimLeft
 5.4.38           TrimRight
 5.4.39           Upper
 5.4.40           ValidatePattern
 5.4.41           XsdMessages
 5.5        Futurama Formulas - Logical
 5.5.1          And
 5.5.2          IsEmpty
 5.5.3          If
 5.5.4          IsEqual
 5.5.5          IsEven
 5.5.6          IsGreater
 5.5.7          IsGreaterEqual
 5.5.8          IsIBANChecksumValid
 5.5.9          IsLess
 5.5.10           IsLessEqual
 5.5.11           IsMemberOfGroup
 5.5.12           IsNotEqual
 5.5.13           IsOdd
 5.5.14           IsValidXml
 5.5.15           Not
 5.5.16           Or
 5.5.17           ValidateNPR
 5.6        Futurama Formulas - Table
 5.6.1          FindNextRow
 5.6.2          FindPreviousRow
 5.6.3          FindRow
 5.6.4          Sort
 5.6.5          VLookUp
 5.7        Futurama Formulas - Document
 5.7.1          CountErrors
 5.7.2          GetPathToDataFiles
 5.7.3          GetPortNumber
 5.7.4          GetRelativePathToDataFiles
 5.7.5          GetSessionID
 5.7.6          IsLicenceAvailable
 5.7.7          ReadError
 5.7.8          ReadIdentityProviderResult
 5.7.9          ReadRequestIP
 5.7.10           ReadRequestParameter
 5.7.11           ReadUserAgent
 5.7.12           ReadVersionNumber
 5.7.13           SessionTimeOut
 5.7.14           URL
 5.7.15           UserName
 5.8        Futurama Formulas - Conversion
 5.8.1          Convert.Excel.to.XML
 5.8.2          ConvertJSONtoXml
 5.8.3          ConvertTextToDate
 5.8.4          ConvertTextToNumber
 5.8.5          ConvertToBoolean
 5.8.6          ConvertToDouble
 5.8.7          ConvertToLong
 5.8.8          ConvertToString
 5.8.9          FormatDate
 5.8.10           FormatNumber
 5.8.11           Value
 5.9        Futurama Formulas - Matrix
 5.9.1          AddMatrices
 5.9.2          AddScalarToMatrix
 5.9.3          Cumulative
 5.9.4          CumulativeProductMatrix
 5.9.5          Distinct
 5.9.6          DivideMatrices
 5.9.7          DivideMatrixScalar
 5.9.8          DivideScalarMatrix
 5.9.9          Exponent
 5.9.10           First
 5.9.11           Floor
 5.9.12           If
 5.9.13           Index
 5.9.14           Inverse
 5.9.15           IsEqual
 5.9.16           IsGreater
 5.9.17           IsGreaterEqual
 5.9.18           IsNotEqual
 5.9.19           IsLess
 5.9.20           IsLessEqual
 5.9.21           Join
 5.9.22           Last
 5.9.23           Length
 5.9.24           MatrixProduct
 5.9.25           Max
 5.9.26           MaxScalarMatrix
 5.9.27           Mean
 5.9.28           Mid
 5.9.29           Min
 5.9.30           MinScalarMatrix
 5.9.31           MultiplyMatrices
 5.9.32           MultiplyMatrixVector
 5.9.33           MultiplyScalarMatrix
 5.9.34           Percentile
 5.9.35           PowerMatrix
 5.9.36           PowerMatrixScalar
 5.9.37           PowerScalarMatrix
 5.9.38           ReadMatrixFromXml
 5.9.39           Repeat
 5.9.40           Replace
 5.9.41           Reshape
 5.9.42           ReverseCumulativeProductMatrix
 5.9.43           ReverseMatrix
 5.9.44           Size
 5.9.45           Split
 5.9.46           SquareRootMatrix
 5.9.47           Step
 5.9.48           SubtractMatrices
 5.9.49           SubtractMatrixScalar
 5.9.50           SubtractScalarMatrix
 5.9.51           Sum
 5.9.52           Transpose
 5.9.53           UnitMatrix
 5.9.54           Vector
 5.10         Creating custom formulas in Futurama
 6      Futurama - Objects
 6.1        Action
 6.2        Aggregation
 6.3        Button
 6.4        ChangeValue
 6.5        CheckBox
 6.6        ClearCache
 6.7        DatabaseField
 6.8        DatabaseView
 6.9        DataTable
 6.10         DateBox
 6.11         DocConverter
 6.12         Document
 6.13         Download
 6.14         DropDownList
 6.15         EmailConverter
 6.16         ExcelConverter
 6.17         FileSaver
 6.18         FileUploader
 6.19         Fixed
 6.20         Formula
 6.21         GraphConverter
 6.22         HTMLInclude
 6.23         InterfacesNode
 6.24         LogMessage
 6.25         Navigator
 6.26         Node
 6.27         RadioButton
 6.28         RadioGroup
 6.29         Range
 6.30         Reference
 6.31         SubDocument
 6.32         TextBox
 6.33         UserTable
 6.34         UserVariable
 6.35         WebLabel
 6.36         WebListBox
 6.37         WebPage
 6.38         WebPanel
 6.39         WebReference
 6.39.1           WebReference - WCF Configuration
 6.40         WebService
 6.41         WebSlider
 6.42         WordConverter
 6.43         XmlBuilder
 6.44         XmlConverter
 6.45         XmlField
 6.46         XmlNode
 7      Futurama - Vision References
 7.1        Data
 7.1.1          ReadData
 7.1.2          WriteMessage
 7.1.3          GetPersonIdentifiers
 7.1.4          CreatePerson
 7.2        DataStore
 7.2.1          DeleteDataItem
 7.2.2          DeleteDataItemHierarchy
 7.2.3          DeleteDataItems
 7.2.4          GetDataItem
 7.2.5          GetDataItemHierarchy
 7.2.6          GetDataItems
 7.2.7          StoreData
 7.3        Accounts
 7.3.1          Activate Account
 7.3.2          Change Account
 7.3.3          Create Account
 7.3.4          GetQuestion
 7.3.5          GetQuestions
 7.3.6          Login
 7.3.7          ReadData
 7.3.8          ReinitializeAccount
 7.4        General
 7.4.1          TestConnection
 8      Futurama Vision
 8.1        Installation Futurama Vision
 8.1.1          Installation Futurama Vision Management Site
 8.1.2          Installation or Upgrade of the Futurama Vision Database
 8.2        Futurama Vision Management Site
 8.2.1          Futurama Vision Management Site - Admin
 8.2.2          Futurama Vision Management Site – Security
 8.2.3          Futurama Vision Management Site – Skinning
 8.2.4          Importing data into Futurama Vision
 8.2.4.1            Importing data by webservice
 8.2.4.2            Importing data from a Zip-file
 8.2.4.3            Importing data with Futurama Vision Batch
 8.2.4.4            Futurama Vision Webservice Security
 8.2.5          Further processing of data into Futurama Vision
 8.3        Futurama Vision File manager
 8.4        Activity overview
 8.5        Storing data in Vision from a Futurama application
 8.6        Futurama Vision – Data
 8.7        Futurama Accounts - Management Site
 8.7.1          Futurama Accounts - Table in Vision Database
 8.8        Futurama Server - Management Site
 8.8.1          Special Futurama Server Jobs
 8.9        Futurama Register - Management Site
 8.9.1          Configuration - Futurama Register
 8.10         Retrieving AppEvents from Futurama Vision
 8.11         Adding CustomPages to Vision
 9      Futurama Intermediate Control Output (FICO)
 9.1        FICO example - Change/Add HTML headers
 9.2        FICO example - Change Graph
 9.3        HTML5 Template
 10       Futurama Web API
 10.1         Postbacks of Futurama webcontrols
 10.2         Retrieving Resources using Web API
 10.3         WebAPI Session management
 11       Tutorials - Overview
 11.1         Tutorials - Examples and Downloads
 11.2         Beginners
 11.2.1           Creating formulas with Futurama
 11.2.1.1             Exercise 1: Pythagorean Theorem (Easy)
 11.2.1.2             Exercise 2: Newspaper stall (Medium)
 11.2.1.3             Exercise 3: Recursive functions (Difficult)
 11.2.1.4             Exercise 4: Leap Year (Difficult)
 11.2.1.5             Exercise 5: The Guessing Game I (Medium)
 11.2.2           Creating a Website Application
 11.2.2.1             Exercise 1: Creating a Website (Easy)
 11.2.3           Styling your website with CSS
 11.2.3.1             Exercise 1: Adding CSS (Easy)
 11.2.4           Adding interactivity to your website
 11.2.4.1             Exercise 1: Summation (Easy)
 11.2.4.2             Exercise 2: The Guessing Game II (Medium)
 11.2.4.3             Exercise 3: Nationality (Medium)
 11.2.4.4             Exercise 4: Nationality - RepeatTarget (Medium)
 11.2.4.5             Exercise 5: Reversed Guessing (Difficult)
 11.2.5           Working with Tables
 11.2.5.1             Exercise 1: Average (Easy)
 11.2.5.2             Exercise 2: Boundary values (Difficult)
 11.2.5.3             Exercise 3: Standard Deviation (Medium)
 11.2.6           Reading and processing XML-data in Futurama
 11.2.6.1             Exercise 1: Shares (Medium)
 11.2.7           Adding Graphs in Futurama
 11.2.7.1             Exercise 1: World Population (Easy)
 11.2.8           Working with Actions in Futurama
 11.2.8.1             Exercise 1: Changing Colors (Easy)
 11.2.8.2             Exercise 2: On and Off (Medium)
 11.2.8.3             Exercise 3: The ChangeValue object (Difficult)
 11.2.8.4             Exercise 4: The Guessing Game III (Medium)
 11.2.8.5             Exercise 5: CheckBox (Medium)
 11.2.9           Multiple Pages and Navigation
 11.2.10            Using XSLT to display data
 11.2.10.1              Exercise 1: Overview Summation (Easy)
 11.2.10.2              Exercise 2: Persons (Medium)
 11.2.10.3              Exercise 3: Leap Year Overview (Difficult)
 11.2.11            Webservices in Futurama
 11.2.11.1              Exercise 1: Example (Easy)
 11.2.12            Creating a Webservice Application
 11.2.12.1              Exercise 1: Add (Easy)
 11.2.12.2              Exercise 2: Webservice Nationality (Medium)
 11.2.13            Creating a Console Application
 11.2.13.1              Exercise 1: Adding extra fields (Easy)
 11.2.14            Generating Documents
 11.2.14.1              Exercise 1: Tax Rate (Medium)
 11.2.14.2              Exercise 2: Tax Rates Table (Difficult)
 11.3         Advanced
 11.3.1           Responsive Design
 11.3.1.1             Exercise 1: Orientation
 11.3.1.2             Exercise 2: Target different screen sizes
 11.4         Older Tutorials (Futurama Version 3.2)
 11.4.1           Futurama Editor Tutorial 1: The first sum
 11.4.2           Futurama Editor Tutorial 2: An annuity
 11.4.3           Futurama Editor Tutorial 3: Working with tables
 11.4.4           Futurama Editor Tutorial 4: Modelling a DB pension plan
 11.4.5           Futurama Editor Tutorial 5: Working with XML
 11.4.6           Futurama Web Tutorial 1: Hello world
 11.4.7           Futurama Web Tutorial 2: Buttons and Actions
 11.4.8           Futurama Web Tutorial 3: Textboxes
 11.4.9           Futurama Web Tutorial 4: DropdownLists
 12       Miscellaneous
 12.1         Responsive website
 12.2         Reducing memory usage for XmlNodes and XmlFields
 12.3         Explaining caching for websites and webservices
 12.4         Certificates - basic information
 12.5         Performance XML operations
 12.6         Creating XSD files and using them in combination with Futurama
 13       Templates
 14       Safe2Save WebAPI Sample
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Exercise 3: Recursive functions (Difficult)

Developer
Tutorial

 

Module: Editor

Version: 4.2.1 +

User: Developer

Difficulty: Difficult

Introduction

This exercise teaches you how to create recursive functions.

 

Prerequisites

- The Futurama Editor must be installed.
- Completing the tutorial Creating formulas with Futurama first, is recommended. 

 

Description

A recursive function is a function that calls itself during its execution.
In this exercise we will create two recursive functions, the factorial function and the Fibonacci number.

Assignment

Factorial

The factorial of the integer n, is the product of all positive integers less than or equal to n.
The factorial is denoted by n!

For example:

5! = 5 x 4 x 3 x 2 x 1 = 120

 

This function can be defined as:
When 
n>0
Use the formula
n! =n x (n-1)!
If n=0 
then use the fixed value 
0! =1

Assignment 1: Create this formula in Futurama (Type Long).

Fibonacci number

The Fibonacci function will enable us to create the Fibonacci sequence of numbers.
By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two.

This creates the sequence:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

 

This function can be defined as:
f(n) = f(n-1) + f(n-2) 
with fixed values 
f(0) = 0 
f(1) = 1

Assignment 2: Create this formula in Futurama (Type Long).

Tips

  • To create a recursive function in Futurama you have to create an argument, in which you refer to the function itself.
  • Make sure your recursive function always has a limiting condition. Try to use the If function to indicate wheter to use a formula or a fixed value.
  • For both formulas you only need one argument (for example n). When referring to your function to create the recursivity, fill the argument(s) with the formulas n-1 and n-2.

Solutions

Answers

- Check your functions with the tables below

n!  f(n) 
0 1 0
1 1 1
2 2 1
3 6 2
4 24 3
5 120 5
6 720 8
7 5040 13
8 40.320 21
9 362.880 34
10 3.628.800 55

Download

image

You can download our solution for this assignment by clicking the image at the right. (Futurama 4.2.1.2)
Please note that you can very well have a different solution that is just as good as ours.

Variations

If you want some more practise on this subject, you could try the extra exercises below.
We won't provide a solution for these variations, just consider them as a way to further experiment with Futurama.

  • (Medium:) Calculate the sum of the numbers 1 to 100, using a recursive function.

Updated: 2012-12-05

 


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