mit-app-inventor

`RecursionTemplate`

About this app

The RecursionTemplate app is a template for implementing recursive procedures to calulate factorial, Fibonacci number, and combinations. The default return value (before implementing each function) is n. Move sliders to recursively calculate factorial(n), fibonacci(n), and C(n, k).

Code

Recursion

http://catb.org/jargon/html/R/recursion.html The Jargon File definition.
You can recognize a recursive procedure / algorithm as follows:
- The recursive call — the procedure / algorithm calls / refers to itself.
- The base case — results of the procedure / algorithm calculated without recurring.
- The inductive step — the recursive call with input(s) one step closer to the base case.

The template is for implementing recursive procedures to calulate factorial, Fibonacci number, and combinations defined as follows:

Description	Definition
Factorial	$\large f(n)= \begin{Bmatrix} 1 & n = 0 \\ n \times f \left( n - 1 \right) & n > 0 \end{Bmatrix}$
Fibonacci	$\large f(n) = \begin{Bmatrix} 0 & n = 0 \\ 1 & n = 1 \\ f(n - 1) + f(n - 2) & n > 1 \end{Bmatrix}$
Combinations (see Pascal’s Triangle)	$\large \large \begin{pmatrix} n \\ k \end{pmatrix} = \begin{Bmatrix} 1 & \begin{pmatrix} n \\ 0 \end{pmatrix} \\ 1 & \begin{pmatrix} n \\ n \end{pmatrix} \\ \begin{pmatrix} n - 1 \\ k - 1 \end{pmatrix} + \begin{pmatrix} n - 1 \\ k \end{pmatrix} & 0 \le k \le n \end{Bmatrix}$

Designer

All components retain their default properties, — except all sliders have a MaxValue of 12, a MinValue of 0, a ThumbPosition of 6, and Width and Height set to Fill parent... where necessary to center UX components.

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