Recursion to calculate Factorial

Recursion is the method of breaking down a problem into sub-parts, progressively into smaller and smaller parts, such that the last part's solution becomes easily/manually solvable.

To know factorial of 5 i.e 5! which is 5*4!, we need factorial of 4.

Hence the recursive code, recursively calls the same logical code/method to find 4!, which in turn would require 3! ; then 2! ; and then 1! and ultimately 0! which is known to be 1.

Knowing 0!=1 ; would trace back the path in backward way i.e we would know 1!=1*0!=1*1=1
2!=2*1!=2*1=2
3!=3*2!=3* 2=6
4!=4*3!=4*6=24
5!=5*4!=5*24=120

Generalizing this algorithmic logic

Similarly to know factorial of any integer n, Recursion goes back all the way from n to (n-1) to (n-2) and so on to 0! ;
and then traces back in the reverse direction, from 0!=1 to 1! to 2! to 3! and so on to ultimately get the answer of n!

          

Conceptual, Java: Understanding modularization in Programming Code

Objective: Displaying need and benefits of modularized code in Programming
using a sample case scenario- To display first three positive odd integers, and their sum.

Learning: Instead of writing all code within a single Main class, using the Main class as controller class, and different methods of different classes ,specialized to perform specific functions.

Benefits: Code becomes generalized, same program can be used for adding other computational operations like Substraction, Multiplication, Division etc by adding the methods to one class, without other classes and methods getting affected. Similarly, code re-usability, maintainability becomes high.

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Directory and Package Structure

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/Java_Core/src/Controller.java

/Java_Core/src/DataProvider.java

/Java_Core/src/Display.java

Result/Output on Running