/*
Online Java - IDE, Code Editor, Compiler

Online Java is a quick and easy tool that helps you to build, compile, test your programs online.
*/

// This has been created to ensure I can utilize any random functions more efficiently.
// It is a creation of the NcR    permutation calculator.
// It has used techniques I learnt including recursion and also memoization to speed up execution.
// I will incorporate this into Java applications I created previously..

import java.math.*;
import java.util.*;

public class Main
{
    public static void main(String[] args) {
        System.out.println("Welcome to Online IDE!! Happy Coding :)");
        
        int originalNumber=6;
        int n=originalNumber;
        int r =3;
        Map <Integer, Long> m = new HashMap<>();
        System.out.println(Permutations (n,r,originalNumber, m));
        
    }
    
    public static long Permutations (int n,  int r, int originalNumber, Map factorialResults)
    {
        
        // n are objects
        // r is sample
       
       /*
       ***CALCULATION***
        P(n,r) =   n! / (n−r)!
        
        */
        
        long result=0;
        int temp;
        int denominator;
        
        if (n>=1)
        {
            
            // EXAMPLE
            
            // P (5,6)   =   5* 4 * 3 * 2 * 1   /   (6-5)!     =    24 / 2!    =  24 / 2 * 1   =    24/2  = 12
            
        
        result = (n* (Permutations (n-1, r,originalNumber, factorialResults)));
        
        factorialResults.put(n,result);
        System.out.println("getting result back out: " + factorialResults.get(n));
        
        
        if (n==originalNumber)
        {
            System.out.println("here1");
            
            denominator = originalNumber-r;
            System.out.println(denominator);
            
            
        // this is using the Java Memoization technique to ensure the factorial outcome is not calculated again, to save program cycles.
        
            if (factorialResults.containsKey(denominator))
            
            {
                System.out.println("here");
                System.out.println("This is exact value of factorial  " + (denominator) + " : " +  factorialResults.get(denominator));
                
                return result / (long)factorialResults.get(denominator);
            }
            
           
        }
        
        
            System.out.println("value of n: " + n);
            System.out.println("value of result: " + r);
            return result;
            
        }
          return 1;   
        }
        
    }