using System;

public class Program

{   

    public static void Main()

    {   

        bool isExpert=false; // Select difficulty

        // SINGLE PILLAR

        int fragments=30; // Select minimum amount of desired fragments.

        // ALL 4 PILLARS (w/ crafting)

        int stardustmin=30; int vortexmin=30; int solarmin=30; int nebulamin=12; // Select minimum amount for each individual fragment. Accounts for the possibility of crafting fragments.

                                                                                 // When there is no requirement, you must input '0'.

        // HALLOWED BARS

        int bars=66; int mechs=3; // Select hallowed bars minimum threshold and mech kills count.

        int chunkmin=12,chunkmax=20,fragmin=1,barmin=15,fragmax=3,barmax=30;

        if (isExpert==true){

            Console.WriteLine("Difficulty = Expert+");

            fragmin=2; barmin=20; fragmax=5; barmax=35;

        }

        else Console.WriteLine("Difficulty = Classic");

        double[] cumul= new double[(chunkmax*fragmax+1)*2];

        double[] exact= new double[(chunkmax*fragmax+1)*2];

        double prob=0; cumul[0]=1; 

        // transform combination counts into probabilities, sum over all possible chunk counts

        for (int f=1;f<2*(fragmax*chunkmax+1);f++){

            cumul[f]=0; exact[f-1]=0;

            long[,] fragmatrix=count(chunkmax,f,fragmin,fragmax);

            for (int chunks=chunkmin;chunks<chunkmax+1;chunks++){

                    prob=Convert.ToDouble(fragmatrix[chunks,f-1])/Math.Pow(fragmax-fragmin+1,chunks);

                    //Console.WriteLine("probability with "+chunks+" chunks ="+prob);

                    cumul[f]=cumul[f]+prob;

                }

            cumul[f]=1-cumul[f]/(chunkmax-chunkmin+1);

            exact[f-1]=cumul[f-1]-cumul[f]; 

            }       

        Console.WriteLine("Probability of at least "+(fragments)+" fragments from a single pillar = "+100*cumul[fragments]+"%");        

        //Console.WriteLine("Probability of exactly "+(fragments)+" pillar fragments = "+100*probs[fragments]+"%");

        int[] p=new int[] {stardustmin,vortexmin,solarmin,nebulamin};

        prob=cumul[p[0]]*cumul[p[1]]*cumul[p[2]]*cumul[p[3]];   // probability of obtaining required values without any crafting

        for (int i=0;i<4;i++){

            for (int n=1;n<p[i]+1;n++){

                prob=prob+exact[p[i]-n]*cumul[p[(i+1)%4]+n]*cumul[p[(i+2)%4]+n]*cumul[p[(i+3)%4]+n]; // introduce possibility of crafting

            }

        }

        Console.WriteLine("Probability of at least "+p[0]+" stardust & "+p[1]+" vortex & "+p[2]+" solar & "+p[3]+" nebula fragments = "+100*prob+"%");  

        double barprob=Convert.ToDouble(count(mechs,bars,barmin,barmax)[mechs,bars-1])/Math.Pow(barmax-barmin+1,mechs);

        Console.WriteLine("Probability of at least "+(bars)+" bars from "+mechs+" mech kills = "+100*(1-barprob)+"%");

    }

    // count combinations of 'trials'-many numbers between 'trymin' and 'trymax' adding up to <= 'maxsum';

    public static long[,] count(int trials,int maxsum,int trymin,int trymax){

        long[,] matrix = new long[trials+1,maxsum]; 

        for (int b=0;b<trials+1;b++){

            for (int m=0;m<maxsum;m++){

                 if (trymin*b>m){

                    matrix[b,m]=0;

                }

                else if (trymax*b<m+1){

                    matrix[b,m]=Convert.ToInt64(Math.Pow(trymax-trymin+1,b));

                }

                else {

                    int j=trymin;

                    while(j<trymax+1 && m>j-1){

                        matrix[b,m]=matrix[b,m]+matrix[b-1,m-j];

                        j++;

                    }

                }

            }

        }

        return matrix;

    }

}