#include <iostream.h>
#include <stdlib.h>
#include <iomanip.h>
#include "textlib.h"

//declaring the two functions walk and average
int walk(int distance);
double average(int numTries,int distance);


int main()
{
	//the program was developped in a generic manner to handle n inputs for n 

        //operations.
	int totDistance,ranWalks,distCovered=1;
	
	//Prompting the user for input data.
	cout<<" Enter the total distance to be covered: ";
	cin>>totDistance;
	cout<<endl;
	cout<<" Enter the number of random walks      : ";
	cin>>ranWalks;
	cout<<endl;	
	cout<<endl;

	cout<<'\t'<<" Distance Interval"<<'\t'<<"Average "<<endl;
			
	cout<<'\t'<<"__________________"<<'\t'<<"_______ "
			<<endl<<endl;

	//This loop will repeat the average calculations 10 times.
	while (distCovered<=totDistance)
	{
		cout<<'\t'<<'\t'<<distCovered<<'\t'<<'\t'<<setreal(1,1)
			<<average(ranWalks,distCovered)
			<<endl<<endl;

	distCovered++;
	}

	return 0;
}



//implementation of the walk function here!
int walk(int distance)
{	
	//the integer objects are initialized here!
	int p=0,numSteps=0;
		
	//this loop is active as long as the absolute value of p is less or equal to the
	//distance!

	while (abs(p)<distance)
			{		
			
				
	//this if statement controls the heads and tails number of occurance.
	//while a counter is active concurrently (numSteps) to yield the overall 
				//number of steps performed!
				if ( rand() % 2 == 0)
					
					 	p++;
					
				
				else

					
						p--;
					

		
				numSteps++;
			}
		
		
		return numSteps;
}






//implementation of the average function here!
double average(int numTries, int distance)
{
	
	double sumSteps=0,count=1;

	//this will activate the loop as long as the counter is not equal to the 

	//number of tries.
	
	while(count<=numTries)
		{
		//the sum is like a bin where the walk function results are accumulated
		sumSteps+= double (walk(distance));
		count++;
		}

return (sumSteps/ count);

}


// Relationship  between both distance and average are:
// average equal approx. distance^2.

//Run:
/*
 Enter the total distance to be covered: 10

 Enter the number of random walks      : 50

  
 
         Distance Interval      Average
        __________________      _______

                1               1.0

                2               4.0

                3               10.2

                4               16.5

                5               25.6

                6               34.2

                7               48.9

                8               73.7

                9               86.4

                10              99.7

Press any key to continue

*/