import java.util.Random;


public class Wiener {

	Random r = null;
	
	public Wiener(){
		r = new Random(System.currentTimeMillis());
	}
	
	
	public double[] approxWiener(int n, double[] ts){
		
		double[] result = new double[ts.length];
		
		//Realisiere ZV Z_n
		double[] zs = new double[(int)Math.floor(getMax(ts)*n)+1];
		for(int i=0; i<zs.length; i++){
			double ber = r.nextDouble();
			if(ber<0.5){
				zs[i] = -1.0;
			}
			else{
				zs[i] = 1.0;
			}
		}
		

		//Berechne X_t(n)
		for(int i=0; i<ts.length; i++){
		
			//Berechne S_floor(nt)
			double nt = ts[i]*n;
			int nt_floor = (int) Math.floor(nt);
			
			result[i] = 0;
			for(int j=1; j<=nt_floor; j++){
				result[i] += zs[j-1]; 
			}
			
			result[i] = result[i] / Math.sqrt(n);
			
			result[i] += ((nt-nt_floor)*zs[nt_floor]) / Math.sqrt(n);
		}
		
		return result;
	}
	
	 public static double getMax(double[] numbers){
        
		
        double max = Double.MIN_VALUE;
        
        for (int i = 0; i < numbers.length; i++) {
            if (numbers[i] > max) {
            	max = numbers[i];
            }
        }
        
        return max;
	 }
	
	 public static double getMean(double[] numbers){
	       
        double mean = 0.0;
        if (numbers.length < 1) {
            return 0;
        }
        for (int i = 0; i < numbers.length; i++) {
            mean += numbers[i];
        }
        
        return mean / (double)numbers.length;
	 }
	 
	 
	 public static double getVar(double[] numbers){
	       
        double var = 0.0;
        if (numbers.length < 1) {
            return 0;
        }
        double mean = getMean(numbers);
        for (int i = 0; i < numbers.length; i++) {
            var += Math.pow(numbers[i]- mean, 2);
        }
        
        return var / (double)(numbers.length-1);
	 }
	 
	public static void main(String[] args) {
		
		int sampleSize = 1000;
		int order = 1000;
		int n_stuetz = 1000;
		double[] sample = new double[sampleSize];
		
		//Bestimme Stützstellen
		System.out.println("Stützstellen:");
		double[] stuetz = new double[n_stuetz+1];
		 for (int i = 0; i < stuetz.length; i++) {
			 stuetz[i] = (double)i / (double)n_stuetz;
			 System.out.println(stuetz[i]);
		 }
		 System.out.println();
		 
		 Wiener w = new Wiener();
		 for (int i = 0; i < sample.length; i++) {
			 double[] val = w.approxWiener(order, stuetz);
			 sample[i] = getMax(val);
		 }
		 
		 //Berechne Mittelwert und Varianz der Maxima-Approximation
		 
		 double mean = getMean(sample);
		 double var = getVar(sample);
		 
		 System.out.println("Mittelwert von Maxima :"+mean);
		 System.out.println("Varianz von Maxima :"+var);
		 
	}

}