import java.util.*;

// T J Finney, 2001
// Not to be sold without my permission.

class Stats {
	
	// static or class variables
	
	// random number generator
	private static Random rand = new Random();
	
	// static or class methods
	
	// get uniformly distributed double in [0, 1]
	public static double getRand () {
		return rand.nextDouble();
	}
	
	// get uniformly distributed integer in [0, N - 1]
	public static int getRandInt (int N) {
		return rand.nextInt(N);
	}
	
	// compute growth increment
	// uses logistic growth eqn
	// dN/dt = rN(1-N/K)
	// N = current size
	// r = annual growth rate
	// K = size limit
	public static double logistic (double N, double r, double K) {
	// calculate dN/dt
	return r * N * (1 - N / K);
	}
	
	public static void main (String [] args) {
		
		//test methods
		
		for (int i = 0; i < 5; i++) {
			System.out.println("Rand: " + Stats.getRand());
		}
		
		System.out.print("RandInt: ");
		for (int i = 0; i < 50; i++) {
			System.out.print(Stats.getRandInt(2));
		}
		System.out.println();
		
		for (int i = 0; i < 5; i++) {
			System.out.println("Trial: " + Stats.trial(0.5));
		}
		
		double[] numbers = {0, 1, 2, 3};
		for (int i = 0; i < 5; i++) {
			System.out.println("Select: " + Stats.select(numbers, -1));
		}
		
		for (int i = 0; i < 5; i++) {
			System.out.println("Zipf: " + Stats.zipf(3));
		}
	}
	
	// select item using power law
	// arguments:
	// * array of numbers ni
	// * exponent p
	// probability of selecting array item:
	// p(ni) = k * (ni^p)
	// k is a normalisation constant
	// p(ni) = 0 if ni is zero, even when p < 0
	// returns index in [0, array size - 1]
	public static int select (double[] nums, double p) {
		// make array of probabilities
		double[] probs = new double[nums.length];
		for (int i = 0; i < probs.length; i++) {
			if (nums[i] == 0) { probs[i] = 0; }
			else { probs[i] = Math.pow(nums[i], p); }
		}
		// sum probabilities
		double sum = 0;
		for (int i = 0; i < probs.length; i++) {
			sum += probs[i];
		}
		// obtain random number in range [0, sum]
		double r = sum * Stats.getRand();
		// subtract probs until result negative
		// no of iterations gives required index
		int i;
		for (i = 0; i < probs.length; i++) {
			r -= probs[i];
			if (r < 0) { break; }
		}
		return i;
	}
	
	// perform trial using uniform prob dist
	// p (probability) must be in [0, 1]
	public static boolean trial (double p) {
		if (p < 0) { p = 0; }
		if (p > 1) { p = 1; }
		if (rand.nextDouble() <= p) { return true; }
		else { return false; }
	}
	
	// select item using Zipf's law
	// parameter is size of ranked array
	// returns index in [0, array size - 1]
	public static int zipf (int size) {
		// make array of numbers
		double[] nums = new double[size];
		for (int i = 0; i < nums.length; i++) {
			nums[i] = i + 1;
		}
		// get index using special case of power law
		return Stats.select(nums, -1.0);
	}
}