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/*
 *  This file is part of "TweetyProject", a collection of Java libraries for
 *  logical aspects of artificial intelligence and knowledge representation.
 *
 *  TweetyProject is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU Lesser General Public License version 3 as
 *  published by the Free Software Foundation.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public License
 *  along with this program. If not, see .
 *
 *  Copyright 2016 The TweetyProject Team 
 */
package net.sf.tweety.commons.util;

import java.util.Collection;

/**
 * This class contains some useful math tools.
 * 
 * @author Matthias Thimm
 */
public class MathTools {

	/**
	 * This method computes "n choose k". If n < 0 or k < 0
	 * the result is defined to be 0.
	 * @param n an integer.
	 * @param k an integer
	 * @return the value of "n choose k".
	 */
	public static Integer binomial(Integer n, Integer k){
		if(n < 0 || k < 0)
			return 0;
		if(n < k) return 0;
		if(k == 0) return 1;
		if(n == 0) return 0;		
		return MathTools.binomial(n-1,k-1) + MathTools.binomial(n-1,k);		
	}
	
	/**
	 * Computes the faculty of the given number.
	 * @param i an integer.
	 * @return the value 1*...*i or 1 if i==0.
	 */
	public static int faculty(int i){
		if(i < 0) return 0;
		if(i == 0) return 1;
		int result = 1;
		for(int j = 2; j <= i; j++)
			result *= j;
		return result;
	}
	
	/**
	 * Compute the average value and the variance of the given list of
	 * numbers.
	 * @param values some values
	 * @return a pair of average value (first element) and variance (second element).
	 */
	public static Pair averageAndVariance(Collection values){
		Pair result = new Pair();
		Double sum = 0d;
		for(Double d: values)
			sum += d;
		result.setFirst(sum/values.size());
		sum = 0d;
		for(Double d: values)
			sum += Math.pow((d-result.getFirst()), 2);
		result.setSecond(sum/(values.size()-1));
		return result;		
	}
}