Data commit

Task/Calkin-Wilf-sequence/Java/calkin-wilf-sequence.java

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+import java.util.ArrayDeque;
+import java.util.Deque;
+
+public final class CalkinWilfSequence {
+
+	public static void main(String[] aArgs) {
+		Rational term = Rational.ONE;
+	    System.out.println("First 20 terms of the Calkin-Wilf sequence are:");
+	    for ( int i = 1; i <= 20; i++ ) {
+	    	System.out.println(String.format("%2d", i) + ": " + term);
+	    	term = nextCalkinWilf(term);
+	    }
+	    System.out.println();
+	
+	    Rational rational = new Rational(83_116, 51_639);
+	    System.out.println(" " + rational + " is the " + termIndex(rational) + "th term of the sequence.");
+
+	}
+	
+	private static Rational nextCalkinWilf(Rational aTerm) {
+		Rational divisor = Rational.TWO.multiply(aTerm.floor()).add(Rational.ONE).subtract(aTerm);
+		return Rational.ONE.divide(divisor);
+	}
+	
+	private static long termIndex(Rational aRational) {
+	    long result = 0;
+	    long binaryDigit = 1;
+	    long power = 0;
+	    for ( long term : continuedFraction(aRational) ) {
+	        for ( long i = 0; i < term; power++, i++ ) {
+	            result |= ( binaryDigit << power );
+	        }
+	        binaryDigit = ( binaryDigit == 0 ) ? 1 : 0;
+	    }
+	    return result;
+	}
+	
+	private static Deque<Long> continuedFraction(Rational aRational) {
+	    long numerator = aRational.numerator();
+	    long denominator = aRational.denominator();
+	    Deque<Long> result = new ArrayDeque<Long>();
+	
+	    while ( numerator != 1 ) {
+	        result.addLast(numerator / denominator);
+	        long copyNumerator = numerator;
+	        numerator = denominator;
+	        denominator = copyNumerator % denominator;
+	    }
+	
+	    if ( ! result.isEmpty() && result.size() % 2 == 0 ) {
+	    	final long back = result.removeLast();
+	    	result.addLast(back - 1);
+	        result.addLast(1L);
+	    }
+	    return result;
+	}
+
+}
+
+final class Rational {
+	
+	public Rational(long aNumerator, long aDenominator) {
+    	if ( aDenominator == 0 ) {
+    		throw new ArithmeticException("Denominator cannot be zero");
+    	}
+    	if ( aNumerator == 0 ) {
+    		aDenominator = 1;
+    	}
+    	if ( aDenominator < 0 ) {
+    		numer = -aNumerator;
+    		denom = -aDenominator;
+    	} else {
+    		numer = aNumerator;
+    		denom = aDenominator;
+    	}    	
+    	final long gcd = gcd(numer, denom);
+    	numer = numer / gcd;
+    	denom = denom / gcd;
+    }
+	
+	public Rational add(Rational aOther) {
+    	return new Rational(numer * aOther.denom + aOther.numer * denom, denom * aOther.denom);
+    }
+	
+	public Rational subtract(Rational aOther) {
+		return new Rational(numer * aOther.denom - aOther.numer * denom, denom * aOther.denom);
+	}
+
+    public Rational multiply(Rational aOther) {
+		return new Rational(numer * aOther.numer, denom * aOther.denom);
+	}
+
+    public Rational divide(Rational aOther) {
+		return new Rational(numer * aOther.denom, denom * aOther.numer);
+	}
+
+    public Rational floor() {
+    	return new Rational(numer / denom, 1);
+    }
+
+    public long numerator() {
+    	return numer;
+    }
+
+    public long denominator() {
+    	return denom;
+    }
+
+    @Override
+    public String toString() {
+    	return numer + "/" + denom;
+    }
+
+    public static final Rational ONE = new Rational(1, 1);
+    public static final Rational TWO = new Rational(2, 1);
+
+    private long gcd(long aOne, long aTwo) {
+    	if ( aTwo == 0 ) {
+    		return aOne;
+    	}
+    	return gcd(aTwo, aOne % aTwo);
+    }
+
+    private long numer;
+    private long denom;
+
+}