Data commit

Task/Harmonic-series/Haskell/harmonic-series-1.hs

@@ -0,0 +1,44 @@
+import Data.List (find)
+import Data.Ratio
+
+--------------------- HARMONIC SERIES --------------------
+
+harmonic :: [Rational]
+harmonic =
+  scanl1
+    (\a x -> a + 1 / x)
+    [1 ..]
+
+-------------------------- TESTS -------------------------
+main :: IO ()
+main = do
+  putStrLn "First 20 terms:"
+  mapM_ putStrLn $
+    showRatio <$> take 20 harmonic
+
+  putStrLn "\n100th term:"
+  putStrLn $ showRatio (harmonic !! 99)
+  putStrLn ""
+
+  putStrLn "One-based indices of first terms above threshold values:"
+  let indexedHarmonic = zip [0 ..] harmonic
+  mapM_
+    putStrLn
+    $ fmap
+      ( showFirstLimit
+          <*> \n -> find ((> n) . snd) indexedHarmonic
+      )
+      [1 .. 10]
+
+-------------------- DISPLAY FORMATTING ------------------
+
+showFirstLimit n (Just (i, r)) =
+  "Term "
+    <> show (succ i)
+    <> " is the first above "
+    <> show (numerator n)
+
+showRatio :: Ratio Integer -> String
+showRatio =
+  ((<>) . show . numerator)
+    <*> (('/' :) . show . denominator)

Task/Harmonic-series/Haskell/harmonic-series-2.hs

@@ -0,0 +1 @@
+Hn=: {{ +/ %1+i.y }}"0

Task/Harmonic-series/Haskell/harmonic-series-3.hs

@@ -0,0 +1,5 @@
+   Hn i.4 5
+      0       1     1.5 1.83333 2.08333
+2.28333    2.45 2.59286 2.71786 2.82897
+2.92897 3.01988 3.10321 3.18013 3.25156
+3.31823 3.38073 3.43955 3.49511 3.54774

Task/Harmonic-series/Haskell/harmonic-series-4.hs

@@ -0,0 +1 @@
+Hni=: {{ 0,+/\ %1+i.y}}

Task/Harmonic-series/Haskell/harmonic-series-5.hs

@@ -0,0 +1,5 @@
+   4 5$Hni 20
+      0       1     1.5 1.83333 2.08333
+2.28333    2.45 2.59286 2.71786 2.82897
+2.92897 3.01988 3.10321 3.18013 3.25156
+3.31823 3.38073 3.43955 3.49511 3.54774

Task/Harmonic-series/Haskell/harmonic-series-6.hs

@@ -0,0 +1,2 @@
+   Hn 1e5
+12.0901

Task/Harmonic-series/Haskell/harmonic-series-7.hs

@@ -0,0 +1,14 @@
+   (Hni 1e5) (] ,. I. ,. I. { [) i.13
+ 0     0       0
+ 1     1       1
+ 2     4 2.08333
+ 3    11 3.01988
+ 4    31 4.02725
+ 5    83 5.00207
+ 6   227 6.00437
+ 7   616 7.00127
+ 8  1674 8.00049
+ 9  4550 9.00021
+10 12367      10
+11 33617      11
+12 91380      12

Task/Harmonic-series/Haskell/harmonic-series-8.hs

@@ -0,0 +1,2 @@
+   (Hn 91380)-12
+3.05167e_6

Task/Harmonic-series/Haskell/harmonic-series-9.hs

@@ -0,0 +1,73 @@
+import java.math.BigInteger;
+
+public class HarmonicSeries {
+	
+	public static void main(String[] aArgs) {
+		
+		System.out.println("The first twenty Harmonic numbers:");
+		for ( int i = 1; i <= 20; i++ ) {
+			System.out.println(String.format("%2s", i) + ": " + harmonicNumber(i));
+		}		
+		
+		System.out.println();
+		for ( int i = 1; i <= 10; i++ ) {
+			System.out.print("The first term greater than ");
+			System.out.println(String.format("%2s%s%5s", i, " is Term ", indexedHarmonic(i)));
+		}
+
+	}
+
+    private static Rational harmonicNumber(int aNumber) {
+		Rational result = Rational.ZERO;
+		for ( int i = 1; i <= aNumber; i++ ) {
+			result = result.add( new Rational(BigInteger.ONE, BigInteger.valueOf(i)) );
+		}
+		
+		return result;
+	}
+	
+	private static int indexedHarmonic(int aTarget) {
+		BigInteger target = BigInteger.valueOf(aTarget);
+		Rational harmonic = Rational.ZERO;
+		BigInteger next = BigInteger.ZERO;
+		
+		while ( harmonic.numerator.compareTo(target.multiply(harmonic.denominator)) <= 0 ) {
+			next = next.add(BigInteger.ONE);
+			harmonic = harmonic.add( new Rational(BigInteger.ONE, next) );						
+		}
+		
+		return next.intValueExact();
+	}	
+	
+	private static class Rational {
+		
+		private Rational(BigInteger aNumerator, BigInteger aDenominator) {
+			numerator = aNumerator;
+			denominator = aDenominator;
+			
+	    	BigInteger gcd = numerator.gcd(denominator);	    	
+	    	numerator = numerator.divide(gcd);
+	    	denominator = denominator.divide(gcd);
+	    }
+		
+		@Override
+		public String toString() {
+			return numerator + " / " + denominator;
+		}
+		
+		private Rational add(Rational aRational) {
+			BigInteger numer = numerator.multiply(aRational.denominator)
+                .add(aRational.numerator.multiply(denominator));
+			BigInteger denom = aRational.denominator.multiply(denominator);
+			
+			return new Rational(numer, denom);
+		}	
+		
+		private BigInteger numerator;
+		private BigInteger denominator;
+		
+		private static final Rational ZERO = new Rational(BigInteger.ZERO, BigInteger.ONE);
+		
+	}
+
+}