Merge pull request #1426 from shellhub/dev

Added AliquotSum and Median

DIRECTORY.md

@@ -117,6 +117,7 @@
   * [AbsoluteMax](https://github.com/TheAlgorithms/Java/blob/master/Maths/AbsoluteMax.java)
   * [AbsoluteMin](https://github.com/TheAlgorithms/Java/blob/master/Maths/AbsoluteMin.java)
   * [AbsoluteValue](https://github.com/TheAlgorithms/Java/blob/master/Maths/AbsoluteValue.java)
+  * [AliquotSum](https://github.com/TheAlgorithms/Java/blob/master/Maths/AliquotSum.java)
   * [AmicableNumber](https://github.com/TheAlgorithms/Java/blob/master/Maths/AmicableNumber.java)
   * [Area](https://github.com/TheAlgorithms/Java/blob/master/Maths/Area.java)
   * [Average](https://github.com/TheAlgorithms/Java/blob/master/Maths/Average.java)
@@ -134,6 +135,7 @@
   * [GCDRecursion](https://github.com/TheAlgorithms/Java/blob/master/Maths/GCDRecursion.java)
   * [LucasSeries](https://github.com/TheAlgorithms/Java/blob/master/Maths/LucasSeries.java)
   * [MaxValue](https://github.com/TheAlgorithms/Java/blob/master/Maths/MaxValue.java)
+  * [Median](https://github.com/TheAlgorithms/Java/blob/master/Maths/Median.java)
   * [MinValue](https://github.com/TheAlgorithms/Java/blob/master/Maths/MinValue.java)
   * [Mode](https://github.com/TheAlgorithms/Java/blob/master/Maths/Mode.java)
   * [NumberOfDigits](https://github.com/TheAlgorithms/Java/blob/master/Maths/NumberOfDigits.java)

Maths/AliquotSum.java

@@ -0,0 +1,35 @@
+package Maths;
+
+/**
+ * <p>
+ * In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n,
+ * that is, all divisors of n other than n itself.
+ * For example, the proper divisors of 15 (that is, the positive divisors of 15 that are not equal to 15)
+ * are 1, 3 and 5, so the aliquot sum of 15 is 9 i.e. (1 + 3 + 5).
+ * </p>
+ * Wikipedia: https://en.wikipedia.org/wiki/Aliquot_sum
+ */
+public class AliquotSum {
+    public static void main(String[] args) {
+        assert aliquotSum(1) == 0;
+        assert aliquotSum(6) == 6;
+        assert aliquotSum(15) == 9;
+        assert aliquotSum(19) == 1;
+    }
+
+    /**
+     * Finds the aliquot sum of an integer number
+     *
+     * @param number a positive integer
+     * @return aliquot sum of given {@code number}
+     */
+    public static int aliquotSum(int number) {
+        int sum = 0;
+        for (int i = 1, limit = number / 2; i <= limit; ++i) {
+            if (number % i == 0) {
+                sum += i;
+            }
+        }
+        return sum;
+    }
+}

Maths/Median.java

@@ -0,0 +1,28 @@
+package Maths;
+
+import java.util.Arrays;
+
+/**
+ * Wikipedia: https://en.wikipedia.org/wiki/Median
+ */
+public class Median {
+    public static void main(String[] args) {
+        assert median(new int[]{0}) == 0;
+        assert median(new int[]{1, 2}) == 1.5;
+        assert median(new int[]{4, 1, 3, 2}) == 2.5;
+        assert median(new int[]{1, 3, 3, 6, 7, 8, 9}) == 6;
+        assert median(new int[]{1, 2, 3, 4, 5, 6, 8, 9}) == 4.5;
+    }
+
+    /**
+     * Calculate average median
+     *
+     * @param values number series
+     * @return median of given {@code values}
+     */
+    public static double median(int[] values) {
+        Arrays.sort(values);
+        int length = values.length;
+        return length % 2 == 0 ? (values[length / 2] + values[length / 2 - 1]) / 2.0 : values[length / 2];
+    }
+}