* add LucasSeries

* add PerfectCube
* PerfectSquare

Author: realDuYuanChao

Maths/LucasSeries.java

@@ -0,0 +1,44 @@
+package Maths;
+
+/**
+ * https://en.wikipedia.org/wiki/Lucas_number
+ */
+public class LucasSeries {
+    public static void main(String[] args) {
+        assert lucasSeries(1) == 2 && lucasSeriesIteration(1) == 2;
+        assert lucasSeries(2) == 1 && lucasSeriesIteration(2) == 1;
+        assert lucasSeries(3) == 3 && lucasSeriesIteration(3) == 3;
+        assert lucasSeries(4) == 4 && lucasSeriesIteration(4) == 4;
+        assert lucasSeries(5) == 7 && lucasSeriesIteration(5) == 7;
+        assert lucasSeries(6) == 11 && lucasSeriesIteration(6) == 11;
+        assert lucasSeries(11) == 123 && lucasSeriesIteration(11) == 123;
+
+    }
+
+    /**
+     * Calculate nth number of lucas series(2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ....) using recursion
+     *
+     * @param n nth
+     * @return nth number of lucas series
+     */
+    public static int lucasSeries(int n) {
+        return n == 1 ? 2 : n == 2 ? 1 : lucasSeries(n - 1) + lucasSeries(n - 2);
+    }
+
+    /**
+     * Calculate nth number of lucas series(2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ....) using iteration
+     *
+     * @param n nth
+     * @return nth number of lucas series
+     */
+    public static int lucasSeriesIteration(int n) {
+        int previous = 2;
+        int current = 1;
+        for (int i = 1; i < n; i++) {
+            int next = previous + current;
+            previous = current;
+            current = next;
+        }
+        return previous;
+    }
+}

Maths/PerfectCube.java

@@ -0,0 +1,27 @@
+package Maths;
+
+/**
+ * https://en.wikipedia.org/wiki/Cube_(algebra)
+ */
+public class PerfectCube {
+    public static void main(String[] args) {
+        assert !isPerfectCube(-1);
+        assert isPerfectCube(0);
+        assert isPerfectCube(1);
+        assert !isPerfectCube(4);
+        assert isPerfectCube(8);
+        assert isPerfectCube(27);
+
+    }
+
+    /**
+     * Check if a number is perfect cube or not
+     *
+     * @param number number to check
+     * @return {@code true} if {@code number} is perfect cube, otherwise {@code false}
+     */
+    public static boolean isPerfectCube(int number) {
+        int a = (int) Math.pow(number, 1.0 / 3);
+        return a * a * a == number;
+    }
+}

Maths/PerfectSquare.java

@@ -0,0 +1,25 @@
+package Maths;
+
+/**
+ * https://en.wikipedia.org/wiki/Perfect_square
+ */
+public class PerfectSquare {
+    public static void main(String[] args) {
+        assert !isPerfectSquare(-1);
+        assert !isPerfectSquare(3);
+        assert !isPerfectSquare(5);
+        assert isPerfectSquare(9);
+        assert isPerfectSquare(100);
+    }
+
+    /**
+     * Check if a number is perfect square number
+     *
+     * @param number the number to be checked
+     * @return <tt>true</tt> if {@code number} is perfect square, otherwise <tt>false</tt>
+     */
+    public static boolean isPerfectSquare(int number) {
+        int sqrt = (int) Math.sqrt(number);
+        return sqrt * sqrt == number;
+    }
+}