BAEL-3519 (#8169)

* BAEL-3519
- Fibonacci Series
- Recursive method
- Iterative method

* - Added new method that uses Golden Ratio to calculate the given term of Fibonacci Series

* added binet formula implementation of constant time for fibonacci term

java-numbers-2/src/main/java/com/baeldung/fibonacci/FibonacciSeriesUtils.java

@@ -0,0 +1,34 @@
+package com.baeldung.fibonacci;
+
+import static java.lang.Math.pow;
+
+public class FibonacciSeriesUtils {
+
+    public static int nthFibonacciTermRecursiveMethod(int n) {
+        if (n == 0 || n == 1) {
+            return n;
+        }
+        return nthFibonacciTermRecursiveMethod(n - 1) + nthFibonacciTermRecursiveMethod(n - 2);
+    }
+
+    public static int nthFibonacciTermIterativeMethod(int n) {
+        if (n == 0 || n == 1) {
+            return n;
+        }
+        int n0 = 0, n1 = 1;
+        int tempNthTerm;
+        for (int i = 2; i <= n; i++) {
+            tempNthTerm = n0 + n1;
+            n0 = n1;
+            n1 = tempNthTerm;
+        }
+        return n1;
+    }
+
+    public static int nthFibonacciTermUsingBinetsFormula(int n) {
+        final double squareRootOf5 = Math.sqrt(5);
+        final double phi = (1 + squareRootOf5)/2;
+        int nthTerm = (int) ((Math.pow(phi, n) - Math.pow(-phi, -n))/squareRootOf5);
+        return nthTerm;
+    }
+}

java-numbers-2/src/test/java/com/baeldung/fibonacci/FibonacciSeriesUtilsUnitTest.java

@@ -0,0 +1,29 @@
+package com.baeldung.fibonacci;
+
+import static org.junit.Assert.assertEquals;
+
+import org.junit.Test;
+
+public class FibonacciSeriesUtilsUnitTest {
+
+    @Test
+    public void givenTermToCalculate_thenReturnThatTermUsingRecursion() {
+        int term = 10;
+        int expectedValue = 55;
+        assertEquals(FibonacciSeriesUtils.nthFibonacciTermRecursiveMethod(term), expectedValue);
+    }
+
+    @Test
+    public void givenTermToCalculate_thenReturnThatTermUsingIteration() {
+        int term = 10;
+        int expectedValue = 55;
+        assertEquals(FibonacciSeriesUtils.nthFibonacciTermIterativeMethod(term), expectedValue);
+    }
+
+    @Test
+    public void givenTermToCalculate_thenReturnThatTermUsingBinetsFormula() {
+        int term = 10;
+        int expectedValue = 55;
+        assertEquals(FibonacciSeriesUtils.nthFibonacciTermUsingBinetsFormula(term), expectedValue);
+    }
+}