Added Recursive implementation to get nth fibonacci number with memoization

src/main/java/com/thealgorithms/maths/FibonacciWithDP.java

@@ -0,0 +1,40 @@
+package com.thealgorithms.maths;
+
+import java.math.BigInteger;
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+/**
+ * author : @pri-sin
+ * This class provides methods for calculating Fibonacci numbers using Recursion with Memoization.
+ */
+public final class FibonacciWithDP {
+	static List<BigInteger> fibonacciList=new ArrayList<>(Arrays.asList(BigInteger.ZERO,BigInteger.ONE));
+
+    private FibonacciWithDP() {
+    }
+
+    /**
+     * Calculates the nth Fibonacci number.
+     *
+     * @param n The index of the Fibonacci number to calculate.
+     * @return The nth Fibonacci number as a BigInteger.
+     * @throws IllegalArgumentException if the input 'n' is a negative integer.
+     */
+    public static BigInteger computeRecursively(final int n) {
+        if (n < 0) {
+            throw new IllegalArgumentException("Input 'n' must be a non-negative integer.");
+        }
+
+        if (n <= 1) {
+            return fibonacciList.get(n);
+        }
+
+        if(fibonacciList.size()<=n) {
+        	fibonacciList.add(computeRecursively(n-2).add(computeRecursively(n-1)));
+        }
+
+        return fibonacciList.get(n);
+    }  
+}

src/test/java/com/thealgorithms/maths/FibonacciWithDPTest.java

@@ -0,0 +1,34 @@
+package com.thealgorithms.maths;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import java.math.BigInteger;
+import org.junit.jupiter.api.Test;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.ValueSource;
+
+public class FibonacciWithDPTest {
+    @Test
+    public void checkValueAtZero() {
+        assertEquals(BigInteger.ZERO, FibonacciWithDP.computeRecursively(0));
+    }
+
+    @ParameterizedTest
+    @ValueSource(ints = {1, 2})
+    public void checkValueAtOneAndTwo(int number) {
+        assertEquals(BigInteger.ONE, FibonacciWithDP.computeRecursively(number));
+    }
+
+    @Test
+    public void checkRecurrenceRelation() {
+        for (int i = 0; i < 100; ++i) {
+            assertEquals(FibonacciWithDP.computeRecursively(i + 2), FibonacciWithDP.computeRecursively(i + 1).add(FibonacciWithDP.computeRecursively(i)));
+        }
+    }
+
+    @Test
+    public void checkNegativeInput() {
+        assertThrows(IllegalArgumentException.class, () -> { FibonacciWithDP.computeRecursively(-1); });
+    }
+}