How can Fibonacci numbers be computed recursively in Java?

"As another example, consider the following Java implementation of the naive recursive Fibonacci sequence. An additional condition has been included to check for “invalid” negative values of n for which an exception is thrown.\n\n1 public static int fibonacci(int n) {\n\n2 if(n < 0) {\n\n3 throw new IllegalArgumentException(\"Undefined for n < 0\");\n\n4 } else if(n <= 1) {\n\n5 return 1;\n\n6 } else {\n\n7 return fibonacci(n-1) + fibonacci(n-2);\n\n8 }\n\n9 }\n\nJava is not a language that provides implicit memoization. Instead, we need to explicitly keep track of values using a table. In the following example, we use a Map data structure to store previously computed values.\n\n1 public static int fibMemoization(int n, Map<Integer, Integer> m) {\n\n2 if(n < 0) {\n\n3 throw new IllegalArgumentException(\"Undefined for n < 0\");\n\n4 } else if(n <= 1) {\n\n5 return 1;\n\n6 } else {\n\n7 Integer result = m.get(n);\n\n8 if(result == null) {\n\n9 Integer a = fibMemoization(n-1, m);\n\n10 Integer b = fibMemoization(n-2, m);\n\n11 result = a + b;\n\n12 m.put(n, result);\n\n13 }\n\n14 return result;\n\n15 }\n\n16 }"