Sockets - Tatiana

lib/fibonacci.rb

@@ -5,8 +5,40 @@
 # ....
 # e.g. 6th fibonacci number is 8
 
-# Time complexity: ?
-# Space complexity: ?
+# Time complexity: O(n) because you execute the fib sequence n times
+# Space complexity: O because no additional space is used to compute
+
+# iterative solution
 def fibonacci(n)
-  raise NotImplementedError
+  raise ArgumentError if n == nil || n < 0 || n.class != Integer
+  return n if n < 2
+
+  if n >= 2
+    current_value= 0
+    previous_value = 1
+    next_value = 0
+    number = n - 1
+
+    number.times do 
+      next_value = current_value + previous_value 
+      current_value = previous_value 
+      previous_value = next_value
+    end
+  end
+
+  return next_value
+end
+
+# simple recursive solution
+# Time complexity: exponential (O2^n) because this recursion has no memory so 
+# the fibonacci tree function calls base case for each branch of the tree (n-1) & (n-2),
+#  which grows exponentially for each subsequently higher level of the binary tree. 
+# Space complexity: I am not sure, but I think that it lineary because of the call stack
+# required for each branch of the binary tree. 
+def fibonacci(n)
+  raise ArgumentError if n == nil || n < 0 || n.class != Integer
+  # base case
+  return n if n < 2
+
+  return fibonacci(n-1) + fibonacci(n-2)
 end