implement closure-scoped memoization for fibonacci

Author: RomanSanaye

Sprint-2/improve_with_caches/fibonacci/fibonacci.py

@@ -1,4 +1,21 @@
 def fibonacci(n):
-    if n <= 1:
-        return n
-    return fibonacci(n - 1) + fibonacci(n - 2)
+    # Initialize the cache dictionary
+    cache = {}
+
+    def helper(number):
+        # Check the cache at the start
+        if number in cache:
+            return cache[number]
+
+        # Base case
+        if number <= 1:
+            return number
+
+        # Compute the result (making sure number decreases!)
+        result = helper(number - 1) + helper(number - 2)
+
+        # Store the result in the cache right before returning
+        cache[number] = result
+        return result
+
+    return helper(n)