Update dynamic_programming/fast_fibonacci.rb

dynamic_programming/fast_fibonacci.rb

@@ -1,6 +1,22 @@
-# Given a number, calculates the nth fibonacci number.
+# The Fibonacci numbers, commonly denoted F(n) form a sequence,
+# called the Fibonacci sequence, such that # each number is the sum
+# of the two preceding ones, starting from 0 and 1. That is,
 
-def fast_fibonacci(number, memo_hash = {})
+# F(0) = 0, F(1) = 1
+# F(n) = F(n - 1) + F(n - 2), for n > 1.
+# Given n, calculate F(n).
+
+#
+# Approach: Bottom-Up Approach using Memoization
+#
+
+# Complexity Analysis:
+#
+# Time complexity: O(n)
+# Space complexity: O(n)
+#
+
+def fibonacci(number, memo_hash = {})
     if number == 0 || number == 1
         return number
     end