From 826d6593b18f59525d44418a3c79b6fa6e351989 Mon Sep 17 00:00:00 2001
From: Jidong Xiao <xiaoj8@rpi.edu>
Date: Fri, 22 Sep 2023 12:16:22 -0400
Subject: [PATCH] adding fib sequence

---
 lectures/07_order_notation_recursion/README.md | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/lectures/07_order_notation_recursion/README.md b/lectures/07_order_notation_recursion/README.md
index 6e12c3b..d026d16 100644
--- a/lectures/07_order_notation_recursion/README.md
+++ b/lectures/07_order_notation_recursion/README.md
@@ -259,3 +259,20 @@ int main() {
 ```
  How can you change the second print vec function as little as possible so that this code prints the contents
 of the vector in reverse order?
+
+## 7.17 Fibonacci Optimization: Order Notation of Time vs. Space
+
+The Fibonacci sequence is defined:
+$$
+F(n) = \begin{cases}
+0 & \text{if } n = 0 \\
+1 & \text{if } n = 1 \\
+F(n-1) + F(n-2) & \text{otherwise}
+\end{cases}
+$$
+
+1. Write a simple recursive version of Fibonacci that is a direct translation of the mathematical definition of the
+Fibonacci sequence.  
+2. Write an iterative version of Fibonacci that uses a vector to improve the running time of the function.  
+3. What is the order notation of the running time for each version?  
+4. What is the order notation of the memory usage for each version?