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adding the fibo sequence

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Jidong Xiao
2023-09-22 12:24:13 -04:00
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lectures/07_order_notation_recursion/README.md
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@@ -263,16 +263,12 @@ of the vector in reverse order?
## 7.17 Fibonacci Optimization: Order Notation of Time vs. Space ## 7.17 Fibonacci Optimization: Order Notation of Time vs. Space
The Fibonacci sequence is defined: The Fibonacci sequence is defined:
$$ ![alt text](fibonacci_sequence.png "fibonacci sequence")
F(n) = \begin{cases}
0 & \text{if } n = 0 \\
1 & \text{if } n = 1 \\
F(n-1) + F(n-2) & \text{otherwise}
\end{cases}
$$
1. Write a simple recursive version of Fibonacci that is a direct translation of the mathematical definition of the 1. Write a simple recursive version of Fibonacci that is a direct translation of the mathematical definition of the
Fibonacci sequence. Fibonacci sequence.
2. Write an iterative version of Fibonacci that uses a vector to improve the running time of the function. 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? 3. What is the order notation of the running time for each version?
- Play this [animation](https://jidongxiao.github.io/CSCI1200-DataStructures/animations/dynamic_memory/example1/index.html), which illustrates the time complexity of the recursvie version.
4. What is the order notation of the memory usage for each version? 4. What is the order notation of the memory usage for each version?