What is $O(2^n)$ called in the video?

Conditions

• The complexity has the form $O(2^n)$ or similar exponential growth.
• The context is the naming and classification of the derived time complexity.

Reasoning, step by step

1. Derive the time complexity $O(2^n)$ by counting the total number of nodes in the recursion tree.
2. Name this specific result as "exponential complexity".
3. Summarize the method of computing the time complexity of recursive algorithms using trees.

Example

Finally, the instructor names this result: $O(2^n)$ belongs to 'exponential complexity'. He then summarizes the method of this segment in one sentence — it is a solution for representing or computing the time complexity of recursive algorithms using a tree.

Common misconceptions

• Confusing exponential complexity with polynomial complexity.
• Assuming that all recursive algorithms have exponential complexity, rather than just this specific naive Fibonacci example.

Watch the explanation

Explore next

• How does summing the number of nodes per level yield $O(2^n)$?
• What role does the base case $f(1) = f(2) = 1$ play in this analysis?
• Which recursive function's time complexity does this video analyze?