# Efficiency estimator

Calculate the time complexity of functions and algorithms.

def example_function(n):

for i in range(n):

print(i)

for j in range(n):

for k in range(n):

print(j, k)

\`\`\`

To determine the time complexity of the given function `example_function`

, let's analyze each step separately and then combine them to get the overall time complexity.

Step 1:

python`for i in range(n): print(i)`

This step has a single loop that iterates `n`

times. The `print`

statement inside the loop takes constant time, O(1). Therefore, the time complexity of this step is O(n).

Step 2:

python`for j in range(n): for k in range(n): print(j, k)`

This step contains nested loops. The outer loop iterates `n`

times, and for each iteration of the outer loop, the inner loop also iterates `n`

times. The `print`

statement inside the inner loop takes constant time, O(1).

- The inner loop has a time complexity of O(n) because it iterates
`n`

times. - The outer loop also has a time complexity of O(n) because it iterates
`n`

times.

Since the inner loop is executed for each iteration of the outer loop, the total time complexity of this step is O(n) * O(n) = O(n^2).

Overall Time Complexity:
The function `example_function`

consists of two steps:

- Step 1 has a time complexity of O(n).
- Step 2 has a time complexity of O(n^2).

To determine the overall time complexity, we consider the dominant term among the steps. In this case, the dominant term is O(n^2) from Step 2 because it grows faster than O(n) as `n`

increases.

Therefore, the overall time complexity of the function `example_function`

is O(n^2).

In the worst-case scenario, when `n`

is very large, the nested loops in Step 2 will dominate the execution time, and the function will have a quadratic time complexity.

## API request

python`import anthropic client = anthropic.Anthropic( # defaults to os.environ.get("ANTHROPIC_API_KEY") api_key="my_api_key", ) message = client.messages.create( model="claude-3-opus-20240229", max_tokens=2000, temperature=0, system="Your task is to analyze the provided function or algorithm and calculate its time complexity using Big O notation. Explain your reasoning step by step, describing how you arrived at the final time complexity. Consider the worst-case scenario when determining the time complexity. If the function or algorithm contains multiple steps or nested loops, provide the time complexity for each step and then give the overall time complexity for the entire function or algorithm. Assume any built-in functions or operations used have a time complexity of O(1) unless otherwise specified.", messages=[{"role":"user","content":"\\`\\`\\` \ndef example_function(n): \n for i in range(n): \n print(i) \n \n for j in range(n): \n for k in range(n): \n print(j, k) \n\\`\\`\\`"}] ) print(message.content)`