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 provided function example_function(n)
, we need to analyze the different operations and loops within the function.

First Loop:
pythonfor i in range(n): print(i)
This loop iterates
n
times, and within each iteration, it performs a constanttime operation (print(i)
). Therefore, the time complexity of this loop is O(n). 
Nested Loop:
pythonfor j in range(n): for k in range(n): print(j, k)
This is a nested loop. The outer loop iterates
n
times, and for each iteration of the outer loop, the inner loop also iteratesn
times. Within the inner loop, a constanttime operation (print(j, k)
) is performed.To calculate the time complexity of the nested loop, we need to multiply the number of iterations of the outer loop by the number of iterations of the inner loop, and then multiply by the constanttime operation.
Time complexity of the nested loop = n × n × O(1) = O(n^2)
Overall, the time complexity of the example_function(n)
is determined by the most expensive operation, which is the nested loop with a time complexity of O(n^2).
Therefore, the time complexity of example_function(n)
is O(n^2).
Here's the stepbystep reasoning:
 The first loop iterates
n
times, and each iteration performs a constanttime operation. Therefore, its time complexity is O(n).  In the nested loop, the outer loop iterates
n
times, and for each iteration of the outer loop, the inner loop iteratesn
times.  Within the inner loop, a constanttime operation is performed.
 The total number of iterations for the nested loop is
n × n = n^2
.  Each iteration of the inner loop performs a constanttime operation, so the time complexity of the nested loop is O(n^2 × 1) = O(n^2).
 Since the nested loop has a higher time complexity of O(n^2) compared to the first loop's O(n), the overall time complexity of the function is determined by the nested loop, which is O(n^2).
Therefore, the time complexity of example_function(n)
is O(n^2).
API request
pythonimport anthropic client = anthropic.Anthropic( # defaults to os.environ.get("ANTHROPIC_API_KEY") api_key="my_api_key", ) message = client.messages.create( model="claude3opus20240229", 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 worstcase 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 builtin 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)