To determine the time complexity of the given code, let’s analyze each function:

1. is_prime(n) Function

This function checks if n is prime by iterating from 2 to n-1 and checking divisibility. For a number k, it performs O(k) operations (since the loop runs k-2 times for k>2).

2. count_primes(n) Function

This function counts primes from 2 to n-1 by calling is_prime(i) for each i in this range.

The total number of operations is the sum of operations from all is_prime(i) calls:
[ \sum_{i=2}^{n-1} O(i) ]

The sum of integers from 2 to n-1 is (\frac{(n-1)n}{2} -1), which is O(n²).

Final Time Complexity

The overall time complexity is O(n²).

Answer: O(n²) (or quadratic time complexity).

If the question was about the function's purpose: it counts the number of primes less than n. For example, count_primes(10) returns 4 (primes: 2,3,5,7).

But the most likely question here is about time complexity: O(n²).

(\boxed{O(n^2)})

作者声明:本文包含人工智能生成内容。