Complexity Analysis of is_prime Function

Complexity Analysis of is_prime Function

Code Inspection

The given Python function is_prime takes an integer n as input and determines whether it is a prime number or not. It does this by iterating through numbers from 2 to n-1 and checking for any divisors.

Time Complexity

• Best Case: O(1) when n is 2 or 3, as the function checks n <= 1 and directly returns True.
• Average Case: O(n/2) or simply O(n) as it iterates through approximately n/2 numbers to check for divisibility.
• Worst Case: O(n) when n is a prime number, as it iterates through all numbers from 2 to n-1.

Space Complexity

The space complexity of the function is O(1) as it uses a constant amount of extra space, irrespective of the input size. It only stores the input n and loop variables.

The most time-consuming part is the loop that iterates through the numbers. If it finds a divisor for n, it exits early, thus making it more efficient for non-prime numbers.

Average-Case Scenario Illustration

For the input n = 1009 (a prime number), the function would iterate through 2 to 1008, resulting in approximately 1007 iterations. Therefore, in the average case, the expected time complexity would be O(n) or approximately O(1007), making it efficient for typical conditions.

This analysis provides a clear understanding of the algorithm's efficiency and scalability, making it valuable for evaluating its performance under different scenarios.