请求协助计算指定Python代码的Big O时间复杂度

Hey there! Since you already have the definition of Big O notation down, let's jump straight into analyzing your code's complexity. First, let's clean up the code formatting to make it easier to follow:

new = int(input("enter number"))
if new <= 10000:
    comm = new * 2 / 100
    print(comm)
else:
    comm = new * 5 / 100
    print(comm)

Key Big O Concept to Remember #

Big O measures how an algorithm's runtime scales with input size. We only care about the dominant behavior—ignoring constants and any steps that don't grow as input gets larger.

Step-by-Step Breakdown of Your Code #

Let's walk through each line to see its time complexity:

• Reading input: int(input(...)) is a constant-time operation (O(1)). No matter how big the number you enter is, this step takes the same amount of work—just one input read and one type conversion.
• Condition check: new <= 10000 is also O(1). Comparing two numbers is a single, fixed-cost operation that doesn't depend on the size of new.
• Arithmetic calculation: Whether you calculate new * 2 / 100 or new * 5 / 100, these are basic arithmetic operations—all O(1). Doing math on a single number doesn't get more expensive as the number gets larger (at least not in the context of Big O, which ignores low-level hardware nuances).
• Printing output: print(comm) is O(1) too. Printing a single value is a fixed step regardless of what that value is.

Final Complexity #

Every single step in your code runs in constant time, and there are no loops, recursive calls, or other logic that would add more steps as the input new grows.

That means the overall Big O complexity of your code is O(1) (constant time). No matter how big or small the input number is, the code will always execute the same number of operations.

内容的提问来源于stack exchange，提问作者Spin 360