Variable-length arguments (*args) in Python - Time & Space Complexity

Time Complexity: Variable-length arguments (*args)

O(n)

Understanding Time Complexity

When using variable-length arguments, the function can take many inputs. We want to know how the time to run changes as the number of inputs grows.

How does the function's work increase when we add more arguments?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

def sum_all(*args):
    total = 0
    for num in args:
        total += num
    return total

This function adds up all the numbers given as arguments.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each argument in args to add it.
• How many times: Once for each argument passed to the function.

How Execution Grows With Input

As we add more numbers to add, the function does more work, going through each number once.

Input Size (n)	Approx. Operations
10	About 10 additions
100	About 100 additions
1000	About 1000 additions

Pattern observation: The work grows directly with the number of inputs.

Final Time Complexity

Time Complexity: O(n)

This means the time to add all numbers grows in a straight line as you add more numbers.

Common Mistake

[X] Wrong: "Using *args makes the function run instantly no matter how many inputs."

[OK] Correct: Even with *args, the function still needs to look at each input once, so more inputs mean more work.

Interview Connect

Understanding how variable inputs affect time helps you explain your code clearly and shows you think about efficiency, a skill valued in many coding situations.

Self-Check

"What if we changed the function to multiply all arguments instead of adding? How would the time complexity change?"