Arithmetic operators in Kotlin - Time & Space Complexity

Time Complexity: Arithmetic operators

O(n)

Understanding Time Complexity

We want to see how the time to run arithmetic operations changes as we use more numbers.

How does the program's work grow when doing simple math on inputs?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

fun sumArray(numbers: IntArray): Int {
    var total = 0
    for (num in numbers) {
        total += num
    }
    return total
}
    

This code adds up all numbers in an array using arithmetic operators.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Addition inside the loop (total += num)
• How many times: Once for each number in the array

How Execution Grows With Input

Each new number means one more addition operation.

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

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

Final Time Complexity

Time Complexity: O(n)

This means the time to add numbers grows in a straight line as the list gets longer.

Common Mistake

[X] Wrong: "Arithmetic operations like addition take more time as numbers get bigger."

[OK] Correct: In most programming languages, simple arithmetic operations take constant time regardless of the number size.

Interview Connect

Understanding how loops with arithmetic operations scale helps you explain code efficiency clearly and confidently.

Self-Check

"What if we replaced the loop with a recursive function doing the same additions? How would the time complexity change?"