L1 · FoundationsNumbers & loops~3 min · 5 tests

Sum of the Digits of a Number

Add up the digits of an integer with % 10 and // 10 instead of string conversion. Handle negatives and zero, and learn why it is O(number of digits).

The problem

Return the sum of the digits of the integer n. Treat negative numbers by their absolute value. Use arithmetic (% and //), not str().

Examples

Example 1
Input
```
digit_sum(1234)
```
Expected output
```
10
```
Example 2
Input
```
digit_sum(9)
```
Expected output
```
9
```

+ 3 hidden tests on Submit.

Edge cases to ask about

Zero
Negative numbers

Hints

0/3

How an interviewer scores this

0/9

1. Understand the problemRestate it, ask about edge cases and input size.
2. Write a brute-force solutionCorrect first, clever later.
3. Get the correct outputautoAll visible examples pass.
4. Analyse time complexityautoCommit to a Big-O in the Complexity Lab.
5. Analyse space complexityautoExtra memory, not the input.
6. Identify the bottleneckautoMeasure your code — where does it bend?
7. OptimiseUsually: a set or dict instead of a scan.
8. Explain why it worksSay it out loud to Solvi.
9. Test the edge casesautoSubmit passes every hidden test.

Python 3.13 · digit_sum

def digit_sum(n):
    """Sum of the digits of n (sign ignored)."""
    # Write your solution here
    pass

⌘/Ctrl + Enter runs the examples

Your code runs in real CPython inside your browser — nothing is sent anywhere. The first run downloads the interpreter (about 6 MB, once). Your code is saved on this device as you type.

Complexity Lab

What does this cost as n grows?

Interviewers score the analysis as much as the code. Commit to an answer first — then check it, and read why.

Time complexity of the optimal solution

Space complexity (extra memory)

Pick both to reveal the answer.

From brute force to optimal

The progression an interviewer wants to hear, one step at a time.

Approach	Time	Space	Idea
str(n) and sum the characters	O(d)	O(d)	Readable, but builds a string.
best% 10 and // 10	O(d)	O(1)	d = number of digits = O(log n).

Walkthrough of the optimal approach (try it yourself first)

n % 10 gives the last digit; n // 10 removes it. Repeat until n is 0. The loop runs once per digit — about log₁₀(n) times — which is why digit problems are O(log n).

Complexity: O(log n) time, O(1) space. Each loop removes one digit, and a number n has about log₁₀(n) digits.

Reveal the reference solution

def digit_sum(n):
    n = abs(n)
    total = 0
    while n:
        total += n % 10
        n //= 10
    return total

Follow-ups interviewers ask

Keep summing until one digit remains (digital root) — in O(1).

Frequently asked interview questions

Core interview concepts, complexities, and follow-ups scored by hiring teams.

What is the time complexity of Sum of the Digits of a Number in Python?

The optimal solution runs in O(log n) time and O(1) auxiliary space. Each loop removes one digit, and a number n has about log₁₀(n) digits.

What is the brute-force approach, and how do you optimise it?

str(n) and sum the characters: O(d) time, O(d) space. Readable, but builds a string. % 10 and // 10: O(d) time, O(1) space. d = number of digits = O(log n).

What follow-up questions do interviewers ask about Sum of the Digits of a Number?

Keep summing until one digit remains (digital root) — in O(1).