L2 · Working engineerLists & arrays~6 min · 5 tests#11

Find the Element That Appears Once

Every value appears twice except one — find it with XOR in O(n) time and O(1) space. Run it in Python and compare against a Counter solution.

The problem

Every value in nums appears exactly twice, except one value that appears once. Return that value.

Bonus: use O(1) extra memory.

Examples

Example 1
Input
```
single_number([4, 1, 2, 1, 2, 4, 7])
```
Expected output
```
7
```
Example 2
Input
```
single_number([2, 2, 1])
```
Expected output
```
1
```

+ 3 hidden tests on Submit — negative single, zero is the answer.

Edge cases to ask about

Single element
Answer is 0
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 · single_number

def single_number(nums):
    """Every value appears twice except one. Return it."""
    # 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 measure your code against the optimal one at growing input sizes.

Time complexity of the optimal solution

Space complexity (extra memory)

Pick both to reveal the answer.

Measure it

Runs the function on inputs of size 250 up to 16,000 and records the time and peak memory. Slow solutions stop early — a short curve is itself the answer.

From brute force to optimal

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

Approach	Time	Space	Idea
Count occurrences	O(n)	O(n)	Counter, then the key with count 1.
bestXOR everything	O(n)	O(1)	x ^ x = 0 and x ^ 0 = x, so pairs cancel and the single value survives.

Walkthrough of the optimal approach (try it yourself first)

XOR has two properties that make this a one-liner: x ^ x == 0 and x ^ 0 == x, and it is commutative. XOR all values together: every pair cancels to 0, leaving only the value that appeared once.

The Counter version is perfectly correct and O(n) — XOR is the answer to the follow-up "now without extra memory".

Complexity: O(n) time, O(1) space. One pass with a single integer accumulator — XOR needs no table.

Reveal the reference solution

def single_number(nums):
    result = 0
    for x in nums:
        result ^= x
    return result

The brute force, for comparison

def single_number(nums):
    from collections import Counter
    for x, c in Counter(nums).items():
        if c == 1:
            return x

Follow-ups interviewers ask

Every value appears three times except one.
Two values appear once — find both.

Frequently asked interview questions

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

What is the time complexity of Find the Element That Appears Once in Python?

The optimal solution runs in O(n) time and O(1) auxiliary space. One pass with a single integer accumulator — XOR needs no table.

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

Count occurrences: O(n) time, O(n) space. Counter, then the key with count 1. XOR everything: O(n) time, O(1) space. x ^ x = 0 and x ^ 0 = x, so pairs cancel and the single value survives.

What follow-up questions do interviewers ask about Find the Element That Appears Once?

Every value appears three times except one. Two values appear once — find both.