DSA With AI
Week 12 ยท Bit Manipulation

Missing Number

Solve Missing Number by recognizing the Bit Manipulation pattern and turning the prompt into a small invariant before coding.

Easy Bit Manipulation Week 12 Practice runner

Frame the problem

  • Implement missing_number with the exact signature used by the interactive runner.
  • Use the visible tests to confirm the input and output shape before reading the final solution.
  • Treat challenge tests as edge-case pressure: empty inputs, repeated values, boundary shapes, or impossible states.
  • State the invariant before code, then dry-run one passing case and one failing-looking case.
1. Reveal example inputs and outputs

Example 1

Input:

missing_number([
  3,
  0,
  1
])

Output:

2
2. Brute force first

What direct brute force would be correct for a tiny input? Name the exact repeated work that the target pattern removes.

3. Reveal the insight ladder
  1. Map the prompt to the Bit Manipulation pattern instead of starting from syntax.
  2. XOR all indices and values plus n.
  3. The missing value can be n itself.
  4. Only reveal the final code after you can explain why each state update is safe.
4. Dry run before code
  1. missing-basic: input [[3,0,1]] should produce 2. Hint to check your state: XOR all indices and values plus n.
  2. missing-last: input [[0,1]] should produce 2. Hint to check your state: The missing value can be n itself.
5. Reveal final Python solution 
def missing_number(nums: list[int]) -> int:
    missing = len(nums)
    for index, value in enumerate(nums):
        missing ^= index ^ value
    return missing

Complexity: Derive the exact bounds from missing_number: count how often each input item is visited and the maximum size of the main state structure.

Interview narration

  • I will first describe the invariant in plain language.
  • Then I will explain what data structure carries that invariant across the traversal, loop, recursion, or DP transition.
  • Finally I will walk one edge case before writing the optimized version.

Common traps

  • Solving only the visible example instead of the invariant.
  • Forgetting empty input, singleton input, duplicate values, or impossible-state cases.
  • Revealing the solution before doing a dry run from the starter signature.

Follow-up drills

1. How do you turn this into a timed interview answer?

Start with the invariant, give the brute force in one sentence, name the optimized state, code the core loop or recursion, and run one visible test aloud before mentioning complexity.

2. How do you scale the same pattern to a larger input?

Track which state grows with the input: hash maps and sets grow with distinct values, queues grow with frontier width, recursion grows with depth, heaps grow with active candidates, and DP tables grow with state count.

3. What should you practice from blank tomorrow?

Rewrite missing_number without looking at the solution, then compare only the invariant and state updates before checking syntax.

Interactive runner

Write the required Python function. Your code runs locally in this browser. Hints reveal one failing case at a time.