Missing Number
An easy Bit Manipulation problem included in Apna College, Love Babbar 450, Striver A2Z. Below: the roles whose interviews prioritise this topic, and how to practise it.
- Topic
- Bit Manipulation
- Sheets
- 3
- Core for
- 9 roles
- Platform
- LeetCode
The problem
Given an array containing n distinct numbers in the range [0, n], return the only number in that range that is missing from the array.
Example 1
- Input
- nums = [3, 0, 1]
- Output
- 2
- Why
- The numbers 0, 1, 2, 3 should all be present in range [0,3]. The number 2 is missing.
Example 2
- Input
- nums = [0, 1]
- Output
- 2
- Why
- The range [0,2] should have 0, 1, 2. The number 2 is missing.
Example 3
- Input
- nums = [9, 6, 4, 2, 3, 5, 7, 0, 1]
- Output
- 8
- Why
- Numbers 0 through 9 should all be present. The number 8 is missing.
Constraints
- n == nums.length
- 1 <= n <= 10^4
- 0 <= nums[i] <= n
- All numbers in nums are unique
How to think about it
Updated 2026-09-09The complete domain [0, n] and the given array together contain every number twice except for the absent value. If you match each index against its expected item, every present number finds its counterpart. Combining the two sets under an operation that cancels duplicates isolates the unmatched survivor.
Approaches, worst first
Sort and scan discrepancies
time O(n log n) · space O(1)
Sort the array and check whether nums[i] matches index i. If an index mismatches, that index is the missing value; otherwise n is missing. Sort overhead is unneeded here.
Gauss arithmetic summation
time O(n) · space O(1)
Compute the expected total n * (n + 1) / 2 and subtract each element in the array. The remaining difference is the missing number. Highly efficient, though multiplications can risk integer overflow on large constraints in 32-bit systems.
Bitwise XOR cancellationWrite this one
time O(n) · space O(1)
Seed an accumulator with n and XOR every index i and element nums[i] into it. Every number present in both the index set and array cancels out, leaving solely the missing value with zero chance of numeric overflow.
Where people lose marks · 2
- Forgetting to include n itself in the expected range [0, n] causes the algorithm to miss cases where the absent element is the upper boundary n.
- Computing `n * (n + 1)` in standard 32-bit signed integers overflows when n exceeds 46340, making bitwise XOR or 64-bit integers safer across wider numeric domains.
The theory behind it
Bit Manipulation — the ground this problem stands on. All Bit Manipulation problems
What Bit Manipulation is
Bit manipulation is the practice of working directly on the individual ones and zeros that form numbers in computer memory. Every integer is stored as a tiny row of electrical switches that are either on or off. Instead of running arithmetic loops, bitwise operations flip, mask, shift, or combine these switches in a single hardware cycle. This allows compact storage of sets and blazing-fast checks without allocating extra memory.
When to reach for it
Reach for bit manipulation when problems ask to find a unique non-duplicate number, count set bits, determine if a value is a power of two, or pack a set of small booleans into a single integer. Prompts mentioning constant O(1) auxiliary space constraints on array queries often hint at XOR cancellation. It is also the foundation of bitmask dynamic programming, where subsets of up to twenty items are tracked as integer masks.
How the pattern works
Think of an integer as a fixed-length set of flags. Use bitwise AND to inspect if a specific bit is set, bitwise OR to turn a bit on, and bitwise XOR to flip a bit or cancel out matched pairs. Learn the standard bit tricks: n AND with n minus one clears the lowest set bit, which counts ones quickly, while n AND with negative n isolates the lowest set bit. When packing sets into masks, represent the empty set as zero and add item i by shifting one left by i and combining with OR.
What each operation costs
| Operation | Time |
|---|---|
| bitwise operation like AND, OR, or XOR | O(1) |
| count set bits across fixed integer width | O(1) |
| find single non-duplicate number using XOR | O(n) |
What usually goes wrong with Bit Manipulation
- Forgetting that bitwise operators have lower operator precedence than equality and arithmetic comparisons in most languages, evaluating expressions in the wrong order without parentheses.
- Using signed right shift instead of unsigned logical right shift when processing negative numbers, which fills high-order bits with ones instead of zeros.
- Shifting bits by thirty-two or more on standard 32-bit integers, causing undefined behavior or wrapped bit shifts that yield incorrect masks.
Which roles need this problem
Bit Manipulation is a core topic for these 9 roles — if you're targeting one of them, this problem is early in your path, not optional.
Secondary for 2 more roles, including ML Engineer, Information Retrieval Engineer.
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