#1117Hard~50 min
Building H2O
Time O(n) · Space O(1) · Official statement on LeetCode
Solutions
// Time: O(n)
// Space: O(1)
class H2O {
public:
H2O() {
}
void hydrogen(function<void()> releaseHydrogen) {
unique_lock<mutex> l(m_);
releaseHydrogen_ = releaseHydrogen;
++nH_;
output();
}
void oxygen(function<void()> releaseOxygen) {
unique_lock<mutex> l(m_);
releaseOxygen_ = releaseOxygen;
++nO_;
output();
}
private:
void output() {
while (nH_ >= 2 && nO_ >= 1) {
nH_ -= 2;
nO_ -= 1;
releaseHydrogen_();
releaseHydrogen_();
releaseOxygen_();
}
}
int nH_ = 0;
int nO_ = 0;
function<void()> releaseHydrogen_ = nullptr;
function<void()> releaseOxygen_ = nullptr;
mutex m_;
};
// Time: O(n)
// Space: O(1)
class H2O2 {
public:
H2O2() {
}
void hydrogen(function<void()> releaseHydrogen) {
{
unique_lock<mutex> l(m_);
cv_.wait(l, [this]() { return (nH_ + 1) - 2 * nO_ <= 2; });
++nH_;
// releaseHydrogen() outputs "H". Do not change or remove this line.
releaseHydrogen();
}
cv_.notify_all();
}
void oxygen(function<void()> releaseOxygen) {
{
unique_lock<mutex> l(m_);
cv_.wait(l, [this]() { return 2 * (nO_ + 1) - nH_ <= 2; });
++nO_;
// releaseOxygen() outputs "O". Do not change or remove this line.
releaseOxygen();
}
cv_.notify_all();
}
private:
int nH_ = 0;
int nO_ = 0;
mutex m_;
condition_variable cv_;
};
// Time: O(n)
// Space: O(1)
// this is much like single thread execution
class H2O3 {
public:
H2O3(): curr_(2) {
m2_.lock();
}
void hydrogen(function<void()> releaseHydrogen) {
m1_.lock();
// releaseHydrogen() outputs "H". Do not change or remove this line.
releaseHydrogen();
if (--curr_) {
m1_.unlock();
} else {
m2_.unlock();
}
}
void oxygen(function<void()> releaseOxygen) {
m2_.lock();
// releaseOxygen() outputs "O". Do not change or remove this line.
releaseOxygen();
curr_ = 2;
m1_.unlock();
}
private:
int curr_ = 0;
mutex m1_, m2_;
};
Beginner Explanation
What is Building H2O?
Building H2O (LeetCode #1117) is a Hard problem that primarily trains concurrency.
How to think about it
- Restate the goal in your own words before coding.
- Work a tiny example by hand so the invariant becomes obvious.
- Identify the pattern — this problem aligns with general problem-solving.
- Only then translate the idea into code.
Why this problem matters
Hard problems force you to combine patterns and prove complexity carefully — interview gold.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Building H2O
Opening (30–60 seconds)
- Clarify inputs/outputs and edge cases (empty input, single element, duplicates, overflow).
- State a brute force so the interviewer knows you can solve it naively.
- Propose the optimal direction tied to general problem-solving.
Core solution narrative
- Define the state you track (pointers, DP cell, set membership, stack top, etc.).
- Explain the transition when you process the next element.
- Call out time (O(n)) and space (O(1)) before coding.
- Code cleanly; narrate variable names.
What interviewers listen for
- Correctness on edge cases
- Complexity honesty
- Ability to discuss trade-offs (e.g., hash map space vs. sort + two pointers)
Follow-up questions they may ask
- Can you solve it with less memory?
- What if the input stream is infinite / doesn't fit in RAM?
- How would tests look for adversarial inputs?
Optimized Approach
Optimized solution notes
The reference solutions on AlgoForge target O(n) time and O(1) space.
Pattern focus: general problem-solving
Use the pattern as a checklist:
- Identify the dominant pattern and stick to one clear invariant
Multiple methods appear in the source solutions — compare them and explain when each is preferable.
Implementation tips
- Prefer readable names over micro-optimizations in interviews.
- Extract helpers only when they clarify (e.g., expand-around-center, DFS visit).
- After AC-level logic, re-scan for off-by-one and null checks.
Complexity Analysis
Complexity
| Measure | Bound |
|---|---|
| Time | O(n) |
| Space | O(1) |
How to justify this in an interview
- Time: count loops, map/set operations, and recursive branching; state average vs worst case if relevant.
- Space: include hash maps, recursion stack, and output allocation when the problem asks for it.
If your implementation differs from the reference, re-derive big-O from your code — never memorize a complexity you cannot defend.
Common Mistakes
Common mistakes on Building H2O
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for general problem-solving — updating state too early or too late.
- Mutating input unexpectedly when the problem forbids it.
- Off-by-one in windows, ranges, or binary search bounds.
- Ignoring overflow / precision for integer arithmetic problems.
- Overengineering — jumping to an advanced structure when a simpler approach works.
Alternative Approaches
Alternatives
The source file includes more than one method. Compare:
- Primary optimized path — best complexity for typical interviews.
- Secondary approach — often brute force, sorting-based, or space-optimized variant.
Practice articulating when you would pick each (constraints, readability, follow-ups).
Edge Cases
Edge cases checklist
- Minimum input size
- Maximum input size / time limits
- Duplicates and already-sorted input
- Negative numbers / zeros (if applicable)
- Disconnected structures (graphs/trees)
- Single path vs branching recursion depth
Pattern Recognition
Spotting this pattern
Signal phrases that point to general problem-solving:
- Sorted input or ability to sort without changing the answer class
- Need for contiguous subarray / substring → consider sliding window
- Need for O(1) membership → hash set/map
- Optimal substructure + overlapping subproblems → DP
- Connectivity / components → graph DFS/BFS or Union-Find
Primary topics: concurrency.
Follow-up Interview Questions
Follow-ups
- How does the solution change if the input is a stream?
- Can you solve it in-place?
- What if duplicates must be handled differently?
- How would you parallelize the approach?
- Design tests that would break a buggy implementation.
Practice Recommendations
What to practice next
- Re-solve Building H2O in a second language (cpp, python).
- Drill 3–5 more problems tagged concurrency.
- Teach the solution out loud in under 5 minutes.
- Add this problem to your revision calendar in 3 days and 14 days.
Visualization
Conceptual diagram for Building H2O: show input structure (concurrency), highlight the moving parts of the general problem-solving approach, and annotate each step with the maintained invariant and complexity.
Study checklist
- Read the official problem statement on LeetCode
- Solve on paper / whiteboard first
- Implement the general problem-solving approach
- Verify edge cases from the checklist
- State time and space complexity aloud
- Compare with the AlgoForge reference solution
- Schedule a revision session
Revision notes
Building H2O (#1117) — Hard. Pattern: general problem-solving. Complexity: O(n) time / O(1) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Building H2O?+
The reference solutions aim for O(n) time and O(1) space. Always re-derive complexity from the code you write in the interview.
What pattern does Building H2O use?+
It primarily maps to general problem-solving, within the broader topic of concurrency.
Is Building H2O good for interviews?+
Yes — as a Hard problem it is a solid practice target. Pair it with related problems in the same pattern family for spaced repetition.
Where can I read the official statement?+
Open the official LeetCode page for constraints and examples: https://leetcode.com/problems/building-h2o/