#1847Hard~50 min
Closest Room
Time O(nlogn + klogk + klogn) · Space O(n + k) · Official statement on LeetCode
Solutions
// Time: O(nlogn + klogk + klogn)
// Space: O(n + k)
class Solution {
public:
vector<int> closestRoom(vector<vector<int>>& rooms, vector<vector<int>>& queries) {
static const auto& by_size_desc = [](const auto& a, const auto& b) { return a[1] > b[1]; };
sort(begin(rooms), end(rooms), by_size_desc);
for (int i = 0; i < size(queries); ++i) {
queries[i].emplace_back(i);
}
sort(begin(queries), end(queries), by_size_desc);
set<int> ids;
vector<int> result(size(queries), -1);
int i = 0;
for (const auto& q : queries) {
int r = q[0], s = q[1], idx = q[2];
for (; i < size(rooms) && rooms[i][1] >= s; ++i) {
ids.emplace(rooms[i][0]);
}
result[idx] = find_closest(ids, r);
}
return result;
}
private:
int find_closest(const set<int>& ids, int r) {
int result = -1, min_diff = numeric_limits<int>::max();
auto it = ids.upper_bound(r);
if (it != begin(ids) && abs(*prev(it) - r) < min_diff) {
min_diff = abs(*prev(it) - r);
result = *prev(it);
}
if (it != end(ids) && abs(*it - r) < min_diff) {
min_diff = abs(*it - r);
result = *it;
}
return result;
}
};
// Time: O(nlogn + klogk + klogn)
// Space: O(n + k)
class Solution2 {
public:
vector<int> closestRoom(vector<vector<int>>& rooms, vector<vector<int>>& queries) {
static const auto& by_size_asc = [](const auto& a, const auto& b) { return a[1] < b[1]; };
sort(begin(rooms), end(rooms), by_size_asc);
for (int i = 0; i < size(queries); ++i) {
queries[i].emplace_back(i);
}
sort(begin(queries), end(queries), by_size_asc);
set<int> ids;
for (const auto& room : rooms) {
ids.emplace(room[0]);
}
vector<int> result(size(queries), -1);
int i = 0;
for (const auto& q : queries) {
int r = q[0], s = q[1], idx = q[2];
for (; i < size(rooms) && rooms[i][1] < s; ++i) {
ids.erase(rooms[i][0]);
}
result[idx] = find_closest(ids, r);
}
return result;
}
private:
int find_closest(const set<int>& ids, int r) {
int result = -1, min_diff = numeric_limits<int>::max();
auto it = ids.upper_bound(r);
if (it != begin(ids) && abs(*prev(it) - r) < min_diff) {
min_diff = abs(*prev(it) - r);
result = *prev(it);
}
if (it != end(ids) && abs(*it - r) < min_diff) {
min_diff = abs(*it - r);
result = *it;
}
return result;
}
};
Beginner Explanation
What is Closest Room?
Closest Room (LeetCode #1847) is a Hard problem that primarily trains sort.
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 sort and binary search.
- Only then translate the idea into code.
Why this problem matters
Hard problems force you to combine patterns and prove complexity carefully — interview gold. Official solution notes mention: Sort, Binary Search.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Closest Room
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 sort and binary search.
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(nlogn + klogk + klogn)) and space (O(n + k)) 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(nlogn + klogk + klogn) time and O(n + k) space.
Pattern focus: sort and binary search
Use the pattern as a checklist:
- sort — confirm the invariant holds after each step
- binary search — confirm the invariant holds after each step
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(nlogn + klogk + klogn) |
| Space | O(n + k) |
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 Closest Room
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for sort and binary search — 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 sort and binary search:
- 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: sort.
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 Closest Room in a second language (cpp, python).
- Drill 3–5 more problems tagged sort.
- 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 Closest Room: show input structure (sort), highlight the moving parts of the sort and binary search 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 sort and binary search 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
Closest Room (#1847) — Hard. Pattern: sort and binary search. Complexity: O(nlogn + klogk + klogn) time / O(n + k) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Closest Room?+
The reference solutions aim for O(nlogn + klogk + klogn) time and O(n + k) space. Always re-derive complexity from the code you write in the interview.
What pattern does Closest Room use?+
It primarily maps to sort and binary search, within the broader topic of sort.
Is Closest Room 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/closest-room/