LeetCode #1847 — HARD

Closest Room

Break down a hard problem into reliable checkpoints, edge-case handling, and complexity trade-offs.

Solve on LeetCode
The Problem

Problem Statement

There is a hotel with n rooms. The rooms are represented by a 2D integer array rooms where rooms[i] = [roomIdi, sizei] denotes that there is a room with room number roomIdi and size equal to sizei. Each roomIdi is guaranteed to be unique.

You are also given k queries in a 2D array queries where queries[j] = [preferredj, minSizej]. The answer to the jth query is the room number id of a room such that:

  • The room has a size of at least minSizej, and
  • abs(id - preferredj) is minimized, where abs(x) is the absolute value of x.

If there is a tie in the absolute difference, then use the room with the smallest such id. If there is no such room, the answer is -1.

Return an array answer of length k where answer[j] contains the answer to the jth query.

Example 1:

Input: rooms = [[2,2],[1,2],[3,2]], queries = [[3,1],[3,3],[5,2]]
Output: [3,-1,3]
Explanation: The answers to the queries are as follows:
Query = [3,1]: Room number 3 is the closest as abs(3 - 3) = 0, and its size of 2 is at least 1. The answer is 3.
Query = [3,3]: There are no rooms with a size of at least 3, so the answer is -1.
Query = [5,2]: Room number 3 is the closest as abs(3 - 5) = 2, and its size of 2 is at least 2. The answer is 3.

Example 2:

Input: rooms = [[1,4],[2,3],[3,5],[4,1],[5,2]], queries = [[2,3],[2,4],[2,5]]
Output: [2,1,3]
Explanation: The answers to the queries are as follows:
Query = [2,3]: Room number 2 is the closest as abs(2 - 2) = 0, and its size of 3 is at least 3. The answer is 2.
Query = [2,4]: Room numbers 1 and 3 both have sizes of at least 4. The answer is 1 since it is smaller.
Query = [2,5]: Room number 3 is the only room with a size of at least 5. The answer is 3.

Constraints:

  • n == rooms.length
  • 1 <= n <= 105
  • k == queries.length
  • 1 <= k <= 104
  • 1 <= roomIdi, preferredj <= 107
  • 1 <= sizei, minSizej <= 107
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: There is a hotel with n rooms. The rooms are represented by a 2D integer array rooms where rooms[i] = [roomIdi, sizei] denotes that there is a room with room number roomIdi and size equal to sizei. Each roomIdi is guaranteed to be unique. You are also given k queries in a 2D array queries where queries[j] = [preferredj, minSizej]. The answer to the jth query is the room number id of a room such that: The room has a size of at least minSizej, and abs(id - preferredj) is minimized, where abs(x) is the absolute value of x. If there is a tie in the absolute difference, then use the room with the smallest such id. If there is no such room, the answer is -1. Return an array answer of length k where answer[j] contains the answer to the jth query.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Binary Search · Segment Tree

Example 1

[[2,2],[1,2],[3,2]]
[[3,1],[3,3],[5,2]]

Example 2

[[1,4],[2,3],[3,5],[4,1],[5,2]]
[[2,3],[2,4],[2,5]]

Related Problems

  • Most Beautiful Item for Each Query (most-beautiful-item-for-each-query)
  • Minimum Time to Kill All Monsters (minimum-time-to-kill-all-monsters)
Step 02

Core Insight

What unlocks the optimal approach

  • Is there a way to sort the queries so it's easier to search the closest room larger than the size?
  • Use binary search to speed up the search time.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Largest constraint values
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #1847: Closest Room
class Solution {
    public int[] closestRoom(int[][] rooms, int[][] queries) {
        int n = rooms.length;
        int k = queries.length;
        Arrays.sort(rooms, (a, b) -> a[1] - b[1]);
        Integer[] idx = new Integer[k];
        for (int i = 0; i < k; i++) {
            idx[i] = i;
        }
        Arrays.sort(idx, (i, j) -> queries[i][1] - queries[j][1]);
        int i = 0;
        TreeMap<Integer, Integer> tm = new TreeMap<>();
        for (int[] room : rooms) {
            tm.merge(room[0], 1, Integer::sum);
        }
        int[] ans = new int[k];
        Arrays.fill(ans, -1);
        for (int j : idx) {
            int prefer = queries[j][0], minSize = queries[j][1];
            while (i < n && rooms[i][1] < minSize) {
                if (tm.merge(rooms[i][0], -1, Integer::sum) == 0) {
                    tm.remove(rooms[i][0]);
                }
                ++i;
            }
            if (i == n) {
                break;
            }
            Integer p = tm.ceilingKey(prefer);
            if (p != null) {
                ans[j] = p;
            }
            p = tm.floorKey(prefer);
            if (p != null && (ans[j] == -1 || ans[j] - prefer >= prefer - p)) {
                ans[j] = p;
            }
        }
        return ans;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n × log n + k × log k)
Space
O(n + k)

Approach Breakdown

LINEAR SCAN
O(n) time
O(1) space

Check every element from left to right until we find the target or exhaust the array. Each comparison is O(1), and we may visit all n elements, giving O(n). No extra space needed.

BINARY SEARCH
O(log n) time
O(1) space

Each comparison eliminates half the remaining search space. After k comparisons, the space is n/2ᵏ. We stop when the space is 1, so k = log₂ n. No extra memory needed — just two pointers (lo, hi).

Shortcut: Halving the input each step → O(log n). Works on any monotonic condition, not just sorted arrays.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Boundary update without `+1` / `-1`

Wrong move: Setting `lo = mid` or `hi = mid` can stall and create an infinite loop.

Usually fails on: Two-element ranges never converge.

Fix: Use `lo = mid + 1` or `hi = mid - 1` where appropriate.