Sliding Window Median
Time O(nlogk) · Space O(k) · Official statement on LeetCode
Solutions
// Time: O(nlogk)
// Space: O(k)
class Solution {
public:
vector<double> medianSlidingWindow(vector<int>& nums, int k) {
multiset<double> min_bst(cbegin(nums), cbegin(nums) + k);
auto mid = next(cbegin(min_bst), k / 2);
vector<double> result = {((*mid) + *prev(mid, 1 - k % 2)) / 2};
for (int i = k; i < size(nums); ++i) {
min_bst.emplace(nums[i]);
if (nums[i] < *mid) {
--mid;
}
if (nums[i - k] <= *mid) {
++mid;
}
min_bst.erase(min_bst.lower_bound(nums[i - k]));
result.emplace_back(((*mid) + *prev(mid, 1 - k % 2)) / 2);
}
return result;
}
};
// Time: O(nlogk)
// Space: O(k)
class Solution2 {
public:
vector<double> medianSlidingWindow(vector<int>& nums, int k) {
multiset<int, less<int>> min_bst;
multiset<int, greater<int>> max_bst;
vector<double> result;
for (int i = 0; i < nums.size(); ++i) {
if (i >= k) {
if (max_bst.find(nums[i - k]) != max_bst.cend()) {
max_bst.erase(max_bst.find(nums[i - k]));
} else {
min_bst.erase(min_bst.find(nums[i - k]));
}
}
if (max_bst.empty() || nums[i] > *max_bst.cbegin()) {
min_bst.emplace(nums[i]);
if (min_bst.size() > max_bst.size() + 1) {
max_bst.emplace(*min_bst.cbegin());
min_bst.erase(min_bst.cbegin());
}
} else {
max_bst.emplace(nums[i]);
if (max_bst.size() > min_bst.size()) {
min_bst.emplace(*max_bst.cbegin());
max_bst.erase(max_bst.cbegin());
}
}
if (i >= k - 1) {
result.emplace_back(min_bst.size() == max_bst.size() ?
*max_bst.cbegin() / 2.0 + *min_bst.cbegin() / 2.0 : *min_bst.cbegin());
}
}
return result;
}
};
Beginner Explanation
What is Sliding Window Median?
Sliding Window Median (LeetCode #480) is a Hard problem that primarily trains binary heap.
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 heap.
- 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: BST, Heap.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Sliding Window Median
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 heap.
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(nlogk)) and space (O(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(nlogk) time and O(k) space.
Pattern focus: heap
Use the pattern as a checklist:
- heap — 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(nlogk) |
| Space | O(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 Sliding Window Median
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for heap — 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 heap:
- 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: binary heap.
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 Sliding Window Median in a second language (cpp, python).
- Drill 3–5 more problems tagged binary heap.
- Teach the solution out loud in under 5 minutes.
- Add this problem to your revision calendar in 3 days and 14 days.
Visualization
Study checklist
- Read the official problem statement on LeetCode
- Solve on paper / whiteboard first
- Implement the heap 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
Sliding Window Median (#480) — Hard. Pattern: heap. Complexity: O(nlogk) time / O(k) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Sliding Window Median?+
The reference solutions aim for O(nlogk) time and O(k) space. Always re-derive complexity from the code you write in the interview.
What pattern does Sliding Window Median use?+
It primarily maps to heap, within the broader topic of binary heap.
Is Sliding Window Median 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/sliding-window-median/