#295Hard~50 min
Find Median from Data Stream
Time O(nlogn) · Space O(n) · Official statement on LeetCode
Solutions
// Time: O(nlogn) for total n addNums, O(logn) per addNum, O(1) per findMedian.
// Space: O(n), total space
// Heap solution.
class MedianFinder {
public:
// Adds a number into the data structure.
void addNum(int num) {
// Balance smaller half and larger half.
if (max_heap_.empty() || num > max_heap_.top()) {
min_heap_.emplace(num);
if (min_heap_.size() > max_heap_.size() + 1) {
max_heap_.emplace(min_heap_.top());
min_heap_.pop();
}
} else {
max_heap_.emplace(num);
if (max_heap_.size() > min_heap_.size()) {
min_heap_.emplace(max_heap_.top());
max_heap_.pop();
}
}
}
// Returns the median of current data stream
double findMedian() {
return min_heap_.size() == max_heap_.size() ?
(max_heap_.top() + min_heap_.top()) / 2.0 :
min_heap_.top();
}
private:
// min_heap_ stores the larger half seen so far.
priority_queue<int, vector<int>, greater<int>> min_heap_;
// max_heap_ stores the smaller half seen so far.
priority_queue<int, vector<int>, less<int>> max_heap_;
};
// BST solution.
class MedianFinder2 {
public:
// Adds a number into the data structure.
void addNum(int num) {
// Balance smaller half and larger half.
if (max_bst_.empty() || num > *max_bst_.cbegin()) {
min_bst_.emplace(num);
if (min_bst_.size() > max_bst_.size() + 1) {
max_bst_.emplace(*min_bst_.cbegin());
min_bst_.erase(min_bst_.cbegin());
}
} else {
max_bst_.emplace(num);
if (max_bst_.size() > min_bst_.size()) {
min_bst_.emplace(*max_bst_.cbegin());
max_bst_.erase(max_bst_.cbegin());
}
}
}
// Returns the median of current data stream
double findMedian() {
return min_bst_.size() == max_bst_.size() ?
(*max_bst_.cbegin() + *min_bst_.cbegin()) / 2.0 :
*min_bst_.cbegin();
}
private:
// min_bst_ stores the larger half seen so far.
multiset<int, less<int>> min_bst_;
// max_bst_ stores the smaller half seen so far.
multiset<int, greater<int>> max_bst_;
};
// Your MedianFinder object will be instantiated and called as such:
// MedianFinder mf;
// mf.addNum(1);
// mf.findMedian();
Beginner Explanation
What is Find Median from Data Stream?
Find Median from Data Stream (LeetCode #295) 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 Find Median from Data Stream
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(nlogn)) and space (O(n)) 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) time and O(n) 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(nlogn) |
| Space | O(n) |
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 Find Median from Data Stream
- 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 Find Median from Data Stream 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
Conceptual diagram for Find Median from Data Stream: show input structure (binary heap), highlight the moving parts of the heap 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 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
Find Median from Data Stream (#295) — Hard. Pattern: heap. Complexity: O(nlogn) time / O(n) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Find Median from Data Stream?+
The reference solutions aim for O(nlogn) time and O(n) space. Always re-derive complexity from the code you write in the interview.
What pattern does Find Median from Data Stream use?+
It primarily maps to heap, within the broader topic of binary heap.
Is Find Median from Data Stream 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/find-median-from-data-stream/