Two balanced heaps
Report the Middle Sensor Reading
01. The question
Sensor readings arrive one at a time. Return the median after every arrival. For an even number of readings, average the two middle values; keep duplicate readings as separate observations.
Before revealing the idea, predict the result and describe what information you would need to track.
02. Worked example
Inputreadings = [7, 2, 10, 4]
Output[7, 4.5, 7, 5.5]
- After 7 the median is 7.
- After 2 the middle pair is 2 and 7, giving 4.5.
- After 10 the median is 7; after 4 it is (4 + 7) / 2 = 5.5.
Try your code
Define solve(data, parameter="") and return your result. Your code runs locally, not on a server.
Edit your test cases
Use 1-10 objects with data and an optional string parameter. Expected outputs are computed from the lesson. An optional expected field must be correct.
Input contract & reference code
Example data: [7,2,10,4]. Parameter: "". Numeric parameters arrive as strings; convert them with int(parameter) when needed.
The example and generated cases use the question’s exact variant. This checks behavior on a small test batch—not performance on every possible input.
Python downloads only when you run code, using compressed runtime assets. Code is not saved or uploaded. Enable JavaScript to run it.
Printed output
Five-second execution limit per batch. Standard-library Python only; additional packages and network access are unavailable. Stop ends execution without blocking the lesson.
03. The idea
Try sketching your own approach first. What would you track, and why would it work?
Reveal the idea
- Keep the lower half in a max-heap, represented by negative values in Python.
- Move its largest value into the upper min-heap, then rebalance the sizes.
- Read the lower root for odd counts, or average both roots for even counts.
04. Watch it happen
Use Step to move slowly, or Play to follow the whole trace. Change a preset or load your own input.
Input & settings
Red = current item / blue = active window or cells / green = completed work. A value docks at its actual destination; the original input stays unchanged. Positions start at 0.
Working state / what changes
Ready to begin
Enable JavaScript to step through the animation. The worked example and solution below remain readable without it.
Python / why it changes
The line behind the step
import heapq
def solve(readings, parameter=""):
lower, upper, medians = [], [], []
for value in readings:
heapq.heappush(lower, -value)
heapq.heappush(upper, -heapq.heappop(lower))
if len(upper) > len(lower):
heapq.heappush(lower, -heapq.heappop(upper))
if len(lower) > len(upper):
median = -lower[0]
else:
median = (-lower[0] + upper[0]) / 2
medians.append(median)
return mediansHow to use this walkthrough
Hover or focus a control for its label. Play forms the input and follows values into the working state. Step shows one change; Back and the slider restore exact snapshots. Reduced motion uses instant updates. Saved snapshots and sorted heap displays are teaching overhead, not algorithm complexity.
05. Python solution
import heapq
def solve(readings, parameter=""):
lower, upper, medians = [], [], []
for value in readings:
heapq.heappush(lower, -value)
heapq.heappush(upper, -heapq.heappop(lower))
if len(upper) > len(lower):
heapq.heappush(lower, -heapq.heappop(upper))
if len(lower) > len(upper):
median = -lower[0]
else:
median = (-lower[0] + upper[0]) / 2
medians.append(median)
return medians06. Cost & edge cases
- Time
- O(n log(n + 1)) for all insertions; O(1) for each median query
- Space
- O(n)
- An empty stream returns [].
- Equal values are separate readings.
- Negative readings and half-integer medians are supported. The displayed priority lists show next-pop order, not the heap array.