Opposing two pointers
Span the Largest Rain Reservoir
01. The question
Vertical posts stand one unit apart. Choose two posts and return the largest rectangular water area: their separation times the shorter height. Original rain-reservoir scenario; the area contract is unchanged. Fewer than two posts gives 0.
Before revealing the idea, predict the result and describe what information you would need to track.
02. Worked example
Input[2, 7, 3, 6, 4]
Output12
- The outside pair stores 4 × 2 = 8.
- Advance the shorter left post to height 7; with the last post this gives 3 × 4 = 12.
- The inner height-6 post also gives 2 × 6 = 12; the area stays 12.
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: [2,7,3,6,4]. 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
- Begin with the widest possible pair.
- Measure the area and keep the best.
- Move a shorter endpoint inward; ties move the left endpoint.
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
def solve(data, parameter=''):
left, right = 0, len(data) - 1
best = 0
while left < right:
area = (right - left) * min(data[left], data[right])
best = max(best, area)
if data[left] <= data[right]:
left += 1
else:
right -= 1
return bestHow 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
def solve(data, parameter=''):
left, right = 0, len(data) - 1
best = 0
while left < right:
area = (right - left) * min(data[left], data[right])
best = max(best, area)
if data[left] <= data[right]:
left += 1
else:
right -= 1
return best06. Cost & edge cases
- Time
- O(n)
- Space
- O(1)
- All zero heights give 0.
- Two posts have width 1.
- Use 0-16 heights, each an integer from 0 to 100.