Prefix and suffix products
Multiply Every Other Sensor
01. The question
For every sensor position, return the product of all other readings. Do not divide. Negative readings and zeros are allowed.
Before revealing the idea, predict the result and describe what information you would need to track.
02. Worked example
Inputreadings = [3, 0, -2, 4]
Output[0, -24, 0, 0]
- A left pass stores the product strictly before each position.
- A right pass multiplies in the product strictly after each position.
- Only the zero position excludes the zero, so its product is 3 × -2 × 4 = -24.
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: [3,0,-2,4]. 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
- Start output entries at 1, the empty-product identity.
- Write prefix products into output.
- Traverse backward with a running suffix and multiply it into output.
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 other_sensors(readings):
output = [1] * len(readings)
prefix = 1
for i, value in enumerate(readings):
output[i] = prefix
prefix *= value
suffix = 1
for i in range(len(readings) - 1, -1, -1):
output[i] *= suffix
suffix *= readings[i]
return outputHow 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 other_sensors(readings):
output = [1] * len(readings)
prefix = 1
for i, value in enumerate(readings):
output[i] = prefix
prefix *= value
suffix = 1
for i in range(len(readings) - 1, -1, -1):
output[i] *= suffix
suffix *= readings[i]
return output06. Cost & edge cases
- Time
- O(n)
- Space
- O(1) auxiliary, plus O(n) output
- One reading returns [1]; empty input returns [].
- Two zeros make every output zero.
- Walkthrough limits keep all integer products exact in JavaScript.