Algorithm Notesworking through it, one step at a time

Running minimum and maximum

MediumPractice ↗

Choose a Strong Amplifier Chain

Original & variantMaximum Product Subarray ↗

Original examples and wording. The question below states the exact input format and output contract.

01. The question

Signed integer gain settings form a line of amplifiers. Choose a nonempty continuous chain and return its largest product. Negative settings reverse the sign and zero resets a chain. Original scenario; the maximum-product task is unchanged.

Before revealing the idea, predict the result and describe what information you would need to track.

02. Worked example

Input[-2, 3, -4, 0, 2]

Output24

  1. At -2 the low and high products are both -2.
  2. At 3 they become -6 and 3.
  3. At -4 the previous minimum -6 becomes the new maximum 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: [-2,3,-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 runtime notices

Python downloads only when you run code, using compressed runtime assets. Code is not saved or uploaded. Enable JavaScript to run it.

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
  1. Keep the lowest and highest products ending here.
  2. Calculate all three candidates using the previous low and high before updating either.
  3. Save the best high across all endings.

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

Small validated inputs: arrays at most 16 entries, text at most 16 characters, tables at most 20 states. Bit questions use unsigned bytes (0-255). See the task for its exact format.

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=''):
    low = high = best = data[0]
    for value in data[1:]:
        candidates = (value, low * value, high * value)
        low, high = min(candidates), max(candidates)
        best = max(best, high)
    return best
How 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=''):
    low = high = best = data[0]
    for value in data[1:]:
        candidates = (value, low * value, high * value)
        low, high = min(candidates), max(candidates)
        best = max(best, high)
    return best

06. Cost & edge cases

Time
O(n)
Space
O(1)
  • One negative gain may be the best available answer.
  • Zero may beat every negative chain.
  • Use 1-14 gains, each -5 to 5, keeping even intermediate products exact.

Keep going

Browse all questionsBack to Arrays & hash mapsPack a Two-Item Parcel Find a Clean Signal Close a Nested Ledger Scan the Warehouse Shelves