Algorithm Notesworking through it, one step at a time

Kadane's algorithm

MediumPractice ↗

Choose the Strongest Energy Run

Original & variantMaximum Subarray ↗

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

01. The question

Signed readings represent energy gained or lost at consecutive stations. Return the largest sum of a nonempty continuous run. At least one reading is required.

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

02. Worked example

Inputreadings = [-3, 4, -1, 2, -6, 3]

Output5

  1. Start a new run at 4 rather than carrying the earlier -3.
  2. Extending through -1 and 2 raises its sum to 5.
  3. The later -6 does not erase the best completed run.

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: [-3,4,-1,2,-6,3]. 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. At each station, either extend the previous run or restart here.
  2. Keep the best sum ending here separate from the best sum anywhere.
  3. Initialize with the first reading, not 0.

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

1-25 readings, each -1,000 to 1,000. The chosen run must be nonempty.

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 energy_run(readings):
    ending = best = readings[0]
    for value in readings[1:]:
        ending = max(value, ending + value)
        best = max(best, ending)
    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 energy_run(readings):
    ending = best = readings[0]
    for value in readings[1:]:
        ending = max(value, ending + value)
        best = max(best, ending)
    return best

06. Cost & edge cases

Time
O(n)
Space
O(1)
  • All-negative readings return the least-negative reading.
  • The empty run is not permitted.

Keep going

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