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Medium / PYTHON

Maximum Subarray with Stable Boundaries

arrays · dynamic_programming 25 minute study target

Not completed

Challenge

Find a nonempty contiguous subarray with maximum sum. Return [sum, start, end], where the interval is nums[start:end] (end excluded). Among equal sums choose the smallest start, then the smallest end. For the exceptional empty input return [0, 0, 0].

Input and output contract

0 ≤ n ≤ 60,000; integer elements with absolute value ≤ 1,000,000. Nonempty input must produce a nonempty interval, even when every element is negative.

All tests follow this contract. You do not need to validate malformed input. Return the requested result from maximum_subarray; printed output is not your answer. Standard-library tools are allowed. Implement your solution in Python 3.12.

Target complexity: O(n) time; O(1) auxiliary space

Return values are checked by type. Use the exact function name. Print output is not your answer. Tests have time and memory limits.

Public examples

Example 1

Arguments

[[-2, 3, -1, 3, -5]]

Expected return

[5, 1, 4]
Example 2

Arguments

[[0, 0]]

Expected return

[0, 0, 1]
Example 3

Arguments

[[-5, -2, -7]]

Expected return

[-2, 1, 2]
Hint

Extend the previous best suffix unless its sum is negative. Preserve a zero-sum prefix because it gives an earlier start.

The worked solution unlocks after completion, or with Premium access.

maximum_subarray.pyPython 3.12

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Results

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Hidden tests reveal only their pass/fail status, never their inputs or expected outputs. Runtime is observed wall time—not an inferred complexity class.

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