ALGORITHM READING NOTE

Maximum Subarray

The maximum subarray problem asks for the contiguous segment with the largest sum. Kadane's algorithm solves it in O(n).

TYPEAlgorithmCATEGORYSets & Dynamic ProgrammingDEPTHAdvancedTYPICAL COMPLEXITYO(n) with Kadane

SHORT INTERVIEW ANSWER

Start with this mental model

The maximum subarray problem asks for the contiguous segment with the largest sum. Kadane's algorithm solves it in O(n).

SIMPLE EXPLANATION

How it works, without unnecessary jargon

At each position decide whether to extend the previous segment or start fresh from the current value.

Track both the best segment ending here and the best seen globally.

EXECUTION

Read the algorithm as a sequence of decisions

Define the state precisely.

Write the transition/choice from smaller states.

Set base cases, then decide memoization, tabulation or backtracking.

A small example to keep in mind

Read a tiny input by hand and write down the state after every important operation. For Maximum Subarray, the goal is to make the invariant visible rather than to memorize code.

READABLE JAVASCRIPT IMPLEMENTATIONJavaScript

function maxSubarray(a) {
  let ending = a[0];
  let best = a[0];
  for (let i = 1; i < a.length; i++) {
    ending = Math.max(a[i], ending + a[i]);
    best = Math.max(best, ending);
  }
  return best;
}

How to read this code

Do not memorize the syntax. Follow the state that changes on each line and connect it to the invariant described above.

COMPLEXITY

O(n) with Kadane

Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.

WHEN TO USE IT

Good fit

Use DP when subproblems overlap and optimal solutions can be composed from smaller optimal states.

COMMON MISTAKES

What usually goes wrong

Writing recurrence before defining state.
Using DP when state space is larger than the original problem.

HOW TO EXPLAIN IT IN AN INTERVIEW

A professional answer shape

Explain the local decision behind Kadane, not only the two variable names. Also handle the all-negative case correctly.

Problem→Core idea→Invariant / state→Big-O→Trade-off

QUICK INTERVIEW CHECK

What problem does Maximum Subarray solve?

The maximum subarray problem asks for the contiguous segment with the largest sum. Kadane's algorithm solves it in O(n).

What should I mention about complexity?

Its typical cost here is O(n) with Kadane, but a complete answer should connect that cost to the representation, input constraints and the dominant operations.

What is the most common mistake?

Writing recurrence before defining state.

Continue readingMemoizationTabulationBacktracking

function maxSubarray(a) { let ending = a[0]; let best = a[0]; for (let i = 1; i < a.length; i++) { ending = Math.max(a[i], ending + a[i]); best = Math.max(best, ending); } return best; }