Find the maximum sum of a subarray within a given window size

Fixed-size sliding window: compute the first window's sum, then slide by adding the incoming element and subtracting the outgoing one. O(n) time, O(1) space — no need to recompute each window.

4 min read·~15 min to think through

This is the canonical fixed-size sliding window problem. The naive solution recomputes every window in O(n·k); the trick is that consecutive windows overlap by k−1 elements, so you only adjust by the difference.

Approach

Sum the first k elements — that's the first window.
Slide: for each new position, add the entering element, subtract the leaving element. That's O(1) per step.
Track the max as you go.

function maxSubarraySum(nums, k) {
  if (nums.length < k) return null; // not enough elements

  let windowSum = 0;
  for (let i = 0; i < k; i++) windowSum += nums[i];

  let max = windowSum;
  for (let i = k; i < nums.length; i++) {
    windowSum += nums[i] - nums[i - k]; // slide
    max = Math.max(max, windowSum);
  }
  return max;
}

Why it's O(n)

Each element is added exactly once and removed exactly once. No nested loop. Space is O(1) — just the running sum and the max.

Don't confuse this with Kadane's

This problem: window of a fixed size k → sliding window.
"Maximum subarray sum" with no size constraint → Kadane's algorithm (current = max(num, current + num)). Different problem, different technique. Interviewers sometimes blur the wording to see if you notice.

Variants

Max average of a window — same thing, divide by k.
Variable-size window ("smallest window with sum ≥ target") → two-pointer expand/contract.
Negative numbers — the fixed-window version still works unchanged; just don't assume the max is positive.

Follow-up questions

•How is this different from Kadane's algorithm?
•How would you handle a variable-size window (smallest window with sum >= target)?
•Does the solution change if the array has negative numbers?
•How would you return the window's start index, not just the sum?

Common mistakes

•Recomputing the whole window sum each step — O(n*k) instead of O(n).
•Confusing this with Kadane's (unconstrained max subarray).
•Off-by-one in the slide: subtracting nums[i-k] wrong index.
•Not handling arrays shorter than k.

Performance considerations

•O(n) time, O(1) space — optimal. The naive O(n*k) is the trap; the overlap insight is the whole point of the problem.

Edge cases

•Array length < k → no valid window.
•k equals the array length → one window.
•All negative numbers — max is still well-defined.
•k = 1 → just the max element.

Real-world examples

•Moving averages over a time series (k-period window).
•Rolling metrics — peak traffic over any 5-minute window.

Senior engineer discussion

Seniors state the O(n)/O(1) bound up front, explicitly distinguish fixed-window sliding from Kadane's, and generalize to the variable-size two-pointer pattern. The 'tell' is recognizing the overlap between consecutive windows as the source of the speedup.