jsschools

Sliding Window

Maintains a contiguous subarray (window) of variable or fixed size, expanding/shrinking from both ends to efficiently compute properties like maximum sum or longest valid substring.

Spec ↗

Syntax

slidingWindow(arr, k)

Parameters

NameTypeRequiredDescription
arr Array<any> Yes The input array or string to apply the window over.
k number No Window size for fixed-size variants. Omit for variable-size windows.

Returns

any — Depends on variant: maximum subarray sum, longest valid substring length, etc.

Examples

// Fixed window: max sum of k consecutive elements
function maxSumWindow(arr, k) {
  let windowSum = arr.slice(0, k).reduce((a, b) => a + b, 0);
  let maxSum = windowSum;
  for (let i = k; i < arr.length; i++) {
    windowSum += arr[i] - arr[i - k];
    maxSum = Math.max(maxSum, windowSum);
  }
  return maxSum;
}

console.log(maxSumWindow([2, 1, 5, 1, 3, 2], 3));
Output 
9

// Variable window: longest substring with at most k distinct characters
function longestSubstringKDistinct(s, k) {
  const freq = new Map();
  let left = 0, maxLen = 0;
  for (let right = 0; right < s.length; right++) {
    freq.set(s[right], (freq.get(s[right]) ?? 0) + 1);
    while (freq.size > k) {
      const c = s[left++];
      if (freq.get(c) === 1) freq.delete(c);
      else freq.set(c, freq.get(c) - 1);
    }
    maxLen = Math.max(maxLen, right - left + 1);
  }
  return maxLen;
}

console.log(longestSubstringKDistinct('araaci', 2));
Output 
4

Notes

| Case | Time | Space | |---------|------|-------| | Best | O(n) | O(1) | | Average | O(n) | O(k) | | Worst | O(n) | O(k) | The sliding window technique reduces an O(n²) brute-force over all subarrays to O(n) by avoiding redundant recomputation. Two pointers (left and right) define the window. In the fixed-size variant, add the new element and subtract the outgoing element. In the variable-size variant, expand by moving right and shrink by moving left until the window satisfies the constraint. A monotonic deque (deque maintaining max/min) extends this to find the max/min in each window in O(n) total.

See also