leetcode/islands/decks/sliding-window.md

Sliding Window

Two pointers plus incremental state between them. Never recompute the window from scratch.

---

Recognition

• "Longest / shortest contiguous subarray or substring such that…"
• Constraint is monotone: growing the window can only make it worse
• Fixed window size k → same idea, both ends move together

---

Template — variable window (LC 3)

function lengthOfLongestSubstring(s) {
  const seen = new Set();
  let best = 0;
  let l = 0;
  for (let r = 0; r < s.length; r++) {
    while (seen.has(s[r])) {   // shrink until valid
      seen.delete(s[l]);
      l++;
    }
    seen.add(s[r]);
    best = Math.max(best, r - l + 1);
  }
  return best;
}

Grow with r, shrink with l only while invalid.

---

Why it's O(n)

• r moves n times, l moves at most n times
• Each element enters and leaves the window once
• The inner while is amortized, not nested work

---

Pitfalls

• State must update in O(1) on both add and remove
• "Shortest window" flips the loop: shrink while valid, record before breaking
• Doesn't apply when the constraint isn't monotone (mixed signs → prefix sum)

---

Recall

• LC 121 Best Time to Buy/Sell: what is the "window state"? (min so far)
• LC 76 Minimum Window: what makes a window "valid"?
• When must you fall back to prefix sums instead?

---

Drill

• 121 Best Time to Buy and Sell Stock
• 3 Longest Substring Without Repeating Characters
• 424 Longest Repeating Character Replacement
• 567 Permutation in String · 76 Minimum Window Substring
• 209 Minimum Size Subarray Sum