leetcode/islands/decks/sliding-window.md

## Sliding Window

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

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## 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

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## Template — variable window (LC 3)

```js
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.

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## 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

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## 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)

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## 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?

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## 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