leetcode/islands/decks/two-pointers.md

## Two Pointers

Walk two indices instead of trying all pairs — **order lets you prune O(n²) → O(n)**.

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## Recognition

- Sorted array + pair/target condition → converge from both ends
- Palindrome / symmetric check → ends inward
- In-place partition or dedupe → slow writer + fast reader
- Two sequences compared → one pointer each

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## Template — converging (LC 167)

```js
function twoSumSorted(nums, target) {
  let l = 0;
  let r = nums.length - 1;
  while (l < r) {
    const sum = nums[l] + nums[r];
    if (sum === target) return [l + 1, r + 1];
    if (sum < target) l++; // need a bigger sum
    else r--;              // need a smaller sum
  }
}
```

Each step discards every pair using the abandoned index — that's the proof.

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## Template — fast/slow writer (LC 977 idea)

```js
function sortedSquares(nums) {
  const out = new Array(nums.length);
  let l = 0;
  let r = nums.length - 1;
  for (let i = nums.length - 1; i >= 0; i--) {
    const a = nums[l] * nums[l];
    const b = nums[r] * nums[r];
    if (a > b) { out[i] = a; l++; }
    else       { out[i] = b; r--; }
  }
  return out;
}
```

Largest squares live at the **edges** — fill the output backwards.

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## Pitfalls

- Moving the wrong pointer breaks the pruning argument
- Duplicates in 3Sum: skip repeats after each fixed element
- `l < r` vs `l <= r`: do the pointers meet or cross?

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## Recall

- Container With Most Water: why move the *shorter* wall?
- 3Sum = sort + fix one + which pattern inside?
- Valid Palindrome: what do you do with non-alphanumerics?

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## Drill

- 125 Valid Palindrome · 167 Two Sum II
- 15 3Sum · 11 Container With Most Water
- 42 Trapping Rain Water · 392 Is Subsequence
- 977 Squares of a Sorted Array · 80 Remove Duplicates II