leetcode/islands/decks/two-pointers.md

Two Pointers

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

---

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

---

Template — converging (LC 167)

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.

---

Template — fast/slow writer (LC 977 idea)

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.

---

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?

---

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?

---

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