Two Pointers

How to think about it

Place left at the start and right at the end (or both at the start for same-direction variants). Each step, compare and move the pointer that can improve the answer. Opposite ends for pair sums; same direction for in-place partitions.

Common variants

Variant	Movement	Example
Opposite ends	left++ / right– by sum vs target	Two Sum II
Same direction	slow/fast for in-place writes	Remove duplicates
Container	move the shorter height inward	Container With Most Water

Complexity baseline

O(n) after sorting (sort is often O(n log n)). Constant extra space unless you store results.

/** Two pointers template: sorted two-sum (1-based indices). */
export function twoSumSorted(numbers: number[], target: number): number[] {
  let lo = 0, hi = numbers.length - 1;
  while (lo < hi) {
    const sum = numbers[lo]! + numbers[hi]!;
    if (sum === target) return [lo + 1, hi + 1];
    if (sum < target) lo++;
    else hi--;
  }
  throw new Error("No solution");
}

/** Two pointers template: sorted two-sum (1-based indices). */
export function twoSumSorted(numbers: number[], target: number): number[] {
  let lo = 0, hi = numbers.length - 1;
  while (lo < hi) {
    const sum = numbers[lo]! + numbers[hi]!;
    if (sum === target) return [lo + 1, hi + 1];
    if (sum < target) lo++;
    else hi--;
  }
  throw new Error("No solution");
}