Two pointer technique is a clever way to optimize nested loops. By using two separate indices (pointers) that move based on certain conditions, you can often reduce an $O(n^2)$ problem to $O(n)$ time.

Imagine you're sorting a pile of laundry with your friend:

• Approach 1 (Brute Force): You pick one sock, then check every other sock in the pile for a match. Then repeat for the next.
• Approach 2 (Two Pointer):
  • You stand at the left end of the pile, your friend stands at the right end.
  • You look at your items, and if they meet a condition (e.g., both are white), you move toward the middle.
  • You never look at the same sock twice because you only move forward.

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High-Level Patterns

1. Opposite Directions: One pointer starts at the beginning (start), and one starts at the end (end). They move toward each other. Great for:
   • Reversing an array.
   • Finding Two Sum in a Sorted array.
   • Palindrome checking.
2. Same Direction (Slow/Fast): Both pointers start at the same side. One moves faster than the other. Great for:
   • Removing duplicates.
   • Detecting cycles in Linked Lists.
   • Finding the middle of an array.

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javascript Standard
/**
 * Finding two numbers in a SORTED array that add up to a Target.
 * Brute force: O(n^2) | Two Pointers: O(n)
 */
function twoSumSorted(nums, target) {
  let left = 0;
  let right = nums.length - 1;

  while (left < right) {
    const sum = nums[left] + nums[right];

    if (sum === target) {
      return [left, right]; // Found the pair!
    } else if (sum < target) {
      // We need a larger sum, so move the left pointer forward
      left++;
    } else {
      // We need a smaller sum, so move the right pointer backward
      right--;
    }
  }
  return []; // No pair found
}

// Example
const nums = [2, 7, 11, 15];
const target = 9;
console.log(twoSumSorted(nums, target)); // [0, 1]

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When to think of Two Pointers?

• Does the problem involve a Sorted array? (Always try two pointers first).
• Are you asked to find Pairs or Triplets?
• Are youasked to modify the array In-Place?

Variations to Practice

• 3Sum: Sorting + a loop + Two Pointers.
• Trapping Rain Water: A classic harder application of two opposite pointers.
• Container With Most Water: Dynamic movement of pointers based on height.
• Move Zeros: Slow and fast pointers moving in the same direction.