container-with-most-water.ts

/**
 * 11. Container With Most Water  (Medium)
 * Link: https://leetcode.com/problems/container-with-most-water/
 *
 * `height[i]` is the height of a vertical line at position i. Pick two lines
 * that, with the x-axis, form a container holding the most water. Return that
 * maximum area.
 *
 * Example:
 *   Input:  height = [1, 8, 6, 2, 5, 4, 8, 3, 7]
 *   Output: 49
 *
 * Approach:
 *   Two pointers at the widest possible span. Area is width * min(left, right).
 *   Moving the taller wall inward can only shrink both width and height, so we
 *   always advance the shorter wall — the only move that might find a taller
 *   line and beat the current best.
 *
 * Time:  O(n)  — pointers meet in one pass.
 * Space: O(1)
 */
export function maxArea(height: number[]): number {
  let left = 0;
  let right = height.length - 1;
  let best = 0;

  while (left < right) {
    const area = (right - left) * Math.min(height[left], height[right]);
    if (area > best) best = area;

    if (height[left] < height[right]) left++;
    else right--;
  }

  return best;
}