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16. Container With Most Water

mediumAsked at MercadoLibre

Find two lines that together with the x-axis form the largest area container.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given n non-negative integers a1..an, where each represents a vertical line at coordinate i with height ai, find two lines that, together with the x-axis, hold the most water. Return the maximum amount of water that can be held.

Constraints

  • n == height.length
  • 2 <= n <= 10^5
  • 0 <= height[i] <= 10^4

Examples

Example 1

Input
height = [1,8,6,2,5,4,8,3,7]
Output
49

Example 2

Input
height = [1,1]
Output
1

Approaches

1. Brute force

Check every pair of lines and compute area.

Time
O(n^2)
Space
O(1)
let best = 0;
for (let i = 0; i < height.length; i++)
  for (let j = i+1; j < height.length; j++)
    best = Math.max(best, (j - i) * Math.min(height[i], height[j]));
return best;

Tradeoff:

2. Two-pointer shrink

Start at both ends; always move the shorter side inward because its height caps the area.

Time
O(n)
Space
O(1)
function maxArea(height) {
  let l = 0, r = height.length - 1, best = 0;
  while (l < r) {
    const h = Math.min(height[l], height[r]);
    best = Math.max(best, (r - l) * h);
    if (height[l] < height[r]) l++; else r--;
  }
  return best;
}

Tradeoff:

MercadoLibre-specific tips

MercadoLibre routing engineers use this to gauge two-pointer instinct — useful when squeezing courier capacity envelopes across last-mile lanes in São Paulo and Buenos Aires.

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