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17. Container With Most Water

mediumAsked at Coupang

Find two lines that form the largest water container, mirroring how Coupang's truck-loading planner picks the pair of pallet heights that maximize same-day delivery routing volume.

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

Problem

Given an integer array height where each value represents a vertical line, find two lines that form a container holding the most water. Return the maximum amount of water it can store.

Constraints

  • 2 <= height.length <= 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

Compute area for every pair.

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, Math.min(height[i], height[j]) * (j - i));
return best;

Tradeoff:

2. Two pointers shrinking inward

Start from both ends; move the shorter side inward each step because moving the taller side can never improve area.

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

Tradeoff:

Coupang-specific tips

Coupang's truck-loading planner picks pallet-height pairs that maximize cubic capacity for same-day delivery routing; two-pointer shrinking is the canonical pattern over O(n^2) scans on dispatch-time data.

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