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16. Container With Most Water

mediumAsked at Gojek

Pick two vertical lines on a number line that together hold the most water and return that area.

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

Problem

You are given an integer array height of length n. There are n vertical lines drawn at positions i with heights height[i]. Find two lines that together with the x-axis form a container, such that the container contains the most water. Return the maximum amount of water a container can store.

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

Try every pair of indices.

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

Tradeoff:

2. Two-pointer convergence

Start at the widest pair and always move the shorter side inward; only the shorter side can possibly produce a larger area as width shrinks.

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, h * (r - l));
    if (height[l] < height[r]) l++; else r--;
  }
  return best;
}

Tradeoff:

Gojek-specific tips

Gojek expects candidates to verbally justify why the greedy two-pointer move never skips a better answer, since their dispatch heuristics are graded on the same shape of reasoning.

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