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13. Container With Most Water

mediumAsked at Revolut

Find two lines forming the maximum-area container via a two-pointer walk, a Revolut screen that mirrors picking the best buy/sell pair in an FX order book.

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

Problem

Given n non-negative integers representing heights of vertical lines on a 2D plane, find two lines that together with the x-axis form a container holding the most water. Return the maximum area.

Constraints

  • 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. All pairs

Try every pair and track max area.

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, Math.min(h[i],h[j])*(j-i));

Tradeoff:

2. Two pointers

Start at edges, move the shorter side inward; only that move can ever increase the area. Linear time.

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:

Revolut-specific tips

Revolut interviewers want you to prove WHY shrinking from the shorter side is safe — explicitly state the invariant before coding, the same way you would prove an FX-pair monotonicity claim.

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Output

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