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19. Container With Most Water

mediumAsked at Udemy

Maximize the area between two height lines using two pointers — Udemy uses this to evaluate greedy intuition for capacity-planning and bandwidth-allocation problems.

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

Problem

Given an integer array height of length n, there are n vertical lines where the i-th line has a height of height[i]. Find two lines that together with the x-axis form a container that holds the most water. Return the maximum amount of water a container 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

Try every pair of lines and compute the area — O(n^2).

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

Tradeoff:

2. Two-pointer greedy

Start with the widest window; move the pointer with the shorter height inward, because keeping a taller wall always has at least as much potential as keeping a shorter one.

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

Tradeoff:

Udemy-specific tips

Udemy asks about e-learning recommendation systems, content search, and marketplace algorithms — balanced mix of arrays, hash maps, and dynamic programming problems.

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