LeetCode 11: Container With Most Water

Problem Description

LeetCode Problem 11

You are given an integer array height of length n. There are n vertical lines drawn such that the two endpoints of the ith line are (i, 0) and (i, 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.

Notice that you may not slant the container.

Example 1:

Input: height = [1,8,6,2,5,4,8,3,7]
Output: 49
Explanation: The above vertical lines are represented by array [1,8,6,2,5,4,8,3,7]. In this case, the max area of water (blue section) the container can contain is 49.

Example 2:

Input: height = [1,1]
Output: 1

Constraints:

• n == height.length
• 2 <= n <= 105
• 0 <= height[i] <= 104

Difficulty: Medium

Tags: array, two pointers, greedy

Rating: 94.11%

Complexity Analysis

The solution has the following complexity characteristics:

• Time Complexity: $O(n)$
• Space Complexity: $O(1)$

Note: This is an automated analysis and may not capture all edge cases or specific algorithmic optimizations.

Solution

Here’s my Python solution to this problem:

class Solution:
    def maxArea(self, height: List[int]) -> int:
        l, r = 0, len(height)-1
        a = 0

        while l < r:
            w = r - l
            h = min(height[l], height[r])
            a = max(a, w*h)

            if height[l] < height[r]:
                l += 1
            else:
                r -= 1
        
        return a