Given n non-negative integers a₁, a₂, …, a_n , where each represents a point at coordinate (i, a_i). n vertical lines are drawn such that the two endpoints of line i is at (i, a_i) and (i, 0). Find two lines, which together with x-axis forms a container, such that the container contains the most water.

Note: You may not slant the container and n is at least 2.

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:

Input: [1,8,6,2,5,4,8,3,7]

Output: 49

Solution

from typing import List

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

        while left < right:
            area = (right-left) * min(height[left], height[right])
            maxArea = max(maxArea, area)
            if height[left] < height[right]:
                left += 1
            else:
                right -= 1

        return maxArea

Test Cases

test = Solution()
assert test.maxArea([1,8,6,2,5,4,8,3,7]) == 49
assert test.maxArea([1,2]) == 1
assert test.maxArea([2,3,4,5,18,17,6]) == 17
print('All Passed!')

Big O Analysis

Space Complexity: O(1)

Time Complexity: O(N)