Given n non-negative integers a1, a2, …, an , where each represents a point at coordinate (i, ai). n vertical lines are drawn such that the two endpoints of line i is at (i, ai) 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)