11. Container With Most Water

Given n non-negative integers a_1, a_2, ..., a_n, where each represents a point at coordinate (i, a_i). n vertical lines are drawn such that the two endpoints of the line i is at (i, a_i) and (i, 0). Find two lines, which, together with the x-axis forms a container, such that the container contains the most water.

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
Example 3:

Input: height = [4,3,2,1,4]
Output: 16
Example 4:

Input: height = [1,2,1]
Output: 2

Constraints:

2 <= height.length <= 3 * 10^4
0 <= height[i] <= 3 * 10^4

Solution in python:

class Solution:
    def maxArea(self, height: List[int]) -> int:
        length = len(height)
        i, j = 0, length-1
        mvolume = (j - i) * min(height[i], height[j])
        while i != j:
            nvolume = (j - i) * min(height[i], height[j])
            if nvolume > mvolume:
                mvolume = nvolume
            if height[i] < height[j]:
                i += 1
                continue
            if height[i] >= height[j]:
                j -= 1
                continue
        return mvolume

Complexity analysis:

• Time complexity: O(N)
• Space complexity: O(1)