11. Container With Most Water

1. Description

You are given an integer array height of length n. There are n vertical lines drawn such that the two endpoints of the $i^{th}$ 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.

2. Example

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

3. Constraints

• n == height.length
• 2 <= n <= 10$^5$
• 0 <= height[i] <= 10$^4$

4. Solutions

Two Pointers

n = height.size()
Time complexity: O(n)
Space complexity: O(1)

class Solution {
public:
    int maxArea(vector<int> &height) {
        const int n = height.size();
        int max_area = 0, left = 0, right = n - 1;
        while (left < right) {
            int left_height = height[left], right_height = height[right];
            max_area = max(max_area, min(left_height, right_height) * (right - left));

            if (left_height <= right_height) {
                while (left < right && height[left] <= left_height) {
                    ++left;
                }
            }
            if (left_height >= right_height) {
                while (left < right && height[right] <= right_height) {
                    --right;
                }
            }
        }

        return max_area;
    }
};