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(const vector<int> &height) {
        int max_area = 0;
        for (int left = 0, right = height.size() - 1; left < right;) {
            int valid_height = min(height[left], height[right]);
            max_area = max(valid_height * (right - left), max_area);

            // As the left–right distance shrinks,
            // we move the higher boundary to potentially obtain a larger area.
            while (left < height.size() && height[left] <= valid_height) {
                ++left;
            }
            while (right >= 0 && height[right] <= valid_height) {
                --right;
            }
        }

        return max_area;
    }
};