11. Container With Most Water

1. Description

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 the line i is at (i, ai) and (i, 0). Find two lines, which, together with the x-axis forms a container, such that the container contains the most water.

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

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

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

3. Constraints

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

4. Solutions

My Accepted Solution

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

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

            while(left < right && heights[left] <= height) {
                ++left;
            }
            while(left < right && heights[right] <= height) {
                --right;
            }
        }

        return max_area;
    }
};