11. Container With Most Water

Prompt

You are given an integer array height of length n. There are n vertical lines drawn such that the two endpoints of the ith 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.

Examples

• 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

Solutions

Two Pointer Solution

In C++

int maxArea(vector<int>& height) {
	size_t l = 0; size_t r = height.size() - 1;
	int max_water = 0;
	while (l < r) {
		int curr_water = (r - l) * min(height[l], height[r]);
		max_water = max(curr_water, max_water);
		if (height[l] > height[r]) --r;
		else ++l;
	}
	return max_water; 
}

Explanation

The idea here is to use Two Pointers to scan through a subset of the possible areas. We acheive this by starting at the outside and scanning in, moving the smaller wall in each time.

Big O Analysis

Time Complexity

$O(n)$

Auxiliary Space Complexity

$O(1)$