11. Container With Most Water

Medium

Array Two Pointers Greedy

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.

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

Constraints:

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

func maxArea(height []int) int {
	n := len(height)

	result := 0
	i := 0
	j := n - 1
	for i < j {
		h := min(height[i], height[j])
		w := j - i
		s := h * w
		result = max(result, s)
		if height[i] < height[j] {
			i++
		} else {
			j--
		}
	}
	return result
}

💡 Hints (3)

Hint 1

If you simulate the problem, it will be O(n^2) which is not efficient.

Hint 2

Try to use two-pointers. Set one pointer to the left and one to the right of the array. Always move the pointer that points to the lower line.

Hint 3

How can you calculate the amount of water at each step?