11. Container With Most Water

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.

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 <= 10⁵
• 0 <= height[i] <= 10⁴

💡 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?

Submitted Code

class Solution:
    def maxArea(self, height: List[int]) -> int:
        left, right = 0, len(height) - 1    # 왼쪽 벽, 오른쪽 벽
        max_area = 0

        while left < right:
            area = min(height[left], height[right]) * (right - left)
            max_area = max(area, max_area)

            if height[left] < height[right]:
                left += 1
            else:
                right -= 1
        
        return max_area

Runtime: 54 ms | Beats 76.04%
Memory: 29.41 MB | Beats 96.11%

물 높이는 더 낮은 쪽 벽이 결정하기 때문에 낮은 벽을 움직여서 더 높은 벽이 있는지 찾으면 된다.