11-container-with-most-water

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Description

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.

 

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

Solution(Python)

class Solution:
    def maxArea(self, height: List[int]) -> int:
        return self.twopointer(height)

    # Time Complexity: O(n^2)
    # Space Complexity: O(1)
    def bruteforce(self, height: List[int]) -> int:
        n = len(height)
        maxArea = 0

        for i in range(n):
            for j in range(i + 1, n):
                area = (j - i) * min(height[j], height[i])

                if area > maxArea:
                    maxArea = area
        return maxArea

    # Time Complexity: O(n)
    # Space Complexity" O(1)
    def twopointer(self, height: List[int]) -> int:
        n = len(height)
        left, right = 0, n - 1

        maxArea = 0
        while left < right:
            area = (right - left) * min(height[left], height[right])
            if area > maxArea:
                maxArea = area

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

        return maxArea