11. Container With Most Water

• categories: Code, Interview Question, leetcode, Medium
• source: https://leetcode.com/problems/container-with-most-water/
• topics: Two Pointers

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.

Idea

Two pointers and proof that it is the optimal solution

Code

class Solution:
    def maxArea(self, height: List[int]) -> int:
        if len(height) < 2:
            return 0
        i = 0
        j = len(height) - 1
 
        ans = 0
 
        while i < j:
            ans = max(ans, min(height[i], height[j]) * (j - i))
            if height[i] < height[j]:
                i += 1
            else: 
                j -= 1
        
        return ans