[LeetCode] 11. Container With Most Water

https://leetcode.com/problems/container-with-most-water/

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

解法1: brute force, time:O(n^2) 

1. 兩個pointer, 找出所有的面積組合

解法2: 左右兩個pointer, time:O(n), space: O(1)

1. 左右兩個pointer算出面積
2. 移動短的height的pointer，向內移動，為什麼保留長的，因為長的可能會是下一次的高

Github Solution

#time: O(n), space: O(1)
class Solution:
    def maxArea(self, height: List[int]) -> int:
        if len(height) < 2:
            return 0
        left = 0
        right = len(height)-1
        result = 0
        while left < right:
            result = max(result, min(height[left], height[right])*(right-left))
            if height[left] < height[right]:
                left += 1
            else:
                right -= 1
        return result