Leetcode11 Container With Most W

11. Container With Most Water

Medium

Given n non-negative integers a₁, a₂, ..., a_n , where each represents a point at coordinate (i, a_i). n vertical lines are drawn such that the two endpoints of line i is at (i, a_i) and (i, 0). Find two lines, which together with x-axis forms a container, such that the container contains the most water.

Note: You may not slant the container and n is at least 2.

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:

Input: [1,8,6,2,5,4,8,3,7]
Output: 49
解题思路，利用类二分查找法
从左右向中间移动

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

假设一开始的区间为[left,right]，
假设height[left]>height[right]，
则area=(right-left)*height[right]
此时我们如果选择从left端向中间移动，
此时area的高度h必定小于等于height[right]，
而area的长变小，
因此area'一定变小。
因此只能从高度小的一端向中间移动。
该算法时间复杂度为O(n)