leetcode 腾讯精选练习（50 题）11. 盛最多水的容器
原题目
Given n non-negative integers a1, a2, …, an , where each represents a point at coordinate (i, ai). n vertical lines are drawn such that the two endpoints of line i is at (i, ai) 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
思路
- 遍历整个序列求容器的容量，从第一个到最后一个，从第二个到最后一个……
O(n)=n^2——超时
第一遍解法
网上好的解法
class Solution:
def maxArea(self, height):
i, j = 0, len(height) - 1
water = 0
while i < j:
water = max(water, (j - i) * min(height[i], height[j]))
if height[i] < height[j]:
i += 1
else:
j -= 1
return water
自己可以改进的地方
面积的计算公式：宽度 × 较小柱的高度
所以需要找尽可能长的宽度和尽量高的（较小柱）高度
首先考虑宽度问题，宽度最大的情况就是第一个元素和最后一个元素，这样可以保证宽度是最大的。记录下此时的面积。然后较小柱向中间移动。
最简代码