容器最大盛水量

Container With Most Water

• 给定n个非负整数a1，a2，…，an，其中每个表示坐标（i，ai）处的点。

• 绘制n条垂直线，使得线i的两个端点在（i，ai）和（i，0）处。

• 找到两条线，它们与x轴一起形成一个容器，使得容器含有最多的水。

注意：您不得倾斜容器，n至少为2。

• 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.

example 1

input: [1,2,4,3]
output: 4

note: arr[1] 和 arr[3]的间隔(width)为2，min(arr[1], arr[3]) = 2，
max_water = 2 * 2 = 4 

example 2

input: [2,3,10,5,7,8,9]
output: 36

example 3

input: 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output: 4913370

思路

1. 考虑到效率问题，两层for循环两两组合数组中的元素为最基本方法，时间复杂度为O(n²)，在example3中明显会导致运行时间太长

2. 由于容器大小和两个因素有关，width和height，假设初始最大盛水量的状态为width = len(arr) - 1，height = min(arr[0], arr[len[arr] - 1])

3. head = 0, tail = len(arr) - 1, 采用头尾两个下标往中间移动靠拢，扫描整个数组，head移动还是tail移动取决于arr[head]和arr[tail]谁比较小(容器最大盛水量取决于短板)，每移动一次计算max_water是否增大

4. 由于只扫描了一次数组，时间复杂度为O(n)

代码

class Solution(object):

    def maxArea(self, height):
        """
        :type height: List[int]
        :rtype: int 返回值为最大盛水量
        """
        head = 0
        tail = len(height) - 1
        max_water = 0
        while head < tail:
            max_water = max(max_water, min(height[head], height[tail]) * (tail - head))
            if height[head] < height[tail]:
                head += 1
            else:
                tail -= 1
        return max_water

本题以及其它leetcode题目代码github地址: github地址