[leetcode] 11. Container With Most Water

题目

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

Constraints:

• n == height.length
• 2 <= n <= 105
• 0 <= height[i] <= 104

思路

双指针收敛，以更短的边为收敛依据，原因是短边的收敛不会影响求最大面积的结果。

没做出来。。

代码

python版本：

# 暴力求解（超时）
class Solution:
    def maxArea(self, height: List[int]) -> int:
        res = 0
        for i in range(len(height)):
            for j in range(i+1, len(height)):
                res = max(res, min(height[i], height[j])*(j-i))
        return res

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