11. Container With Most Water

Description

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

Solutions

　　最开始可能会想到暴力，但是连测试都过不了，超时了。

# Time Complexity: O(n^2)
# Space Complexity: O(n)
class Solution:
    def maxArea(self, height: List[int]) -> int:
        if not height:
            return 0
        n = len(height)
        res = 0
        for i in range(n-1):
            for j in range(i+1, n):
                res = max(res, min(height[i], height[j])*(j-i))
        return res
# Timeout

1. 双指针方式

　　两个指针刚开始指向最两端，然后比较，挪动较矮的那根指针。

# Time Complexity: O(n)
# Space Complexity: O(1)
class Solution:
    def maxArea(self, height: List[int]) -> int:
        if not height:
            return 0
        n = len(height)
        l, r = 0, n - 1
        res = 0
        while l < r:
            if height[l] > height[r]:
                area = (r-l) * height[r]
                r -= 1
            else:
                area = (r-l) * height[l]
                l += 1
            res = max(res, area)
        return res
# Runtime: 120 ms, faster than 99.78% of Python3 online submissions for Container With Most Water.
# Memory Usage: 14.4 MB, less than 74.74% of Python3 online submissions for Container With Most Water.

References