Container With Most Water

Posted 2020-10-12 Peyton_Li

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.

 

分析：

方法一：使用最简单的嵌套循环遍历，找出每一种组合。但此方法超时

方法二：容器的盛水量取决于两块板中的最短板，所以两个指针，一头一尾，记录其盛水量，然后向中间移动其较短的板，期间记录最大盛水量，直至两个指针相遇。这样时间复杂度就由方法一的O(N²)变为了O(N)。使用两个指针，一头一尾的方法很值得借鉴。

class Solution(object):
    def maxArea(self, height):
        """
        :type height: List[int]
        :rtype: int
        """
        n = len(height)
        i = 0
        j = n-1
        max_area = 0
        while(i<j):
            if height[i] < height[j]:
                area = (j-i)*height[i]
                i += 1
            else:
                area = (j-i)*height[j]
                j -= 1
            if area > max_area:
                max_area = area
        return max_area