LeetCode 11

LeetCode 11. Container With Most Water

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.

解题思路

由题意，要求给定多个容器中能够容纳水的最大量。设定指针first, last分别表示高度的最前端和最后端，在指针每一次移动过程中，都计算当前能够存储的水量，并与之前算得的最大存储量相比较，更新最大存水量。由于容器的体积由较小的边界决定，故求解过程中将高度定义为有效高度，并且如果更新后的容器高度比原来高度低，则求得的存水量必然没有之前的最大存水量大，所以当出现这种情况时，指针继续前移或后移，直到出现更大的容器高度。

源代码

class Solution(object):
    def maxArea(self, height):
        """
        :type height: List[int]
        :rtype: int
        """
        water = 0
        first = 0
        last = len(height) - 1
        while first < last:
            h = min(height[first], height[last])
            water = max(water, (last - first) * h)
            while height[first] <= h and first < last:
                first += 1
            while height[last] <= h and first < last:
                last -= 1
        return water