42. Trapping Rain Water

最新推荐文章于 2025-08-23 16:01:06 发布

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最新推荐文章于 2025-08-23 16:01:06 发布

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文章标签：数据结构与算法

原文链接：http://www.cnblogs.com/bernieloveslife/p/9794359.html

本文介绍了一种计算雨后地面积水的算法。通过给定的一系列非负整数表示地形高度，算法能够计算出降雨后能留住多少水量。文章提供了两种解决方案，一种是直接遍历比较每个位置的左右最高点，另一种是预先计算每个位置的左右最大值，然后进行计算，避免了重复计算，提高了效率。

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Given n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it is able to trap after raining.

avatag

The above elevation map is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 6 units of rain water (blue section) are being trapped. Thanks Marcos for contributing this image!

Example:

Input: [0,1,0,2,1,0,1,3,2,1,2,1]
Output: 6

Solution1:(TLE)

class Solution:
    def trap(self, height):
        """
        :type height: List[int]
        :rtype: int
        """
        res = 0
        for i in range(1,len(height)-1):
            maxleft,maxright = 0,0
            for j in range(i,-1,-1):
                maxleft = max(maxleft,height[j])
            for j in range(i,len(height)):
                maxright = max(maxright,height[j])
            res += min(maxright,maxleft) - height[i]
            # print('i',i,'maxleft',maxleft,'maxright',maxright,'ans',min(maxright,maxleft) - height[j])
        return res

每个位置的组左右高度，不是其相邻位置的高度，而是整个左边部分和右边部分的最大值

Solution2:

class Solution:
    def trap(self, height):
        """
        :type height: List[int]
        :rtype: int
        """
        if len(height)==0:
            return 0
        res = 0
        leftmax = [0 for i in range(len(height))]
        rightmax = [0 for i in range(len(height))]
        leftmax[0] = height[0]
        for i in range(1,len(height)):
            leftmax[i] = max(height[i],leftmax[i-1])
        rightmax[-1] = height[-1]
        for i in range(len(height)-2,-1,-1):
            rightmax[i] = max(height[i],rightmax[i+1])
        for i in range(1,len(height)-1):
            res += min(leftmax[i],rightmax[i])-height[i]
        return res

先用动态规划求出每个点的情况，然后再算。

转载于:https://www.cnblogs.com/bernieloveslife/p/9794359.html