leetcode42_Trapping Rain Water

一.问题描述

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.

For example, 
Given [0,1,0,2,1,0,1,3,2,1,2,1], return 6.

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!

二.代码编写

第一轮循环从左至右找到每一个位置左边的最大值存入list_flag；

第二轮循环从右至左找到每一个位置右边的最大值，若该值比list_flag[i]小，则替换list_flag[i]

第三轮循环如果当前list_flag[i]大于height[i]，则sum=sum+list_flag[i]-height[i]。【list_flag[i]-height[i]为当前位置可储水量】。

很明显时间复杂度和空间复杂度都是O(N)。

实现代码如下：

'''
@ 2016.11.20 by wttttt
@ for problem detail, see https://leetcode.com/problems/trapping-rain-water/
@ for solution detail, see http://blog.youkuaiyun.com/u014265088/article/details/53241669

@tarverse
@ for similar problem, see https://leetcode.com/problems/container-with-most-water/
@ or maybe for better solution, see http://blog.youkuaiyun.com/u014265088/article/details/52575323
'''
class Solution(object):
    def trap(self, height):
        """
        :type height: List[int]
        :rtype: int
        """
        len_hei = len(height)
        list_flag = [0 for i in range(len_hei)]
        max_v = 0
        for i in range(len_hei):
            list_flag[i] = max_v
            if height[i]>max_v:
                max_v = height[i]
        print list_flag
        max_right = 0
        for i in range(len_hei-1,-1,-1):
            if max_right<list_flag[i]:
                list_flag[i] = max_right 
            if height[i]>max_right:
                max_right = height[i] 
        print list_flag
        sum = 0
        for i in range(len_hei):
            if list_flag[i]>height[i]:
                sum = sum+list_flag[i]-height[i]
        return sum
        
so = Solution()
height = [4,2,3]
print so.trap(height)

三.代码改进

提交之后发现效率不太好，再看代码发现第三遍循环完全可以合并到第二遍里面呀，这样就减少一次循环，效率还是有很好的提高的，代码：

'''
@ 2016.11.20 by wttttt
@ for problem detail, see https://leetcode.com/problems/trapping-rain-water/
@ for solution detail, see http://blog.youkuaiyun.com/u014265088/article/details/53241669
@ traverse
@ for similar problem, see https://leetcode.com/problems/container-with-most-water/
@ or maybe for better solution, see http://blog.youkuaiyun.com/u014265088/article/details/52575323
'''
class Solution(object):

    def trap(self, height):

        """

        :type height: List[int]

        :rtype: int

        """

        len_hei = len(height)

        list_flag = [0 for i in range(len_hei)]

        max_v = 0

        for i in range(len_hei):

            list_flag[i] = max_v

            if height[i]>max_v:

                max_v = height[i]

        sum = 0

        max_right = 0

        for i in range(len_hei-1,-1,-1):

            vv = min(max_right, list_flag[i])

            if vv > height[i]:

                sum = sum+vv-height[i]

            #if max_right<list_flag[i]:

                #list_flag[i] = max_right 

            if height[i]>max_right:

                max_right = height[i] 

        #for i in range(len_hei):

            #if list_flag[i]>height[i]:

                #sum = sum+list_flag[i]-height[i]

        return sum

        

so = Solution()

height = [4,2,3]

print so.trap(height)