Leetcode -- Trapping Rain Water

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. 

class Solution {public:    int trap(vector<int>& height) {        int n=height.size();        if(n==0) return 0;        vector<int> left(n,height[0]),right(n,height[n-1]);        for(int i=1;i<n;++i)        left[i]=max(height[i],left[i-1]);        for(int i=n-2;i>=0;--i)        right[i]=max(height[i],right[i+1]);        int sum=0,water=0;        for(int i=0;i<n;++i)        {            sum+=height[i];            water+=min(left[i],right[i]);        }        return water-sum;    }};