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. Thanks Marcos for contributing this image!

 class Solution {
 public:
     int trap(vector<int>& height) {
         int n=height.size();
         int result=;
         vector<int> left(n),right(n);
         for(int i=;i<n;i++)
         {
             left[i]=i?max(left[i-],height[i]):height[i];
         }
         for(int j=n-;j>=;j--)
         {
             right[j]=(n--j)?max(right[j+],height[j]):height[j];
         }
         for(int k=;k<n;k++)
         {
             result+=min(left[k],right[k])-height[k];
         }
         return result;
     }
 };