42. Trapping Rain Water

class Solution {
public:
    int trap(vector<int>& height) {
        int n=height.size();
        vector<int>lm(n);  // to store left max value
        vector<int>rm(n);  // to store right max value
        int max=height[0];  // because first element will always max in right left side
        lm[0]=max;
        // assigning the max value in the lm
        for(int i=1; i<n; i++){
            if(max<height[i])
               max=height[i];
            lm[i]=max;
        }

        max=height[n-1];  // because last element will always max in left side
        rm[n-1]=max;
        int total=0;

        // assigning the max value in the rm
        for(int i=n-2; i>=0; i--){
            if(max<height[i])
               max=height[i];
            rm[i]=max;
        }

        for(int i=1; i<n-1; i++)
        {
            if((lm[i-1] > height[i])&& (rm[i+1]>height[i]))
              total+=min((lm[i-1]-height[i]),(rm[i+1]- height[i]));  //because at that index total water will be this 
        }
        return total;
    }
};