Is there any faster implementation for this Splay Tree range sum?

Question

I have coded a splay tree. The nodes are represented like this.

struct Node{
    Node *l;  /// The left  Node
    Node *r;  /// The right Node
    int v;    /// The Value
};

Now, I need to know the summation of all the numbers in the tree within a certain range. For this, i implemented the following function named summation.

void summation(Node *R, int st, int ed)
{
    if(!R) return;
    if(R->v < st){        /// should not call left side
        summation(R->r, st, ed);
    }
    else if(R->v > ed){   /// should not call right side
        summation(R->l, st, ed);
    }
    else{                /// should call both side
        ret+=R->v;
        summation(R->l, st, ed);
        summation(R->r, st, ed);
    }
    return;
}

ret is a global int variable which is initialized to 0 before calling the summation function. The two parameters st & ed defines the range (inclusive).

The summation function works at a complexity of O(n). Can anyone suggest any faster implementation for this??

Answer 1

This is the splay tree implementation I did some time ago and tested against SPOJ evaluation system (written in C++) :

https://ideone.com/aQgEpF

This tree implementation supports what u are asking for (range sum in O(log(n)).

The key idea here is to use split and merge, to extract the subtree covering the range. Additionally each node contains a field sum, which is a sum of all keys in its subtree. The sum field is lazily evaluated and only relayed during split operation (along the splitting line), which allows not to go deeper into the levels not required to be calculated.