二分搜索树中Java方法的成本

Question

We have the Java method rangeQuery_count(BSTNode,int,int) . Given the root of a BST (keys int) and an interval [a,b], this method returns number of keys of the BST belong to the interval.

static int rangeQuery_count(BSTNode v, int a, int b) { //a<=b
   if(v==null) return 0;
   if(v.key < a) return rangeQuery_count(v.right, a, b);
   else if(v.key > b) return rangeQuery_count(v.left, a, b);
   else return 1 + rangeQuery_count(v.right, a, b) + rangeQuery_count(v.left, a, b);
}

I have to determine an asymptotic estimate of the cost of the algorithm in function of the number of nodes n of the BST. I'm just starting to study these topics and I would like to understand how to calculate the cost of a program.

Answer 1

The first thing to recognise is that the cost depends on the particular values of the input parameters, in your case it depends, for instance, on how many nodes in the search tree fall within the interval. The usual simplifying assumption made here is to calculate the worst possible case. In this case, that will be when all of the nodes in the tree lie within the interval. In that case you will always take the final clause of the else as long as v is not null, you will visit each node of the tree once, and if there n nodes in the tree the cost will go up roughly linearly with n.