Suppose we have a balanced binary search tree T holding n numbers. We are given two numbers L and H and wish to sum up all the numbers in T that lie between L and H. Suppose there are m such numbers in T. If the tightest upper bound on the time to compute the sum is O( n^a log^b n + m^c log^d n ), the value of a + 10b + 100c + 1000d is _______.

A prime attribute of a relation scheme $$R$$ is an attribute that appears

Consider the following relational schema:

employee (empId, empName, empDept )

customer (custId, custName, salesRepId, rating)

SalesRepId is a foreign key referring to empId of the employee relation. Assume that each employee makes a sale to at least one customer. What does the following query return?

SELECT empName 
FROM employee E 
WHERE NOT EXISTS (SELECT custId 
       FROM customer C 
       WHERE C.salesRepId = E.empId 
       AND C.rating <> 'GOOD');

What is the optimized version of the relation algebra expression $$\pi_{A1}(\pi_{A2}(\sigma_{F1}(\sigma_{F2}(r))))$$, where $$A1, A2$$ are sets of attributes in r with $$A1 \subset A2$$ and $$F1,F2$$ are Boolean expressions based on the attributes in r?