A program takes as input a balanced binary search tree with n leaf nodes and computes the value of a function g(x) for each node x. If the cost of computing g(x) is min{ no. of leaf-nodes in left-subtree of x, no. of leaf-nodes in right-subtree of x } then the worst-case time complexity of the program is

Consider the following entity relationship diagram $$(ERD),$$ where two entities $$E1$$ and $$E2$$ have a relation $$R$$ of cardinality $$1:m.$$

The attributes of $$E1$$ are $$A11, A12$$ and $$A13$$ where $$A11$$ is the key attribute. The attributes of $$E2$$ are $$A21, A22$$ and $$A23$$ where $$A21$$ is the key attribute and $$A23$$ is a multi-valued attribute. Relation $$R$$ does not have any attribute. A relational database containing minimum number of tables with each table satisfying the requirements of the third normal form $$(3NF)$$ is designed form the above $$ERD.$$ The minimum number of tables in the database is

The relation scheme student Performance (Name, CourseNo, RollNo, Grade) has the following functional dependencies:

Name, courseNo $$\,\, \to \,\,$$ grade
RollNo, courseNo $$\,\, \to \,\,$$ grade
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,$$ Name $$\,\, \to \,\,$$ rollNo
$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,$$ RollNo $$\,\, \to \,\,$$ name

The highest normal form of this relation scheme is

A relation Empdt $$1$$ is defined with attributes empcode (unique), name, street, city, state and pincode. For any pincode, there is only one city and state. Also, for any given street city and the state, there is just one pincode. In normalization terms, Empdt$$1$$ is a relation in