Part A: Indexing 1} Consider an initially emptyr ertendible hashing hide]: with a directory size of one, where the directory entry points to an empty bucket. 1Write down a sequence of data insertions into this index such that the nal index structure has a directory sire of eight. You should also draw the nal index structure after the insertions [including the directory, buckets. hash entries, local depths and global depth}- You can assume that each bucket can hold at most two data entries. I} Consider an initiallyr empty linear hashing index with one empty bucket. Write down a sequence of 3 data insertions into this index such that the nal index structure has exactly one overow bucket. You should also draw the final index structure after the insertions {including the position of the next pointer]. You can assume that a split occurs whenever an overflow bucket is created. Further, you can assume that each bucket can hold at most two data entries. {5 points} 3) Consider a completely full B-tree of order 2 and height 3. Give the maximum number of entries that can he deleted from the E-tree so that its height remains 5. Your answer should be a number. 4) Consider a relation HABLL where A is an integer attribute. E is a oating point attribute} and C is a string attribute. Assume that the only index on relation R is an unclustered E+tree on attribute A. The E--tree has height 4, and each leaf-level index page has lEI'IZIEI' (hey: rid] pairs on the average. R. has l,U,U.-U tuples in l pages. The 1.-'alues of attribute A are uniformly distributed om l to l. Now consider the following query: SELECT A, El FROM R 1iI'Ii'HEFi'E A := Isa! Compute the minimum value of yrs! such that the most e'ieient way of executing the above query is to use the E+-tree index. Assume that the cost metric is the number of page L"Ds. In your analysis, you can assume the worstcase scenario in computing the cost of a range scan using an unclustered B-tree index. Your answer should be a number. 5) Repeat the above question when the SQL query is: SELECT A. FRGM H I|WHERE A :- val Your answer should be a number