2. [30 marks] Consider the Linear Hashing index shown in Figure 2. Assume that we split whenever an overflow page is created. Answer the following questions about this index:

Figure 2. Linear Hashing (1) Show the index after inserting an entry with hash value 80. 46 20* 25* 34* 38* 46* 53* 58* 70* 84* 90* 96* 20 34 70 90 (2) Show the index after inserting an entry with hash value 38 into the original tree. (3) Find a list of entries whose insertion into the original index would lead to a bucket with two overflow pages. Use as few entries as possible to accomplish this. What is the maximum number of entries that can be inserted into this bucket before a split occurs that reduces the length of this overflow chain?

Figure 2. Linear Hashing