1. (20 Points) Insert records with the keys below into the smallest table with a packing factor 85 percent using; H(key)= key mod P hashing function and I(key)=Quotient(key/P) mod P increment function and G(key)= key mod 3 chain selection function and the computed chaining collision resolution method. Keys: 15, 17, 32, 28, 30, 41, 54, 67, 80, 43, 26 2. (20 Points) Insert the given keys below into an IPR (Internal Path Reduction) tree Keys: 34, 27, 89, 73, 15, 41, 69, 55 3. Keys: 60, 5, 70, 65, 20, 30, 35, 40, 15, 25, 10, 45, 50, 55, 80, 85, 75 a. (15 Points) Construct a B-tree of order 2 (ie. d-2) for the given keys above. (PS: You don't have to draw the tree for each insertion process) b. (10 Points) Delete 45 from the B-Tree that you construct in the previous question (ie. 3a) 4. Keys: 12, 52, 28, 17, 55, 10, 35, 6 (20 Points) Insert records with the keys above into a file using linear hashing with the given criteria: N=2, primary page capacity=2, overflow page capacity = 1 Space Utilization Bounds % 40 - % 80 Hashing functions Ho-key mod 2, H-key mod 4, H-key mod 8, ... 5. (15 Points) Construct a 3-d tree using the following data with "height" as the first dimension, "weight" as the second dimension and "age" as the third dimension. Name Height (cm) Weight (kg) Melda Okan Kaya Leyla Hakan Kaan Rya Sema 165 187 171 155 199 186 179 161 66 91 58 45 102 80 89 70 Age 17 18 17 19 18 17 18 19