Please answer all questions thank you

3. B-trees (4 points) (1) (2 points) Show the results of inserting the keys E, F, G,U, V, W, H in order into the B-tree shown below. Assume this B-tree has minimum degree k - 2. Draw only the configurations of the tree just before some node(s) must split, and also draw the final configuration B,D.J R.S,T (2) (2 points) Suppose you have a B-tree of height h and minimum degree k What is the largest number of keys that can be stored in such a B-tree? Prove that your answer is correct (Hint: Your answer should depend on k and h. This is similar to theorem we proved in the B-tree notes) 4. Choose Function (4 points) Given n andwith n > k > 0, we want to compute the choose function (t using the following recurrence Base Cases: ( and (1, for n > 0 0 Recursive Case: (2) C)-(n-1), for n > k > 0 (1) (1 point) Compute (5) using the above rccurrenco (2) (2 points) Give pseudo-code for a bottom-up dynamic programming algorithm to compute () using the above recurrence (3) (1 point) Show the dynamic programming table your algorithm creates 3. B-trees (4 points) (1) (2 points) Show the results of inserting the keys E, F, G,U, V, W, H in order into the B-tree shown below. Assume this B-tree has minimum degree k - 2. Draw only the configurations of the tree just before some node(s) must split, and also draw the final configuration B,D.J R.S,T (2) (2 points) Suppose you have a B-tree of height h and minimum degree k What is the largest number of keys that can be stored in such a B-tree? Prove that your answer is correct (Hint: Your answer should depend on k and h. This is similar to theorem we proved in the B-tree notes) 4. Choose Function (4 points) Given n andwith n > k > 0, we want to compute the choose function (t using the following recurrence Base Cases: ( and (1, for n > 0 0 Recursive Case: (2) C)-(n-1), for n > k > 0 (1) (1 point) Compute (5) using the above rccurrenco (2) (2 points) Give pseudo-code for a bottom-up dynamic programming algorithm to compute () using the above recurrence (3) (1 point) Show the dynamic programming table your algorithm creates