problem 1:  Insert the following characters with their respective priorities (shown as ordered pairs) into an empty heap:

(K, 17), (F, 22), (P, 29), (M, 10), (N, 15), (L, 26), (G, 13), (X, 20), (A, 44), (P, 19), (Q, 30).

Show the result after each insertion.

problem 2: Given a Skip list with probability p and maximum node size M that contains N nodes, show the expected distribution of node sizes (how many nodes of each size).

problem 3: How would choose a large value (close to 1) of p or a small value (close to 0) affect the performance of a skip list? Justify your answer.

problem 4: Insert the values 89, 19, 50, 59, 76 and 26 into an empty hash table of size 11 that uses f( k ) = k mod 11 for its hash function and linear probing using f(i) = i for collision resolution.

problem 5: Is a hash table a good choice to implement a priority queue? Justify your answer.