1. Given input {4371, 1323, 6173, 4199, 4344, 9679, 1989} and a hash function h(x) = x mod 10, show the resulting:

a. Separate Chaining hash table

b. Hash Table using linear probing

c. Hash table using quadratic probing

d. Hash table with second hash function h2(x) = 7 ( x mod 7)

2. A min-max heap is a data Structure that supports both deleteMin and deleteMax in O(logN) per operation. The structure is identical to a binary heap, but the heap-order property is that for any node, X, at even depth, the element stored at X is smaller than the parent but larger than the grandparent ( where this makes sense), and for any node X at odd depth, the element stored at X is larger than the parent but smaller than grandparent. See Fig.

a. How do we find the minimum and maximum element?

b. Give an algorithm to insert a new node into the min-max heap.

3. [5 Points] Merge the two binomial queues