The 2-0 heap is a data structure that allows each item to have two individual keys. The deleteMin operation can be performed with respect to either of these keys. The 2-D heap-order property is that for any node X at even depth, the item stored at X has the smallest key #1 in its subtree, and for any node X at odd depth, the item stored at X has the smallest key #2 in its subtree. Do the following.
a. Draw a possible 2-D heap for the items (1, lo), (2, 9), (3, 8), (4,7), and (5,6).
b. Explain how to find the item with minimum key #I.
c. Explain how to find the item with minimum key #2.
d. Give an algorithm to insert a new item in the 2-D heap.
e. Give an algorithm to perform deleteMin with respect to either key.
f. Give an algorithm to perform buildHeap in linear time.