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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.

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.

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