The 2-d heap is a data structure that allows each item to have two individual keys. deleteMin can be performed with respect to either of these keys. The 2-d heap is a complete binary tree with the following order property: For any node X at even depth, the item stored at X has the smallest key #1 in its subtree, while for any node X at odd depth, the item stored at X has the smallest key #2 in its subtree.
a. Draw a possible 2-d heap for the items (1,10), (2,9), (3,8), (4,7), (5,6).
b. How do we find the item with minimum key #1?
c. How do we find the item with minimum key #2?
d. Give an algorithm to insert a new item into the 2-d hea
.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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