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Heaps, Binary Files and Bit Sets

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A complete binary tree B, containing 50 nodes, is stored in a vector.

(a). What is the level of the tree?
(b). How many nodes are leaf nodes? Nonleaf nodes?
(c). What is the index of the parent of B[35]?
(d). What are the indices of the children of node B[20]?
(e). What is the index of the first node with no children? With one child?
(f). What are the indices for all nodes at level 4 in the tree?

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Solution Preview

The binary tree is as follows.
Level 1: B[0]
Level 2: B[1], B[2]
Level 3: B[3], B[4], B[5], B[6]
Level 4: B[7], B[8], B[9], B[10], B[11], B[12], B[13], B[14]
Level 5: B[15], ..., B[30]
Level 6: B[31], ..., ...

Solution Summary

Heaps, binary files and bit sets are examined.