GATE | GATE-CS-2006 | Question 77

A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3 children. A 3-ary heap can be represented by an array as follows: The root is stored in the first location, a[0], nodes in the next level, from left to right, is stored from a[1] to a[3]. The nodes from the second level of the tree from left to right are stored from a[4] location onward. An item x can be inserted into a 3-ary heap containing n items by placing x in the location a[n] and pushing it up the tree to satisfy the heap property.

Suppose the elements 7, 2, 10 and 4 are inserted, in that order, into the valid 3- ary max heap found in the above question, Which one of the following is the sequence of items in the array representing the resultant heap?

(A) 10, 7, 9, 8, 3, 1, 5, 2, 6, 4
(B) 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
(C) 10, 9, 4, 5, 7, 6, 8, 2, 1, 3
(D) 10, 8, 6, 9, 7, 2, 3, 4, 1, 5


Answer: (A)

Explanation: After insertion of 7

                                          9
                                      /   |   \
                                    /     |     \
                                  7       6       8
                               / | \
                             /   |  \
                            3    1    5    

After insertion of 2

                                           9
                                      /    |   \
                                    /      |     \
                                  7        6       8
                               / | \       /
                             /   |  \     /
                            3    1    5  2

After insertion of 10

                                 10
                             /    |   \
                           /      |     \
                        7         9       8
                    / | \       / |
                  /   |  \     /  |
                3    1    5  2    6

After insertion of 4

                                 10
                             /   |   \
                           /     |     \
                         7        9       8
                      / | \      / | \
                    /   |  \    /  |   \
                  3    1    5  2   6    4


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