Data Structures | Heap | Question 4

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

Hence Option(A) is the correct answer.

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