The problem with implementing merge for binary heaps using a tree representation:

    Binary heaps are also leftist heaps, but the worst possible ones! The naive merging
    algorithm (discussed in lecture) used to merge leftists heaps
    might result in a right heavy tree. For example, consider merging two
    binary (min) heaps A and B, where the root of B is greater than all nodes in A.
    The resulting resulting tree A+B is very right heavy since B ends up at the rightmost end of A.
    And fixing completness of A+B can require upto O(total number of elements) time,
    which is the same as inserting all elements from one heap into another.

    Another option is to build a binary heap from sratch by converting both heaps
    to sequences, concatenating them, and calling buildHeap() on the final sequence,
    but this would also cost O(total number of elements)---which is also as bad as before.