algorithm - Does the median value in a heap have to be in the bottom row? -

we learned in class binary heap has n/2 leaves, have assure median of heap leaf? or can node has left/right child? also, depend on n?

here's counterexample using numbers 1, 2, 3, 4, 5, 6, 7:

                  1                4     2               5 6   3 7 

here, median 4, , it's not in bottom row.

here's example 1, 2, 3, ..., 15: (median 8)

                         1                 8               2             9      10        3     4           11 12  13 14      5 6   7 15 

if have 2ⁿ - 1 total elements n ≥ 3. can build binary heap containing elements , median element (2^n-1) in second row follows: put 1 @ top, put 2^n-1 left child , 2 right child. put number 2^n-1 + 1 through 2ⁿ - 2 children of median, , put numbers 3 through 2^n-1 - 1 , 2ⁿ - 1 children of 2.

the time won't work when have 1 or 3 elements, since 1 element median element , it's root , 3 elements median can't root , therefore must in bottom row.

hope helps!