I'm constructing a binary tree for a sequence of data and the tree is store in a 1-based array. So if index of parent node is idx,

the left child is 2 * idx and the right is 2 * idx + 1.

Every iteration, I sort current sequence based on certain criteria, select the median element as parent, tree[index] = sequence[median], then do same operation on left(the sub sequence before median) and right(the subsequence after median) recursively.

Eg, if 3 elements in total, the tree will be:

1

/ \

2 3, the array size to store the tree is also 3

4 elements:

1

/ \

2 3

/

4 , the array size to store the tree is also 4

5 elements:

1

/ \

2 3

/ \ /

4 null 5 , the array size to store the tree has to be 6, since there is a hole between 4 and 5.

Thus, the array size is only determined by number of elements, I believe there is an anlytical solution for it, just can't prove it.

Any suggestion will be appreciated.

Thanks.