I have a binary tree which leafs have a size of 1, and the parent double in size at each level.
I project those nodes on a linear axe (memory space).
I need to get the equation that gives the adress of the node with the id of the node.
Here is the tree :
7 <- size=8
3 11 <- size=4
1 5 9 13 <- size=2
0 2 4 6 8 10 12 14 <- size=1
The address space with the sizes of the nodes :
1 2 1 4 1 2 1 8 1 2 1 4 1 2 1
So the first results are :
f(0) = 0
f(1) = 1
f(2) = 3
f(3) = 4
f(4) = 8
f(5) = 9
f(6) = 11
f(7) = 12
f(8) = 20
What is the formula of this layout ?