2-trees
A 2-tree is a tree in which every vertex except leaves has exactly two children
- Similar to, but not the same as, binary tree
Interesting properties of a 2-tree:
- Each level has at most twice the vertices of the next lower level
- Number of vertices on level t is at most 2t for t ? 0
- Related to binary number representation:
- Level 0, (20) = 0000001 vertices maximum
- Level 1, (21) = 0000010 vertices maximum
- Level 2, (22) = 0000100 vertices maximum
- Level 3, (23) = 0001000 vertices maximum
- Notice that the maximum number of vertices on any level may be up to 1 greater than the total vertices in all lower levels
- A 2-tree with n levels must have fewer than 2n+1 vertices