Reduce or eliminate use of null when updating tree structure

[jotok]

In the original pointer based tree implementation, we used null values to indicate the absence of a parent or sibling node. In the new compact implementation, we use int and short indexes instead of pointers, and we define a constant NULL to indicate absence. Mixing null and NULL makes code hard to follow and maintain.

This task is to follow up on #103 to improve code maintainability by reducing or eliminating the use of null when updating tree states.

[jotok]

Closed by #122 .