A Practical Introduction to Data Structures and Algorithm Analysis

220 Chap. 6 Non-Binary TreesRVal SizeR 2ABA 3 B 1CDEFC 0 D 0 E 0 F 0(a)(b)Figure 6.12 A dynamic general tree representation with fixed-size arrays for thechild pointers. (a) The general tree. (b) The tree representation. For each node,the first field stores the node value while the second field stores the size of thechild pointer array.space, and the old space is then returned to free store. As an alternative to relyingon the system’s garbage collector, a memory manager for variable size storage unitscan be implemented, as described in Section 12.3. Another possibility is to use acollection of free lists, one for each array size, as described in Section 4.1.2. Notein Figure 6.12 that the current number of children for each node is stored explicitlyin a size field. The child pointers are stored in an array with size elements.Another approach that is more flexible, but which requires more space, is tostore a linked list of child pointers with each node as illustrated by Figure 6.13.This implementation is essentially the same as the “list of children” implementationof Section 6.3.1, but with dynamically allocated nodes rather than storing the nodesin an array.6.3.4 Dynamic “Left-Child/Right-Sibling” ImplementationThe “left-child/right-sibling” implementation of Section 6.3.2 stores a fixed numberof pointers with each node. This can be readily adapted to a dynamic implementation.In essence, we substitute a binary tree for a general tree. Each node of the“left-child/right-sibling” implementation points to two “children” in a new binarytree structure. The left child of this new structure is the node’s first child in thegeneral tree. The right child is the node’s right sibling. We can easily extend thisconversion to a forest of general trees, because the roots of the trees can be consideredsiblings. Converting from a forest of general trees to a single binary treeis illustrated by Figure 6.14. Here we simply include links from each node to itsright sibling and remove links to all children except the leftmost child. Figure 6.15shows how this might look in an implementation with two pointers at each node.