Data Structures and Algorithm Analysis - Computer Science at ...

Sec. 6.3 General Tree Implementations 209RVal 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.The alternative is to allocate variable space for each node. There are two basicapproaches. One is to allocate an array of child pointers as part of the node. Inessence, each node stores an array-based list of child pointers. Figure 6.12 illustratesthe concept. This approach assumes that the number of children is knownwhen the node is created, which is true for some applications but not for others.It also works best if the number of children does not change. If the number ofchildren does change (especially if it increases), then some special recovery mechanismmust be provided to support a change in the size of the child pointer array.One possibility is to allocate a new node of the correct size from free store and returnthe old copy of the node to free store for later reuse. This works especially wellin a language with built-in garbage collection such as Java. For example, assumethat a node M initially has two children, and that space for two child pointers is allocatedwhen M is created. If a third child is added to M, space for a new node withthree child pointers can be allocated, the contents of M is copied over to the newspace, 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.