A Practical Introduction to Data Structures and Algorithm Analysis

212 Chap. 6 Non-Binary TreesRWABXYZC D E FParent’s Index 0 0 1 1 1 2 7 7 7LabelRABCNode Index 0 1 2 3 4 5 6 7 8 9 10Figure 6.5 The parent pointer array implementation. Each node corresponds toa position in the node array stores its value and a pointer to its parent. The parentpointers are represented by the position in the array of the parent. The root of anytree stores ROOT, represented graphically by a slash in the “Parent’s Index” box.This figure shows two trees stored in the same parent pointer array, one rootedat R, and the other rooted at W.DEIFWXYZABDFJCHEGFigure 6.6 A graph with two connected components.Equivalence classes can be managed efficiently with the UNION/FIND algorithm.Initially, each object is at the root of its own tree. An equivalence pair isprocessed by checking to see if both objects of the pair are in the same tree usingfunction differ. If they are in the same tree, then no change need be madebecause the objects are already in the same equivalence class. Otherwise, the twoequivalence classes should be merged by the UNION function.Example 6.2 As an example of solving the equivalence class problem,consider the graph of Figure 6.6. Initially, we assume that each node of thegraph is in a distinct equivalence class. This is represented by storing eachas the root of its own tree. Figure 6.7(a) shows this initial configuration