A Practical Introduction to Data Structures and Algorithm Analysis

Sec. 6.3 General Tree Implementations 217RA BC D E FIndex Val Par01234567RACBDFE0101311 32 4 65Figure 6.9 The “list of children” implementation for general trees. The columnof numbers to the left of the node array labels the array indices. The columnlabeled “Val” stores node values. The column labeled “Par” stores pointers to theparents. For clarity, these pointers are shown as array indices. The last columnstores pointers to the linked list of children for each internal node. Each elementon the linked list stores a pointer to one of the node’s children (shown as the arrayindex of the target node).6.3.1 List of ChildrenOur first attempt to create a general tree implementation is called the “list of children”implementation for general trees. It simply stores with each internal node alinked list of its children, in order from left to right. This is illustrated by Figure 6.9.The “list of children” implementation stores the tree nodes in an array. Eachnode contains a value, a pointer to its parent, and a pointer to a linked list of thenode’s children, stored from left to right. Each list element contains a pointer toone child. Thus, the leftmost child of a node can be found directly because it isthe first element in the linked list. However, to find the right sibling for a node ismore difficult. Consider the case of a node M and its parent P. To find M’s rightsibling, we must move down the child list of P until the linked list element storingthe pointer to M has been found. Going one step further takes us to the linked listelement that stores a pointer to M’s right sibling. Thus, in the worst case, to findM’s right sibling requires that all children of M’s parent be searched.Combining trees using this representation is difficult if each tree is stored in aseparate node array. If the nodes of both trees are stored in a single node array, then