A Practical Introduction to Data Structures and Algorithm Analysis

164 Chap. 5 Binary Trees/** Binary tree node implementation: Pointers to children */class BSTNode implements BinNode {private Key key;// Key for this nodeprivate E element;// Element for this nodeprivate BSTNode left; // Pointer to left childprivate BSTNode right; // Pointer to right child}/** Constructors */public BSTNode() {left = right = null; }public BSTNode(Key k, E val){ left = right = null; key = k; element = val; }public BSTNode(Key k, E val, BSTNode l, BSTNode r){ left = l; right = r; key = k; element = val; }/** Return and set the key value */public Key key() { return key; }public void setKey(Key k) { key = k; }/** Return and set the element value */public E element() { return element; }public void setElement(E v) { element = v; }/** Return and set the left child */public BSTNode left() { return left; }public void setLeft(BSTNode p) { left = p; }/** Return and set the right child */public BSTNode right() { return right; }public void setRight(BSTNode p) { right = p; }/** Return true if this is a leaf node */public boolean isLeaf(){ return (left == null) && (right == null); }Figure 5.7 A binary tree node class implementation.As an example of a tree that stores different information at the leaf and internalnodes, consider the expression tree illustrated by Figure 5.9. The expressiontree represents an algebraic expression composed of binary operators such as addition,subtraction, multiplication, and division. Internal nodes store operators,while the leaves store operands. The tree of Figure 5.9 represents the expression4x(2x + a) − c. The storage requirements for a leaf in an expression tree are quitedifferent from those of an internal node. Internal nodes store one of a small set ofoperators, so internal nodes could store either a small code identifying the operatoror a single byte for the operator’s character symbol. In contrast, leaves must storevariable names or numbers. Thus, the leaf node value field must be considerably