1. Podcast Ch17d Title: Drawing a Binary Tree
Description: Drawing a binary tree; building a shadow tree, the displayTree method
Participants: Barry Kurtz (instructor); John Helfert and Tobie Williams (students)
Textbook: Data Structures for Java; William H. Ford and William R. Topp

2. Drawing a Binary Tree
The methods displayTree(), drawTree(), and drawTrees() display a binary tree as a string or graphically. The algorithms employ many of the basic features of a binary tree.

3. Drawing a Binary Tree (continued)
View the display of the tree as a rectangular grid with a cell denoted by the pair (level, column). The level is a row in the grid corresponding to a level in the tree. The column coordinate designates a region of the display measured left to right.

4. Drawing a Binary Tree (continued)

5. Drawing a Binary Tree (continued)
The algorithm to display a tree is a two step process.
The first step uses the recursive function buildShadowTree() to carry out an inorder scan of the tree which creates a second tree, called a shadow tree. Its nodes store the value of the node in the original tree formatted as a string and the (level, col) position of the shadow tree node in the grid.
The second step performs a level order scan of the shadow tree to display the nodes.

6. Building a Shadow Tree
As buildShadowTree() uses an inorder scan it moves from one grid column to another. For instance, with Tree 0, the order of visit is B D A E C. Note in the figure that this is the column-order for the nodes in the tree.

7. Student Question
Carefully explain how BOTH the level and the column can be found from the inorder traversal

8. Building a Shadow Tree (continued)
The nodes of a shadow tree are objects of type TNodeShadow.
class TNodeShadow {
public static int columnValue;
public String nodeValueStr;
public int level, column;
public TNodeShadow left, right;
public TNodeShadow () {} }

9. Building a Shadow Tree (continued)
Each recursive call of buildShadowTree() allocates a TNodeShadow object and assigns it the node value string. It then makes recursive calls that create the left and right subtrees.
Each recursive call in the inorder scan creates a node in the column specified by the static value columnValue and then increments the variable for the next recursive call.

10. buildShadowTree() // inorder scan used to build the shadow tree
private static <T> TNodeShadow buildShadowTree(TNode<T> t, int level) {
// reference to new shadow tree node
TNodeShadow newNode = null;
if (t != null) {
// create the new shadow tree node
newNode = new TNodeShadow();
// allocate node for left child at next level
// in tree; attach node
newNode.left =
buildShadowTree(t.left, level+1);

11. buildShadowTree() (concluded)
// initialize variables of the new node
// format conversion
newNode.nodeValueStr = t.nodeValue.toString();
newNode.level = level;
newNode.column = TNodeShadow.columnValue;
// update column to next cell in the table
TNodeShadow.columnValue++;
// allocate node for right child at next level
// in tree; attach node
newNode.right =
buildShadowTree(t.right, level+1); }
return newNode;

12. Student Question
When displaying the shadow tree, what factors need to be taken into account to decide the proper indention before printing a node value?

13. Displaying a Shadow Tree
The method displayTree() takes the root, t, of the binary tree as an argument and calls buildShadowTree() to create the shadow tree.
// build the shadow tree
TNodeShadow shadowRoot = buildShadowTree(t, 0);

14. Displaying a Shadow Tree (cont)
Display the tree with a level order scan of the shadow tree. The scan uses the node data to position and display each node.
// use for the level-order scan of the shadow tree
LinkedQueue<TNodeShadow> q =
new LinkedQueue<TNodeShadow>();
String displayStr = "";
int colWidth = maxCharacters + 1;
int currLevel = 0, currCol = 0;
// use during the level order scan of the shadow tree
TNodeShadow currNode;

15. displayTree() // return a string that displays a binary tree;
// output of a node value requires no more than
// maxCharacters
public static <T> String displayTree(TNode<T> t,
int maxCharacters) {
// use for level-order scan of the shadow tree
LinkedQueue<TNodeShadow> q =
new LinkedQueue<TNodeShadow>();
String displayStr = "";
int colWidth = maxCharacters + 1;
int currLevel = 0, currCol = 0;
TNodeShadow.columnValue = 0;
if (t == null)
return displayStr;
// build the shadow tree
TNodeShadow shadowRoot = buildShadowTree(t, 0);

16. displayTree() (continued)
// use during level order scan of the shadow tree
TNodeShadow currNode;
// insert the root in the queue and set current
// level to 0
q.push(shadowRoot);
// continue the iterative process until the queue
// is empty
while(!q.isEmpty()) {
// delete front node from queue and make it
// the current node
currNode = q.pop();

17. displayTree() (continued)
// if level changes, output a newline
if (currNode.level > currLevel) {
currLevel = currNode.level;
currCol = 0;
displayStr += '\n'; }
// if a left child exists, insert the child
// in the queue
if (currNode.left != null)
q.push(currNode.left);
// if a right child exists, insert the child
if (currNode.right != null)
q.push(currNode.right);

18. displayTree() (concluded)
// output formatted node value
if (currNode.column > currCol) {
displayStr += formatChar((
currNode.column - currCol) *
colWidth, ' ');
currCol = currNode.column; }
displayStr += formatString(colWidth,
currNode.nodeValueStr);
currCol++;
displayStr += '\n';
// delete the shadow tree
shadowRoot = clearShadowTree(shadowRoot);
return displayStr;

19. Student Question
How could this approach be adapted to draw a binary tree in a GUI interface so that the tree has branches displayed as well as node values?