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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
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.
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.
Drawing a Binary Tree
(continued)
Drawing a Binary Tree
(continued)
•
The algorithm to display a tree is a two
step process.
1. 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.
2. The second step performs a level order scan
of the shadow tree to display the nodes.
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.
Student Question
• Carefully explain how BOTH the level and the
column can be found from the inorder traversal
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 ()
{}
}
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.
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);
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;
}
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?
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);
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.
col0 col1 col2 col3 col4
A
level 0
level 1
level 2
B
Cell (level, col) = (1,4)
Indent 3*colWidth spaces
from last node output.
C
D
E
// 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;
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);
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();
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
// in the queue
if (currNode.right != null)
q.push(currNode.right);
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;
}
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?