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CS350: Data Structures © James Moscola James Moscola Department of Engineering & Computer Science York College of Pennsylvania CS350: Data Structures Tree Traversal
CS350: Data Structures © James Moscola
College Catalog2009–2011
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2009–2011
!""#$%&'()*+,--.../ 012$1$"..."34#3$4.56
College Catalog2009–2011
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05?3352775?30?EEEF+C:F(A;
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James MoscolaDepartment of Engineering & Computer ScienceYork College of Pennsylvania
CS350: Data StructuresTree Traversal
CS350: Data Structures
Defining Trees Recursively
• Trees can easily be defined recursively
• Definition of a binary tree (a tree with arity of 2) - A binary tree is either empty (represented by
a null pointer), or is made of a single node,where the left and the right pointers eachpoint to a binary tree
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Subtree1
Subtree2
CS350: Data Structures
Defining Trees Recursively
• More generally, a tree with unspecified arity is defined as - A tree is a collection of nodes (one node is called the root)- A collection of nodes can be empty, otherwise a tree consists of a
root node (R) and zero or more non-empty subtrees each of whose roots are connected by an edge to the root R
• Because they are easily defined recursively, it is also easy to traverse them (visit each node) recursively
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CS350: Data Structures
Duplicating a Tree
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/** * Return a reference to a node that is the root of a * duplicate of the binary tree rooted at the current node. */public BinaryNode<AnyType> duplicate( ){ // Create the new node for the new tree BinaryNode<AnyType> root = new BinaryNode<AnyType>(element, null, null);
if( left != null ) // If there's a left subtree root.left = left.duplicate( ); // Duplicate and attach if( right != null ) // If there's a right subtree root.right = right.duplicate( ); // Duplicate and attach return root; // Return resulting tree}
data
left subtree
right subtree
CS350: Data Structures
Determining the Size of a Tree
• The size of a tree can be defined as: -LeftSubtree.size( ) + RightSubtree.size( ) + 1
- Determine the size of each subtree, add them together, add 1 additional node to represent theroot node
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Subtree1
Subtree2
CS350: Data Structures
Determining the Size of a Tree (Cont.)
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/** * Return the size of the binary tree rooted at t. */ public static int size( BinaryNode<AnyType> t ) { if( t == null ) return 0; else return 1 + size( t.left ) + size( t.right ); }
CS350: Data Structures
Tree Traversal
• A tree traversal is a systematic method of visiting each node in a tree
• Different tree traversal algorithms visit nodes of a tree in different orders
• Tree traversal algorithms - Preorder traversal- Postorder traversal- Inorder traversal- Level-order traversal
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CS350: Data Structures
Preorder Traversal
• In preorder traversal, a node is processed and then its children are processed recursively - The duplicate method is an example of a preorder traversal -- the root
is created first, then the subtrees are duplicated
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A
D E
B C
F
G A B D E G C F
Nodes are visited in the following order:
CS350: Data Structures
Preorder Traversal
• In preorder traversal, a node is processed and then its children are processed recursively - The duplicate method is an example of a preorder traversal -- the root
is created first, then the subtrees are duplicated
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1
3 4
2 6
7
5
CS350: Data Structures
Preorder Traversal
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// Print tree rooted at current node using preorder traversal. public void printPreOrder( ) { System.out.println( element ); // Process Node if( left != null ) left.printPreOrder( ); // Process Left Subtree if( right != null ) right.printPreOrder( ); // Process Right Subtree }
CS350: Data Structures
Postorder Traversal
• In postorder traversal, a node is processed after both children are processed recursively - The size method is an example of a postorder traversal -- the size of
subtrees are determined to find the size of the current tree
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A
D E
B C
F
G D G E B F C A
Nodes are visited in the following order:
CS350: Data Structures
Postorder Traversal
• In postorder traversal, a node is processed after both children are processed recursively - The size method is an example of a postorder traversal -- the size of
subtrees are determined to find the size of the current tree
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7
1 3
4 6
5
2
CS350: Data Structures
Postorder Traversal
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// Print tree rooted at current node using postorder traversal public void printPostOrder( ) { if( left != null ) left.printPostOrder( ); // Process Left Subtree if( right != null ) right.printPostOrder( ); // Process Right Subtree System.out.println( element ); // Process Node }
CS350: Data Structures
Inorder Traversal
• In inorder traversal, the left child is processed recursively, then the current node is processed, then the right child is recursively processed
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A
D E
B C
F
G D B E G A F C
Nodes are visited in the following order:
CS350: Data Structures
Inorder Traversal
• In inorder traversal, the left child is processed recursively, then the current node is processed, then the right child is recursively processed
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5
1 3
2 7
6
4
CS350: Data Structures
Inorder Traversal
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// Print tree rooted at current node using inorder traversal public void printInOrder( ) { if( left != null ) left.printInOrder( ); // Process Left Subtree System.out.println( element ); // Process Current Node if( right != null ) right.printInOrder( ); // Process Right Subtree }
CS350: Data Structures
Level-order Traversal
• In level-order traversal, nodes are processed in the tree from top to bottom, left to right - The first level is the root node, the second level consists of the
children of the root node, the third level consists of the grandchildren of the root node, etc.
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A
D E
B C
F
G A B C D E F G
Nodes are visited in the following order:
CS350: Data Structures
Level-order Traversal
• In level-order traversal, nodes are processed in the tree from top to bottom, left to right - The first level is the root node, the second level consists of the
children of the root node, the third level consists of the grandchildren of the root node, etc.
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1
4 5
2 3
6
7
CS350: Data Structures
Level-order Traversal
• A recursive implementation is not well-suited for level-order traversal
• A queue can be used to implement level-order traversal instead
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q = [instantiate a queue] q.push(root);
while (!q.isEmpty()) { n = q.dequeue(); visit(n); for each child of n { q.enqueue(child); } }
