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07-0: Binary Tree Definition
class Node { Node() { } Node(Comparable elem) { element_ = element; } Node(Object element, Node left, Node right) { element_ = element; left_ = left; right_ = right; } /* Access methods on next slide */ private Node left_; private Node right_; private Comparable element_; }
07-1: Binary Tree Access Methods
Node left() { void setLeft(Node left) { return left_; left_ = left; } }
Node right() { void setRight(Node right) { return right_; right_ = right; } }
Comparable element() { return element_; }
void setElement(Comparable element) { element_ = element; }
07-2: Tree Operations – Height
- Returns the height of the tree
- (Length of the path to the deepest leaf) + 1
Height = 5 Height = 6 07-3: Tree Operations – Height
int height(Node tree) { if (tree == null) return 0; return 1 + MAX(height(tree.left()), height(tree.right())); }
07-4: Tree Operations – NumNodes
- Returns the number of nodes in a tree
Number of Nodes = 8 Number of Nodes = 6 07-5: Tree Operations – NumNodes
int numNodes(Node tree) { if (tree == null) return 0; return 1 + numNodes(tree.left(), tree.right());
07-6: Writing Tree Functions
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2
3
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5
1
2 3 4 5
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7 8
9 10 11 12
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14 15
8
3
2 4
5
Tree1 (^) Tree
Tree
07-10: PREORDER Traversal
Printing out trees (Showing the shape of the tree in the printout)
A
B C
E F
G
A B C E G H H
D
D
F
07-11: PREORDER Traversal Printing out trees (Showing the shape of the tree in the printout)
- First print the root at current indent level
- Print the left subtree with larger indentation
- Print the right subtree with larger indentation
07-12: Printing Binary Trees
void print(Node tree, int indent) { if (tree != null) { for(int i=0; i<indent; i++) { System.out.print("\t"); System.out.println(tree.element().toString()); print(tree.left(), indent + 1); print(tree.right(), indent + 1); }
07-13: INORDER Traversal Printing all elements in a Binary Search Tree in order
- (Already covered in previous slides)
07-14: POSTORDER Traversal Calculating the Value of an expression tree
07-15: POSTORDER Traversal
Calculating the Value of an expression tree
- Base case:
- Return value stored at leaf
- Recursive case:
- Calculate value of left subtree
- Calculate value of right subtree
- Calculate expression value
07-16: Expression Tree Value
int value(Node tree) { if (tree.left() == null && tree.right() == null) return ((Integer) tree.element()).intValue(); int left = value(tree.left()); int right = value (tree.right()); char op = ((Character) tree.element()).charValue(); switch (op) { case ’+’: return left + right; case ’*’: return left * right; ... } }
