Trees

www.tudorgirba.com

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edge

node

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leaf

root

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parent

child

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subtree

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path

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height = 1

depth = level = 2

degree = 1

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height = 1

depth = level = 1

degree = 3

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0

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ordered tree

leftmost rightmost

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isomorphic trees

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left right

left leftright right

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not a binary tree binary tree

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complete binary tree

breadth-first traversal

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breadth-first traversal

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1

breadth-first traversal

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2

1

breadth-first traversal

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2 3

1

breadth-first traversal

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2 3

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1

breadth-first traversal

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1

breadth-first traversal

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2 3

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1

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preorder(node)

visit(node).preorder(node.left).preorder(node.right).

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preorder(node)

visit(node).preorder(node.left).preorder(node.right).

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2

1

preorder(node)

visit(node).preorder(node.left).preorder(node.right).

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2

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preorder(node)

visit(node).preorder(node.left).preorder(node.right).

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preorder(node)

visit(node).preorder(node.left).preorder(node.right).

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preorder(node)

visit(node).preorder(node.left).preorder(node.right).

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preorder(node)

visit(node).preorder(node.left).preorder(node.right).

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inorder(node)

inorder(node.left).visit(node).inorder(node.right).

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inorder(node)

inorder(node.left).visit(node).inorder(node.right).

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2

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inorder(node)

inorder(node.left).visit(node).inorder(node.right).

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inorder(node)

inorder(node.left).visit(node).inorder(node.right).

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inorder(node)

inorder(node.left).visit(node).inorder(node.right).

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inorder(node)

inorder(node.left).visit(node).inorder(node.right).

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inorder(node)

inorder(node.left).visit(node).inorder(node.right).

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postorder (node)

postorder(node.left).postorder(node.right).visit(node).

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postorder (node)

postorder(node.left).postorder(node.right).visit(node).

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postorder (node)

postorder(node.left).postorder(node.right).visit(node).

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postorder (node)

postorder(node.left).postorder(node.right).visit(node).

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postorder (node)

postorder(node.left).postorder(node.right).visit(node).

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postorder (node)

postorder(node.left).postorder(node.right).visit(node).

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postorder (node)

postorder(node.left).postorder(node.right).visit(node).

!"#$%&'(")$*

!

"#$#%&'!&$()*+,%&)$!&-!.,--#/!)$!(*)+!0#$#*,%&)$!%)!0#$#*,%&)$1!

Example (group 15)

!"#$%&'(")$*

!

"#$#%&'!&$()*+,%&)$!&-!.,--#/!)$!(*)+!0#$#*,%&)$!%)!0#$#*,%&)$1!

Example (group 15)

Hierarchical structure

Binary search tree

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n4 n2 n5 n1 n6 n3

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n4 n2 n5 n1 n6 n3

2 61 53 4

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Binary search tree

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a + b - c * d

a + b - c * d

a

+

b

-

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*

d

a

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b

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*

d

operator

operand

Infix notation

a

+

b

-

c

*

d

Postfix notation

Prefix notation

Infix notation

a

+

b

-

c

*

d

Postfix notation

Prefix notation -+ab*cd

Infix notation

a

+

b

-

c

*

d

a+b-c*dPostfix notation

Prefix notation -+ab*cd

Infix notation

a

+

b

-

c

*

d

a+b-c*dPostfix notation ab+cd*-

Prefix notation -+ab*cd

Tudor Gîrbawww.tudorgirba.com

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