1. Tree and its terminologies
The root
Ancestors a
the links is directed, always pointing down 1
Descendants
height of b = 4 b c 1 1
height of c = 1 2
leaf
depth of d =2
Parent of e,f,g,h,i 2 d
Children of d
Siblings e f g h i 3
leaf
leaf
leaf
Siblings j k
Siblings m n k 4
leaf
leaf
leaf
leaf
leaf
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2. More Terminologies
In-degree: the number of links pointing to a node (always 1 or 0); the root is the only node with in-degree 0.
2. Out-degree: the number of link pointing out from a node; leaves are node with out-degree 0
3 . Degree of a tree (arity): the maximum out-degree of nodes in the tree a b c d e f g h i j k
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3. Binary Tree (2 degree tree)
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Linked Lists
Binary Tree (2 degree tree)
data
Data field
Right and Left Children 2
Left child
Right child 24 34 13 4 34
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4. C++ : template<typename T> class BinaryTree { public: … private:
struct Node {
Node(T item, Node *left, Node *right):
data(item), left(left), right(right) {};
T data;
Node<T> *left;
Node<T> *right; };
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5. A perfect-tree or complete tree is a perfect example for using arrayd1 d1 d2 d3 d2 d3 d7 d4 d4 d5 d6 d5 d6 d7 d8 d8 d9
d10
d11
d12
d13
d14
d15 d9
d10
complete tree
full-tree
(no single child)
perfect-tree
24-1
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6. a b g d h i j k c l m v w x y z f g h q i
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7. Tree Implementation: linked lists  arrays
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Tree Implementation: linked lists  arrays
Links
data
data field
enough fields for pointers pointing the children
Usually, we use the degree of the tree as the number of the pointer fields.
Fixed, if the degree is small, e.g., binary tree (degree is 2).
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8. a b g d h i j k c l m v w x y z f g h q i
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