IB Computer Science Topic 5.1.8 Trees Revision Notes (HL)

IB Computer Science Topic 5.1.8 Trees Revision Notes (HL) | RevisionDojo

Trees

While you imagine forest, trees are a fundamental data structure in computer science, used to represent hierarchical data.

Note

Trees are a type of graph but with a key distinction: they have no cycles, meaning there's only max one path between any two nodes.

Terminology

Definition

Node

A basic unit containing data and one or more pointers.

Definition

Edge

Connection between two nodes.

Definition

Root

The topmost node of the tree.

Root has no parent.
All other nodes are descendants of the root.
There is always exactly one root node.

Definition

Subtree

The portion of the tree rooted at a particular node, consisting of that node together with all of its descendant nodes and the edges connecting them.

Analogy

Think of a subtree as a smaller tree growing from a branch of a larger tree.
It has its own root (the branch) and its own structure (the leaves and branches below it).

Definition

Child

A node that is directly connected and one level below another node.

Note

Nodes without children are called leaves.

Definition

Parent

A node that has one or more children.

Each node (except the root) has exactly one parent.

Example

For instance, here:

Node A (marked green) is root.
Nodes B and C are children of node A.
Node A is parent of B and C
Nodes D and E are leaves.

Note

One of the most common tree type is binary tree, a tree where each node has at most 2 children.
In binary trees we additionally can distinguish:
- Left Child: The node directly connected to the left of a parent node.
- Right Child: The node directly connected to the right of a parent node.
For instance, in the example above, node D is left child of B and C is right child of A.

Practical Applications of Binary Trees

Binary Search Trees (BSTs)
1. Organize data for efficient searching, insertion, and deletion.
2. Left child nodes contain values less than the parent.
3. Right child nodes contain values greater than or equal to the parent.
Expression Trees
1. Represent mathematical expressions.
2. Operators are stored in parent nodes.
3. Operands are stored in leaf nodes.
Trie
1. A specialized tree for fast string searching.

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Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

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Lorem ipsum dolor sit amet, consectetur adipiscing elit. Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

Duis aute irure dolor in reprehenderit

Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit aut fugit, sed quia consequuntur magni dolores eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci velit.

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

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Trees

While you imagine forest, trees are a fundamental data structure in computer science, used to represent hierarchical data.

Note

Trees are a type of graph but with a key distinction: they have no cycles, meaning there's only max one path between any two nodes.

Terminology

Definition

Node

A basic unit containing data and one or more pointers.

Definition

Edge

Connection between two nodes.

Definition

Root

The topmost node of the tree.

Root has no parent.
All other nodes are descendants of the root.
There is always exactly one root node.

Definition

Subtree

The portion of the tree rooted at a particular node, consisting of that node together with all of its descendant nodes and the edges connecting them.

Analogy

Think of a subtree as a smaller tree growing from a branch of a larger tree.
It has its own root (the branch) and its own structure (the leaves and branches below it).

Definition

Child

A node that is directly connected and one level below another node.

Note

Nodes without children are called leaves.

Definition

Parent

A node that has one or more children.

Each node (except the root) has exactly one parent.

Example

For instance, here:

Node A (marked green) is root.
Nodes B and C are children of node A.
Node A is parent of B and C
Nodes D and E are leaves.

Note

One of the most common tree type is binary tree, a tree where each node has at most 2 children.
In binary trees we additionally can distinguish:
- Left Child: The node directly connected to the left of a parent node.
- Right Child: The node directly connected to the right of a parent node.
For instance, in the example above, node D is left child of B and C is right child of A.

Practical Applications of Binary Trees

Binary Search Trees (BSTs)
1. Organize data for efficient searching, insertion, and deletion.
2. Left child nodes contain values less than the parent.
3. Right child nodes contain values greater than or equal to the parent.
Expression Trees
1. Represent mathematical expressions.
2. Operators are stored in parent nodes.
3. Operands are stored in leaf nodes.
Trie
1. A specialized tree for fast string searching.

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

1. System fundamentals2 subtopics

2. Computer organization1 subtopic

3. Networks1 subtopic

4. Computational thinking, problem-solving and programming3 subtopics

5. Abstract data structures (HL)1 subtopic

6. Resource management (HL)1 subtopic

7. Control (HL)1 subtopic

A. Databases4 subtopics

B. Modelling and simulation4 subtopics

C. Web science6 subtopics

D. Object-oriented programming (OOP)4 subtopics

IB Computer Science 5.1.8 Trees Notes

1. System fundamentals2 subtopics

2. Computer organization1 subtopic

3. Networks1 subtopic

4. Computational thinking, problem-solving and programming3 subtopics

5. Abstract data structures (HL)1 subtopic

6. Resource management (HL)1 subtopic

7. Control (HL)1 subtopic

A. Databases4 subtopics

B. Modelling and simulation4 subtopics

C. Web science6 subtopics

D. Object-oriented programming (OOP)4 subtopics

Trees

Terminology

Practical Applications of Binary Trees

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

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Trees

Terminology

Practical Applications of Binary Trees

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account