Binary Trees (Cambridge International A-Level Computer Science)

Binary trees

What is a binary tree?

• A binary tree is a rooted tree where every node has a maximum of 2 nodes

• A binary tree is essentially a graph and therefore can be implemented in the same way

• You must understand:

  • Tree traversal of a tree data structure
  • Add new data to a tree
  • Remove data from a tree

• The most common way to represent a binary tree is by storing each node with a left and right pointer

This information is usually implemented using 2D arrays

Tree terminology

How do you program a tree?

• In the following example:

  • A tree is represented using a TreeNode structure, which includes:

    • A value field to store the data held in the node
    • A children field to store a collection (e.g. list or array) of child nodes

  • The createTreeNode function is used to initialise a new tree node, setting its value and creating an empty collection for its children

  • The addChild function allows a new child node to be added to a parent node

    • It creates a new TreeNode with the given value and appends it to the parent's children collection

  • Finally, the createTreeNode function is used to create the root node

    • Additional child nodes are added using the addChild function, allowing a multi-level tree structure to be built with branches and sub-branches

Algorithm to traverse a tree structure

• For a tree like: Root ├── Child 1 │ └── Grandchild 1.1 └── Child 2
• The output will be: Root Child 1 Grandchild 1.1 Child 2

Algorithm to add data to a tree structure

• These examples all create a new node with the provided value and attach it to the given parent node
• This approach allows dynamic construction of trees with multiple levels

Algorithm to remove data to a tree structure

• This only removes the first matching child from the direct children of a node
• If you want to remove nodes anywhere in the tree, you’d need a recursive version
• REMOVE and del and .remove() work because the children collection is a list/array