Array Representation of a Tree

Representing a tree with an array

You've seen two approaches to implementing a sequence data structure: either using an array, or using linked nodes. We extended our idea of linked nodes to implement a tree data structure. It turns out we can also use an array to represent a tree.

Here's how we implement a binary tree:

The root of the tree will be in position 1 of the array (nothing is at position 0). We can define the position of every other node in the tree recursively:
The left child of a node at position n is at position 2n.
The right child of a node at position n is at position 2n + 1.
The parent of a node at position n is at position n/2.

Self-test: ArrayBST representation

For each of the following self-tests, we will give you an instance of an ArrayBST. Match it to one of the four possible binary search trees below.

Tree 1	Tree 2	Tree 3	Tree 4

Self-test 1

Which of tree options above could be represented by the ArrayBST shown here?

	Tree 1	Correct! The `ArrayBST` suggests there is a root with one left child and no right child, and the left child has a left child.
	Tree 2	Incorrect. The `ArrayBST` shows the root has no right child.
	Tree 3	Incorrect. The `ArrayBST` shows the root has no right child.
	Tree 4	Incorrect. The `ArrayBST` shows the root has no right child.

Check Solution

Self-test 2

Which of tree options above could be represented by the ArrayBST shown here?

	Tree 1	Incorrect. The `ArrayBST` shows that the root has a right child.
	Tree 2	Correct! The `ArrayBST` shows that the root has both a left and right child.
	Tree 3	Incorrect. The `ArrayBST` shows that the root has a left child.
	Tree 4	Incorrect. The `ArrayBST` shows that the root has a left child.

Check Solution

Self-test 3

Which of tree options above could be represented by the ArrayBST shown here?

	Tree 1	Incorrect. The `ArrayBST` shows the root has no left child.
	Tree 2	Incorrect. The `ArrayBST` shows the root has no left child.
	Tree 3	Correct! The `ArrayBST` shows the root has a right child which has a left child.
	Tree 4	Incorrect. Because there is nothing in position 7, the right child of the root can't have a right child.

Check Solution