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en/docs/chapter_tree/array_representation_of_tree.md
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# 7.3   Array Representation of Binary Trees
Under the linked list representation, the storage unit of a binary tree is a node `TreeNode`, and nodes are connected by pointers. The previous section introduced the basic operations of binary trees under the linked list representation.
In the linked-list representation, the storage unit of a binary tree is a node `TreeNode`, and nodes are connected by pointers. The previous section introduced the basic operations of binary trees in this representation.
So, can we use an array to represent a binary tree? The answer is yes.
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<p align="center"> Figure 7-13 &nbsp; Level-order traversal sequence corresponds to multiple binary tree possibilities </p>
To solve this problem, **we can consider explicitly writing out all `None` values in the level-order traversal sequence**. As shown in Figure 7-14, after this treatment, the level-order traversal sequence can uniquely represent a binary tree. Example code is as follows:
To solve this problem, **we can explicitly write out all `None` values in the level-order traversal sequence**. As shown in Figure 7-14, once we do this, the level-order traversal sequence can uniquely represent a binary tree. Example code is as follows:
=== "Python"
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tree = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]
```
![Array representation of any type of binary tree](array_representation_of_tree.assets/array_representation_with_empty.png){ class="animation-figure" }
![Array representation of an arbitrary binary tree](array_representation_of_tree.assets/array_representation_with_empty.png){ class="animation-figure" }
<p align="center"> Figure 7-14 &nbsp; Array representation of any type of binary tree </p>
<p align="center"> Figure 7-14 &nbsp; Array representation of an arbitrary binary tree </p>
It's worth noting that **complete binary trees are very well-suited for array representation**. Recalling the definition of a complete binary tree, `None` only appears at the bottom level and towards the right, **meaning all `None` values must appear at the end of the level-order traversal sequence**.
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<p align="center"> Figure 7-15 &nbsp; Array representation of a complete binary tree </p>
The following code implements a binary tree based on array representation, including the following operations:
The following code implements a binary tree using an array representation, including the following operations:
- Given a certain node, obtain its value, left (right) child node, and parent node.
- Given a node, obtain its value, left (right) child node, and parent node.
- Obtain the preorder, inorder, postorder, and level-order traversal sequences.
=== "Python"