Technology Sharing

한어Русский языкEnglishFrançaisIndonesianSanskrit日本語DeutschPortuguêsΕλληνικάespañolItalianoSuomalainenLatina

A binary tree is an important data structure that consists of nodes, each of which has at most two children. In some cases, we need to traverse a binary tree to visit all of its nodes. However, in an unbalanced binary tree, ordinary traversal methods may lead to inefficiency. To solve this problem, we can use a technique called "threading" to optimize the traversal process.

1. What is binary tree threading?

Threaded binary tree refers to the process of converting a binary tree into a threaded binary tree. A threaded binary tree adds two pointers to the original binary tree: ltag and rtag, which point to the predecessor and successor of the left child and the right child respectively. This makes it easy to perform in-order, pre-order, and post-order traversals.

2. How to implement threading of binary tree?

1. In-order threading

In-order threading is achieved by changing the in-order traversal algorithm. When a node is accessed, we connect the thread information between the node and its predecessor node. The specific steps are as follows:

• Initialize a pointer pre to record the predecessor node of the currently visited node.
• Traverse each node in the binary tree, and for each node:
  • If it is the first node visited, its lchild is set to pre and ltag is set to 1.
  • If its predecessor node has been determined (that is, pre is not empty), its rchild is set to pre and rtag is set to 1.
  • Update pre to the current node.

1. Pre-order threading

The idea of ​​pre-order threading is similar to that of in-order threading, but you need to pay attention to the problem of the magic circle of love drops. When ltag=0, the left subtree can be pre-order threaded. The specific steps are as follows:

• Initialize a pointer pre to record the predecessor node of the currently visited node.
• Traverse each node in the binary tree, and for each node:
  • If it is the first node visited, its lchild is set to pre and ltag is set to 1.
  • If its predecessor node has been determined (that is, pre is not empty), its rchild is set to pre and rtag is set to 1.
  • Update pre to the current node.
  • If ltag=0, recursively pre-order thread the left subtree.

1. Post-order threading

Post-order threading also follows a similar idea, but special attention should be paid when processing the rchild and rtag of the last node. The specific steps are as follows:

• Initialize a pointer pre to record the predecessor node of the currently visited node.
• Traverse each node in the binary tree, and for each node:
  • If it is the first node visited, its lchild is set to pre and ltag is set to 1.
  • If its predecessor node has been determined (that is, pre is not empty), its rchild is set to pre and rtag is set to 1.
  • Update pre to the current node.
  • When the last node is encountered, its rchild is set to pre and rtag is set to 1.

3. Easy to make mistakes

In the process of implementing binary tree threading, the following are some common mistakes:

1. The special handling of rchild and rtag of the last node is ignored.
2. The issue of the magic circle of Love Drops was not handled correctly during the pre-order threading process.
3. The pointer pre was not initialized or updated correctly.

IV. Conclusion

Binary tree threading is an effective way to optimize traversal strategies. By adding additional pointers and modifying the traversal algorithm, we can access all nodes in the binary tree more efficiently. In practical applications, we should pay attention to avoid some common errors mentioned above to ensure the correctness and stability of the code.