83 lines
3 KiB
Markdown
83 lines
3 KiB
Markdown
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# Trees
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A general tree is a data structure where each node can have zero or more children. Each node has exactly one parent except for the root that has no parent.
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```cpp
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std::vector<TreeNode*> stack;
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```
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## Definition
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A tree T is defined by a root r and a (possibly empty) list of subtrees $T^1, T^2, ..., T^n$ where $n \geq 0$. Each subtree is itself a general tree according to the same definition.
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## Diagram
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`TreeNode`
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```text
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|------------------|
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| Data |
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| l1 l2 |
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|------------------|
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/ \
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/ \
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|--------------| |----------------------------|
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| Data | | Data |
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| l1 l2 | | l1 l2 l3 |
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|--------------| |----------------------------|
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/ \ / / \
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/ |--------| |------| |------| |----------|
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|------| | Data | | Data | | Data | | Data |
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| Data | | l1 | |------| |------| | l1 l2 |
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|------| |--------| |----------|
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/ / \
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|------| / \
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| Data | |------| |------|
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|------| | Data | | Data |
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|------| | l1 |
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|------|
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/
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/
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|------|
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| Data |
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|------|
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```
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---
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Trees are traversed starting at the root. Traversals are often recursive because of the recursive nature of trees. It is **bad** practice to expose a reference of any node externally. However, in this lab you have the following publicly exposed:
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- `TreeNode* root`
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- `void add Child()`
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- `TreeNode* getRoot()`
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- `TreeNode* findNode()`
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- `collection(TreeNode*) getChildren()`
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---
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Python-like pseudocode for Level-Order Traversal:
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```py
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LOT(root):
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# q is a queue of TreeNode references
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q;
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while q is not empty:
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node = q.dequeue()
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visit node
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for each child of ode:
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q.enqueue(child)
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```
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```py
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LOT_ReportLevels(root):
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# result is a list of lists of TreeNode references
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result;
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# q is a queue of TreeNode refs
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q;
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while q is not empty:
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# level is a list of TreeNode references
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level;
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# levelSize is q.size(?)
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# incomplete
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```
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