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161 lines
3.0 KiB
Markdown
161 lines
3.0 KiB
Markdown
## trees and graphs
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<br>
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---
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### breath-first search
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* similar to pre-order, but work with queue (level order problem)
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<br>
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---
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### depth-first search
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* if the depth of the tree is too large, stack overflow might happen, therefore iterative solutions might be better.
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* work with stacks
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<br>
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#### in-order
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- left -> node -> right
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```python
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def inorder(self, root):
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if root is None:
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return []
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return inorder(root.left) + [root.val] + inorder(root.right)
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````
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<br>
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#### pre-order
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- node -> left -> right
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```python
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def preorder(self, root):
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if root is None:
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return []
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return [root.val] + preorder(root.left) + preorder(root.right)
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````
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- top-down (parameters are passed down to children), so deserialize with a queue.
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<br>
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#### post-order
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- left -> right -> node
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```python
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def postorder(self, root):
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if root is None:
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return []
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return postorder(root.left) + postorder(root.right) + [root.val]
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````
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- bottom-up solution (if you know the answer of the children, can you concatenate the answer of the nodes?):
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- deletion process is always post-order: when you delete a node, you will delete its left child and its right child before you delete the node itself.
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- also, post-order is used in mathematical expressions as it's easier to write a program to parse a post-order expression. using a stack, each time when you meet a operator, you can just pop 2 elements from the stack, calculate the result and push the result back into the stack.
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<br>
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---
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### `Tree.py`
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<br>
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```python
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> python3 Trees.py
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🌴🌴🌴 Testing SimpleTree 🌴🌴🌴
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a
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b
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d
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e
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c
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h
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g
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🌳🌳🌳 Testing BinaryTree 🌳🌳🌳
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🟡 Adding [4, 1, 4, 6, 7, 9, 10, 5, 11, 5] to the tree...
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🟢 Printing the tree in preorder...
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4
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1
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6
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9
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5
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5
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11
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10
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7
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4
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🟢 Searching for node 5: True
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❌ Searching for node 15: False
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❌ Is root a leaf? False
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🟢 Is root full? True
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❌ Is the tree balanced? False
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❌ Is the tree a binary search tree? False
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🎄🎄🎄 Testing BinarySearchTree 🎄🎄🎄
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🟡 Adding [4, 1, 4, 6, 7, 9, 10, 5, 11, 5] to the tree...
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❌ Item 4 not added as BSTs do not support repetition.
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❌ Item 5 not added as BSTs do not support repetition.
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🟢 Printing the tree in preorder:
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4
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1
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6
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5
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7
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9
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10
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11
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🟢 Searching for node 5: True
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❌ Searching for node 15: False
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❌ Is root a leaf? False
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🟢 Is root full? True
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🟢 Largest node? 11
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🟢 Smallest node? 1
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❌ Is the tree balanced? False
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🟢 Is the tree a binary search tree? True
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```
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<br>
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### `BinaryTree.py`
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<br>
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* a clean implementation adapted from the class above.
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```python
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> python3 BinaryTree.py
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🌳🌳🌳 Testing BinaryTree 🌳🌳🌳
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🟡 Adding [4, 1, 4, 6, 7, 9, 10, 5, 11, 5] to the tree...
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🟢 Print the tree preorder: [4, 1, 6, 9, 5, 5, 11, 10, 7, 4]
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🟢 Print the tree inorder: [4, 1, 6, 9, 5, 5, 11, 10, 7, 4]
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🟢 Print the tree postorder: [4, 1, 6, 9, 5, 5, 11, 10, 7, 4]
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🟢 Search for node 5: True
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❌ Search for node 15: False
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```
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