trees and graphs



tree tranversals


  • if the depth of the tree is too large, stack overflow might happen, therefore iterative solutions might be better.
  • in-order are similar to breath-first search (level order problems) - work with queues
  • pre-order is top-down (parameters are passed down to children). - work with stacks
  • post-order is a bottom-up solution (if you know the answer of the children, can you concatenate the answer of the nodes?):
    • 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.
    • 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.


Tree.py


> python3 Trees.py


🌴🌴🌴 Testing SimpleTree 🌴🌴🌴
a
	b
		d
		e
	c
		h
		g



🌳🌳🌳 Testing BinaryTree 🌳🌳🌳

🟡 Adding [4, 1, 4, 6, 7, 9, 10, 5, 11, 5] to the tree...
🟢 Printing the tree in preorder...
4
1
6
9
5
5
11
10
7
4

🟢 Searching for node 5: True
 Searching for node 15: False
 Is root a leaf? False
🟢 Is root full? True
 Is the tree balanced? False
 Is the tree a binary search tree? False


🎄🎄🎄 Testing BinarySearchTree 🎄🎄🎄

🟡 Adding [4, 1, 4, 6, 7, 9, 10, 5, 11, 5] to the tree...
 Item 4 not added as BSTs do not support repetition.
 Item 5 not added as BSTs do not support repetition.
🟢 Printing the tree in preorder:
4
1
6
5
7
9
10
11

🟢 Searching for node 5: True
 Searching for node 15: False
 Is root a leaf? False
🟢 Is root full? True
🟢 Largest node? 11
🟢 Smallest node? 1
 Is the tree balanced? False
🟢 Is the tree a binary search tree? True

BinaryTree.py


  • a clean implementation adapted from the class above.
> python3 BinaryTree.py

🌳🌳🌳 Testing BinaryTree 🌳🌳🌳

🟡 Adding [4, 1, 4, 6, 7, 9, 10, 5, 11, 5] to the tree...
🟢 Print the tree preorder: [4, 1, 6, 9, 5, 5, 11, 10, 7, 4]
🟢 Print the tree inorder: [4, 1, 6, 9, 5, 5, 11, 10, 7, 4]
🟢 Print the tree postorder: [4, 1, 6, 9, 5, 5, 11, 10, 7, 4]

🟢 Search for node 5: True
 Search for node 15: False