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Summary - Trees

Walk a small binary tree and print its values in a mini task.

Summary - Trees

Tree: hierarchical, acyclic; n nodes, n-1 edges. Root, internal, leaf. Binary tree has at most 2 children.

Height: longest path; node count: 1 + left + right. Inorder/preorder/postorder traversals are O(n).

Trees underpin file systems, expression parsing and search (BST).

Practice Summary: inorder traversal

Write inorder(node). Left-root-right, print values. Print 1 2 3 with root = Node(2); root.left = Node(1); root.right = Node(3); inorder(root).

Starter code

solution.py
def inorder(node):
    # Left-root-right traversal

Sample solution

solution.py
class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None
def inorder(node):
    # Left-root-right traversal
    if node is None:
        return
    inorder(node.left)
    print(node.val)
    inorder(node.right)
root = Node(2)
root.left = Node(1)
root.right = Node(3)
inorder(root)

Expected output

1
2
3

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 Summary - Trees: match the terms

Term Meaning
Root Topmost
Leaf No children
Height Longest path
Inorder Left-root-right

2 Node-edge

Question 
n nodes → ____ edges
Answer 
n nodes → n - 1 edges

Explanation: n - 1 is right.

3 What does inorder give on a BST?

  • Increasing order Correct answer
  • Random
  • Leaves
  • Decreasing order

Explanation: Increasing order

All lessons in Intermediate

1 Merge sort

  1. Divide and conquer
  2. Merge operation
  3. Full merge sort
  4. Summary - Merge sort

2 Quick sort

  1. Pivot selection
  2. Partitioning
  3. Recursive quick sort
  4. Summary - Quick sort

3 Heap sort

  1. What is a heap?
  2. Heapify
  3. Build heap and sort
  4. Summary - Heap sort

4 Counting sort

  1. Counting idea
  2. Count array
  3. Output array
  4. Summary - Counting sort

5 Radix sort

  1. Radix idea
  2. Digit pass
  3. Stable sub-sort
  4. Summary - Radix sort

6 Sorting project

  1. Project: Overview
  2. Score array
  3. Apply merge sort
  4. Print statistics

7 Tree

  1. What is a tree?
  2. Node and edge
  3. Binary tree
  4. Summary - Trees

8 Binary search tree

  1. BST rule
  2. BST insert
  3. BST search
  4. Summary - BST

9 AVL tree

  1. Balanced tree
  2. Rotation
  3. Balance after insert
  4. Summary - AVL tree

10 Heap

  1. Min and max heap
  2. Insert
  3. Extract
  4. Summary - Heap

11 Priority queue

  1. What is a priority queue?
  2. Heap-based implementation
  3. Push and pop
  4. Summary - Priority queue

12 Data structures project

  1. Project: Overview
  2. Undo stack
  3. Pending queue
  4. Print the state

13 Graph basics

  1. What is a graph?
  2. Adjacency list
  3. Adjacency matrix
  4. Summary - Graph

14 Breadth-first search

  1. BFS idea
  2. Using a queue
  3. Marking visited
  4. Summary - BFS

15 Depth-first search

  1. DFS idea
  2. Stack or recursion
  3. Backtracking
  4. Summary - DFS

16 Greedy algorithms

  1. Greedy approach
  2. Coin change
  3. Greedy limits
  4. Summary - Greedy

17 Divide and conquer

  1. Three steps
  2. Recursive structure
  3. Master theorem
  4. Summary - Divide and conquer

18 Backtracking

  1. What is backtracking?
  2. State tree
  3. Pruning
  4. Summary - Backtracking

19 Graph project

  1. Project: Overview
  2. City graph
  3. BFS for reachability
  4. Print the result

20 Intermediate final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4