7)The Complete Tree & BST Roadmap: 12 Algorithms from Beginner to Expert (2026 Guide)

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Welcome to the most important Data Structure in your interview preparation.

Arrays are linear; they are easy. But the real world is hierarchical—file systems, HTML DOMs, and databases are all Trees.

If you are aiming for top-tier product companies, you cannot simply memorize “Inorder Traversal.” You need to understand tree construction, serialization, and coordinate geometry within a tree. This guide breaks down the 12 Core Patterns you need to master.

Part 1: The Foundation (The “Must-Pass” Basics)

These are the non-negotiables. You cannot proceed without them.

1. DFS Traversals (The “Stack” Logic)

  • Concept: Going deep before going wide.
  • The Variations:
    • Preorder (Root to Left to Right): Used to copy a tree.
    • Inorder (Left to Root to Right): Gives sorted data in a BST.
    • Postorder (Left to Right to Root): Used to delete a tree (delete children first, then root).

2. BFS: Level Order Traversal (The “Queue” Logic)

  • Concept: Scanning the tree layer-by-layer.
  • The Logic: Recursion doesn’t work well here. Use a Queue.
    1. Push Root.
    2. While Queue not empty to Pop Node to Print to Push Left & Right Children.
  • Trigger: “Find the Left View or Right View of a tree.”

3. Height & Diameter (The “Max Path” Logic)

  • Concept: Finding the longest route in the tree.
  • The Trap: The Diameter (longest path between two nodes) does not always pass through the root.
  • The Logic: At every node, calculate Height(Left) + Height(Right). Keep updating a global Max_Diameter variable.

Part 2: The “View” Problems (Coordinate Geometry)

These questions test if you can track “Spatial Coordinates” (Row and Column) during recursion.

4. Vertical Order Traversal

  • The Question: “If you look at the tree from the top, which nodes appear in which vertical column?”
  • The Logic:
    • Assign Root at x=0.
    • Go Left to x-1.
    • Go Right to x+1.
    • Use a Map (x to List of Nodes) to store them.
  • Variations: Top View (First node in every x), Bottom View (Last node in every x).

5. Boundary Traversal

  • The Question: “Print the outline of the tree (Left edge + Leaves + Right edge reversed).”
  • The Logic: It is a combination of 3 distinct logic blocks:
    1. Get Left Boundary (exclude leaf).
    2. Get All Leaves (using simple DFS).
    3. Get Right Boundary (reverse order, exclude leaf).

Part 3: Relationships & Ancestry

Understanding how nodes relate to each other.

6. Lowest Common Ancestor (LCA)

  • The Question: “Find the first common parent of Node A and Node B.”
  • The Logic:
    • If Root splits the nodes (A is on Left, B is on Right), then Root is the LCA.
    • If both are on Left, recurse Left.
  • Why it matters: This is the most asked Tree question in Rounds 1 and 2.

Part 4: Tree Construction (The “Architect” Pattern)

These test deep recursion skills. Can you build a tree from scratch?

7. Construct Tree from Preorder & Inorder

  • The Question: “I give you two arrays: Preorder and Inorder. Reconstruct the unique Binary Tree.”
  • The Logic:
    • Preorder tells you the Root (First element).
    • Inorder tells you what is on the Left vs Right of that root.
    • Strategy: Pick root from Preorder, find it in Inorder, split arrays, recurse.

8. Serialize and Deserialize Binary Tree

  • The Question: “Convert a Tree into a String (to save in a file) and convert it back.”
  • The Logic: Use Preorder Traversal with a special marker (like N, #, or null) for empty nodes.
    • Tree: 1 -> 2, 3 $\to$ String: "1,2,N,N,3,N,N"
  • Why Important: This is a System Design concept (how databases store trees).

Part 5: BST Mastery (The “Sorted” Tree)

Binary Search Trees have special properties ($Left < Root < Right$) that we must exploit.

9. Validate BST

  • The Trap: Checking left < root < right locally is wrong.
  • The Logic: You must pass a Range(min, max) down the recursion.
    • Left child must be in range (min, current_val).
    • Right child must be in range (current_val, max).

10. Delete Node in BST

  • The Logic: Handling the 3 cases:
    1. Leaf: Just delete.
    2. One Child: Replace node with its child.
    3. Two Children (Hard): Find the Inorder Successor (smallest node in the right subtree), copy its value to the current node, and then recursively delete the successor.

Part 6: Advanced Optimization (The “Genius” Level)

For when the interviewer asks: “Can you do this without extra space?”

11. Morris Traversal

  • The Question: “Perform Inorder Traversal using O(1) Space (No Recursion Stack, No Queue).”
  • The Logic:Threaded Binary Trees.
    • Create a temporary link from the “Rightmost node of the left subtree” back to the “Current node”.
    • This allows you to return to the parent without a stack.
  • Status: This is a “Staff Engineer” level algorithm.

12. Burn a Tree (Graph Conversion)

  • The Question: “How long does it take to burn the tree if we start a fire at Node X?”
  • The Logic: You cannot go “up” in a normal tree. You must convert the Tree into a Graph (Parent Pointers) and run BFS from the starting node.

The Professor’s Cheat Sheet

Tell your students to stick this on their wall.

Problem TypeThe Algorithm StrategyTime Complexity
Height / Depth / PathDFS (Depth First Search)O(N)
Level by Level / ViewBFS (Level Order)O(N)
Sorted Data / K-th SmallestInorder Traversal (BST)O(N)
Common ParentLCA AlgorithmO(N)
Vertical / Top ViewMap (x to Nodes)O(N log N)
System Design / SavingSerialize / DeserializeO(N)
Hard OptimizationMorris TraversalO(N) Time, O(1) Space

Professor’s Advice for Teaching This

“Students, here is the hierarchy of mastery:

  1. Level 1 (Internship): Master the Basics, Views, and LCA. You will pass 70% of interviews.
  2. Level 2 (Full Time Job): Master Tree Construction and BST Validation. This proves you can handle complex logic.
  3. Level 3 (Top Product Companies): Master Serialization, Morris Traversal, and Graph Conversion. This shows you understand memory and system architecture.”

Root Your Knowledge Deep!

The Complete Tree & BST Roadmap: 12 Algorithms from Beginner to Expert (2026 Guide)

Tree Algorithms for Interview , Binary Tree Interview Questions, BFS vs DFS Algorithm, Validate Binary Search Tree

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Author: Lead C++ Developer & Founder, Vscodingacademy

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