The Most Important Tree and Graph Algorithms for Interviews

General
1

I’m currently preparing for coding interviews and trying to focus on Trees and Graphs, but the number of algorithms and concepts is a bit overwhelming.

From your experience, what are the most important tree and graph algorithms that every candidate should master for technical interviews? I’m looking for the high-impact topics that show up frequently rather than trying to cover everything.

It would be really helpful if you could also share why those algorithms matter, common question patterns, and any tips on how to practice them effectively. If there are any must-do problems or resources, feel free to mention those as well!

2

Most interview questions on Trees and Graphs repeat the same patterns. You don’t need to learn everything — just the few algorithms that show up again and again.

Most Important Tree Algorithms

1) Tree Traversals (DFS — inorder, preorder, postorder)

  • Why it matters: This is the base of almost every tree problem.

  • Common patterns: Validate BST, kth smallest element, tree traversal problems.

  • Practice tip: Learn recursive first, then iterative.

2) Level Order Traversal (BFS)

  • Why it matters: Used whenever problems involve levels.

  • Common patterns: Level order traversal, right/left view, minimum depth.

  • Practice tip: Practice queue-based solutions until they feel natural.

3) Binary Search Trees (BST)

  • Why it matters: BST logic is tested very often.

  • Common patterns: Validate BST, search/insert/delete, BST-based LCA.

4) Lowest Common Ancestor (LCA)

  • Why it matters: Very common interview question.

  • Common patterns: Find LCA, distance between nodes.

5) Tree Height and Diameter

  • Why it matters: Tests recursion and combining subtree results.

  • Common patterns: Diameter of binary tree, balanced tree.

Most Important Graph Algorithms

6) DFS and BFS Traversals

  • Why it matters: Almost every graph problem starts here.

  • Common patterns: Number of islands, connected components, flood fill.

7) Cycle Detection

  • Why it matters: Extremely common in interviews.

  • Common patterns: Detect cycle in directed or undirected graphs, course schedule.

8) Topological Sort

  • Why it matters: Used in dependency problems.

  • Common patterns: Course scheduling, task ordering.

  • Practice tip: Learn both BFS (Kahn’s algorithm) and DFS versions.

9) Shortest Path (Dijkstra)

  • Why it matters: Core algorithm for weighted graphs.

  • Common patterns: Network delay time, shortest path problems.

10) Union-Find (Disjoint Set)

  • Why it matters: Very useful for connectivity problems.

  • Common patterns: Connected components, minimum spanning tree.

High-Impact Problems You Should Definitely Practice

Focus on patterns like:

  • Number of Islands

  • Binary Tree Level Order Traversal

  • Validate Binary Search Tree

  • Lowest Common Ancestor

  • Course Schedule

  • Clone Graph

  • Diameter of Binary Tree

  • Word Ladder

These appear repeatedly on platforms like LeetCode and NeetCode.

How To Practice Without Feeling Overwhelmed

1) Start with DFS and BFS
They are the backbone of both Trees and Graphs.

2) Practice by pattern, not randomly
Do 10–15 problems from the same pattern.

3) Revisit problems
Solve them again after a few days without looking.

4) Do mock interviews
Even one per week makes a big difference.

If You Have Limited Time, Learn In This Order

1) DFS and BFS
2) Tree Traversals
3) Binary Search Trees
4) Cycle Detection
5) Topological Sort
6) Dijkstra
7) Union-Find

If you cover these well, you’ll be prepared for most Tree and Graph interview questions, not just a few random ones.