Algorithm Teacher: Data Structures and Algorithm Analysis

Algorithms and data structures cannot be learned by watching. The gap between listening to someone explain quicksort and sorting an array yourself on paper, step by step, shows up the moment you see the exam sheet or the interview question. So when you choose a teacher, the thing to look at is not how much they know but how much work they make you do. This guide covers what kind of teacher fits your goal, what to look for in a trial lesson, when private lessons do not help, and the order in which to study the topics.

Three Goals, Three Kinds of Lesson

If you are taking a first-year introduction to programming and algorithms, your problem is usually programming itself, not algorithms. Until flowcharts, pseudocode, loops and arrays make sense, there is no point discussing complexity analysis. At this stage you need someone patient who solves small problems with you and makes you think before giving the answer. If your foundations are weak, following the path in how to start programming first may be the better move.

If you are preparing for a midterm or final in a data structures or algorithm analysis course, your need is very concrete: being able to solve the types of question your lecturer sets. These exams are mostly on paper. You are asked to insert elements into a tree and draw it, show every step of a sorting algorithm, or work out the complexity of a piece of code. The right teacher for you agrees to work in the language your course uses (C, Java, Python) and with your lecturer's notation, and asks for past papers in the first session.

If you are a working developer preparing for technical interviews, expectations change again. You do not need to write proofs. You need to solve an unfamiliar problem while thinking aloud, explain why you picked a data structure, and state the complexity of your solution. The person you are looking for does not make you memorise questions. They teach problem patterns and put you through mock interviews.

What to Look For in a Trial Lesson

The best way to evaluate an algorithms teacher is to watch them solve a problem unprepared. Bring a medium-difficulty question of your own choosing to the trial lesson and suggest solving it together. Can they narrate their thinking? When they take a wrong turn, do they notice and back out? This is where someone repeating memorised solutions differs from someone who can actually solve problems.

Ask these questions too:

• Which language will we work in, and can you follow the notation used in my course?
• Is there a written topic order, and will it be adapted to my exam date?
• Will you set problems after each session, and how will you look at my solutions?
• Will we practise tracing algorithms by hand on paper?
• Do you have published solutions, articles or code?

Two small checks are useful. Why is binary search O(log n)? Why is quicksort's worst case O(n²), and on which input does it occur? A good teacher does not stop at stating the result; they have you count on an example until you find it yourself. Deriving complexity rather than having you memorise it is worth far more, because the exam will contain a piece of code you have never seen.

In a good first lesson the pen is mostly in your hand. The teacher draws a data structure, demonstrates one operation, has you do the next, and asks you to explain back in your own words. You leave with a few solved problems and a few new ones to attempt alone.

Situations that call for caution:

• A guaranteed grade or interview result
• A "memorise these 300 problems" approach with no discussion of patterns
• Only code on a screen, never tracing by hand
• The solution handed over before you have started thinking
• An offer to do your assignment for you
• A prepaid package sold without a written plan

Private Lessons, Books or Videos?

Free material in this field is plentiful and good. Open university lecture recordings (MIT OpenCourseWare, for example), visualization sites such as VisuAlgo, and problem platforms like LeetCode are more than enough for self-study. The classic textbooks are comprehensive but heavy. They work well as a reference, less well as a first resource.

The weakness of self-study is that you cannot see your own misunderstandings. Your solution passes the test inputs, its complexity is worse than expected, and nobody tells you. Video lectures are good for meeting a topic for the first time. The danger is believing you know the material because you could follow the explanation. In algorithms, knowing means being able to write it on a blank page.

One-to-one lessons pay for themselves in these cases: limited time before an exam and no idea what to prioritize, being stuck on the same topic for a long time (usually recursion or trees), or needing mock interviews and feedback on your solutions. They do not pay off if you come to lessons without having attempted the problems yourself, if you cannot yet write loops and functions (then you need programming lessons), or if you cannot make time to solve problems between sessions. Struggling is part of learning this subject. A teacher who gives you the solution too quickly takes that part away, however well meant.

A Study Sequence for Data Structures and Algorithms

1. Programming foundations: loops, arrays, functions and simple recursion. Nothing else can be built without them.
2. Complexity analysis. Big O notation and time complexity is the yardstick you will use in every later topic.
3. Linear structures: array, linked list, stack and queue. Compare the cost of insertion, deletion and search in each.
4. Searching and sorting. You should be able to carry out selection, insertion, merge and quick sort by hand, step by step. The sorting algorithms exam questions and solutions were written for exactly that.
5. Recursion and divide and conquer. Learning to draw the call tree makes many later topics easier.
6. Hash tables. To see what they look like in practice in one language, read List, Set and Map in Dart.
7. Trees and the binary search tree. For insertion, deletion and traversal questions see the binary search tree exam questions.
8. Heaps and priority queues.
9. Graphs: representations, BFS, DFS and shortest-path algorithms.
10. Greedy algorithms and dynamic programming.

If you are preparing for an exam, compare this list with your course syllabus and study only what is covered. If you are preparing for interviews, steps three, six, seven and nine are the ones you will meet most often.

You Decide How Much a Lesson Gives You

Come to each session with problems you worked on for at least twenty minutes and could not solve, and show where you got stuck. Your half-finished attempt is the most valuable information a teacher can get, because it reveals which concept is missing. After seeing a solution, put it away and solve the same problem again on a blank page a few days later. If you cannot, you did not understand it; you only recognized it.

If the exam is on paper, your practice should be on paper. Autocomplete and the compiler will not be with you in the exam room. Solve past papers against the clock and ask your teacher to look at them the way a marker would. Knowing which missing step costs you marks often raises your grade more than learning a new topic.

The Lessons I Teach

I give one-to-one online lessons and exam preparation support in algorithms and data structures. Details are on the exam support page. You are welcome to ask me the questions in this guide too.

Frequently Asked Questions

Which programming language do I need for learning algorithms?

The concepts are language independent. For an exam, use the language of your course; for interviews, pick the one you write most comfortably. What matters is being able to write loops, arrays and functions in it without having to think.

How much maths do I need for algorithms?

For the basics of complexity analysis, summation formulas, logarithms and a little induction are enough. Proof-heavy analysis courses need more discrete mathematics, but for interviews and practical work, school maths plus a few additions will do.

Does tutoring help two weeks before an exam?

It helps if you focus on past question types, but do not expect miracles. A whole term cannot be recovered in two weeks. The realistic plan is to identify the topics that are certain to appear and practise solving them by hand.

How many hours of lessons per week are enough?

One or two hours a week is enough for most people. What decides the outcome is the number of problems you solve alone between sessions. A lesson that follows a week without independent problem solving is largely repetition.