How can I learn all algorithms? The ultimate step-by-step guide

ByNelson Ayers

Learning algorithms can seem daunting at first. With hundreds of complex algorithms spanning categories like sorting, searching, dynamic programming, and graphs, how can any programmer reasonably master them all?

The key is having the right learning strategies and resources. Consistent, focused effort over time to build up your algorithms knowledge will help you succeed.

In this comprehensive 2600+ word guide, I‘ll walk you through a step-by-step approach to learn algorithms efficiently based on proven techniques. I‘ll also share insider tips, statistics, examples, and opinions from my 10+ years as a software engineer to help you on your algorithms journey.

Why you should learn algorithms

Let‘s first discuss why algorithms matter for programmers:

  • Get better at problem solving – Algorithms require breaking problems into logical, discrete steps. This analytical thinking strengthens overall programming abilities.

  • Write optimized code – Knowing which algorithms and data structures to use lets you implement efficient solutions.

  • Understand computational complexity – Analyzing time and space complexity teaches you how to balance performance tradeoffs.

  • Do well in interviews – Algorithms questions are standard in programming interviews. Solid algo knowledge makes getting hired easier.

  • Open up job opportunities – Companies need developers with strong algorithms skills for challenging technology problems.

  • Future-proof your skills – Algorithms form the backbone of software engineering. Learning them will serve you well for decades to come as technology evolves.

I can‘t stress enough how foundational algorithms are for programmers. Making a serious effort to learn them will pay dividends throughout your career.

How to learn algorithms step-by-step

Here is a structured 6-step approach to master algorithms efficiently based on proven techniques:

Step 1: Start with the building blocks

First learn elementary algorithms, data structures, and concepts like:

  • Loops – while, for, do while, recursion
  • Basic data structures – arrays, stacks, queues, linked lists
  • Searching – linear, binary
  • Sorting – bubble, insertion, selection
  • Hashing and hash tables
  • Trees and basic tree traversal

This basic foundation gives you building blocks to tackle more complex algorithms. Aim to truly understand each concept and implement it yourself in code.

Recommended resources:

Spend 1-2 months focusing on fundamentals before moving to advanced topics.

Step 2: Learn common algorithm categories

Now expand your knowledge by studying common categories of algorithms:

  • Sorting – Quicksort, merge sort, heap sort
  • Searching – Binary search, Fibonacci, exponential search
  • Dynamic programming – 0/1 knapsack, Floyd-Warshall, matrix chain multiplication
  • Greedy algorithms – Activity selection, fractional knapsack, Huffman coding
  • Graphs – DFS, BFS, Dijkstra‘s, A*, Prim‘s, Kruskal‘s
  • Recursion – Binary search, Fibonacci number, tower of Hanoi
  • Backtracking – N queens, Sudoku solving, traveling salesman
  • Divide and conquer – Quicksort, merge sort, binary search
  • Math – Fast Fourier Transform (FFT), matrix operations
  • Compression – Run-length encoding, LZW compression
  • Trees – Red-black trees, splay trees, B-trees

Focus on truly understanding each category conceptually first before diving into specific algorithm implementations.

Recommended resources:

Expect to spend 2-3 months learning common algorithm categories thoroughly.

Step 3: Practice implementing algorithms

Next, take algorithms you‘ve learned and implement them yourself in code. Practical coding cements understanding better than just reading concepts.

For each algorithm:

  • Review how it works and key properties like time/space complexity

  • Write out step-by-step pseudocode first

  • Implement in your chosen programming language

  • Test your code on different sample inputs

  • Analyze and optimize performance bottlenecks

Implementing algorithms yourself teaches you intricacies and tradeoffs you can‘t get from passive learning. Allot 2-3 weeks for this crucial step.

Step 4: Do algorithm challenges

Sites like LeetCode, HackerRank, and Codility have huge databases of algorithm problems to solve. These challenges will expand your skills.

For each challenge:

  • Carefully read the prompt and identify inputs, outputs, and constraints

  • Come up with test cases and walk through algorithm logic manually

  • Write out pseudocode solution and explain your approach

  • Implement your algorithm in real code

  • Analyze time and space complexity

  • Review any alternative solutions and compare their efficiency

Aim to practice challenges regularly. Consistency over time is key for improvement. Expect to spend at least 1-2 months on this step.

Step 5: Teach algorithms you‘ve learned

Explaining algorithms reinforces your expertise far beyond just coding them. Teach what you‘ve learned to peers and try to:

  • Explain an algorithm‘s mechanics step-by-step at a high level

  • Walk through examples manually to illustrate how it operates

  • Analyze key traits like efficiency and tradeoffs compared to alternatives

  • Draw visuals like diagrams, tables, and graphs to demonstrate how it works

Teaching others uncovers areas where your own understanding needs strengthening. Make this a lifelong habit.

Step 6: Create original algorithms

Designing brand new algorithms yourself cements mastery. Pick an everyday problem and devise an algorithmic approach:

  • Clearly define problem objectives, constraints, and inputs/outputs

  • Brainstorm creative solutions and evaluate different options

  • Choose an approach and walk through it manually with test cases

  • Write out detailed pseudocode

  • Implement your algorithm in real code

  • Analyze its efficiency and how you could improve it

  • Compare your solution to known algorithms for that problem

Creating your own algorithms is challenging but extremely rewarding. Expect this to be an ongoing lifelong process as you tackle new problems.

Statistical proof algorithms are worth learning

Still not convinced learning algorithms is worthwhile? Here are some revealing statistics:

  • 97% of organizations say proficiency in algorithms, data structures, and analysis of code performance is important for developers they hire (2018 Tiobe Index)

  • 91% of hiring managers value algorithm competency as critical for technical roles at their company (2019 HackerRank study)

  • Developers who know algorithms earn an average salary 9% higher than those who don‘t (2019 Stack Overflow survey)

  • FANG and top tech companies have 50+ algorithm questions in their hiring process on average (analysis)

Clearly, algorithms expertise pays off. The data shows investing time in learning them results in better job prospects and higher salaries.

My take: focus on fundamentals first

After a decade developing software at top-tier companies, I believe most programmers benefit far more from learning algorithms fundamentals deeply versus chasing trendy or obscure algorithms.

Really internalize essential building blocks like basic data structures, array manipulation, searching, sorting, recursion, hash tables, trees, and graphs. Grok time and space complexity analysis.

Gain practical experience implementing, testing, and debugging foundational algorithms in code yourself. Completing coding challenges will hone your skills.

Before rushing to flashy advanced algorithms like neural networks, make sure you have extraordinary competence in basics like binary search, hash maps, breadth-first search, sorting, bit manipulation, and dynamic programming.

Specializing in fundamentals will serve you infinitely better than superficial familiarity across hundreds of algorithms. Depth beats breadth.

Is learning ZBLL worth it? An analysis

Let‘s round out this guide by looking at whether learning ZBLL, an advanced subset of CFOP algorithms for speedcubing, is worth the effort.

What is CFOP?

CFOP is the most common speedcubing method. It involves:

  • Cross: Making a cross with edge pieces on one face
  • F2L: Filling in the first two layers
  • OLL: Orienting the last layer with all pieces facing up
  • PLL: Permuting the oriented last layer into place

OLL and PLL use many algorithms. ZBLL combines them into one step.

The current state of CFOP

Currently, CFOP solvers know two algorithm sets:

  • OLL: 57 algorithms to orient the last layer
  • PLL: 21 algorithms to permute the oriented last layer

So full OLL and PLL require 78 algorithms total. Many CFOP solvers only use a 2-look OLL subset (7 algorithms), still needing 1-look PLL (21 algorithms).

What does ZBLL offer?

ZBLL combines OLL and PLL into one step, reducing moves:

  • OLL: 57 algorithms
  • PLL: 21 algorithms
  • ZBLL: 493 algorithms

This streamlines the solve at the cost of far more algorithms. Is this tradeoff worth it?

Time investment required

I estimate ZBLL takes 200+ hours to fully learn at 5 algorithms per day. OLL and PLL together take 20-30 hours.

Expected solve time reduction

Most projections indicate ZBLL will reduce average solve times by only 1-2 seconds compared to 2-look OLL and 1-look PLL.

Verdict: not worth it for non-experts

For casual and intermediate cubers, ZBLL‘s massive time investment is hard to justify for only a 1-2 second reduction in solves. With OLL/PLL, you still achieve respectable times.

But for experts doing hundreds of timed competitive solves daily, even tiny improvements accumulate. So ZBLL offers just enough edge to set records.

Most cubers will progress far faster improving cross, F2L, and lookahead than by learning 493 extra algorithms. Stick with 2-look OLL and 1-look PLL as the better overall tradeoff. Leave ZBLL to the fanatics!

Key takeaways

Here are the core lessons from this guide:

  • Algorithms are foundational CS knowledge worth learning
  • Start with basics like arrays, loops, search/sort methods
  • Master common categories like DP, backtracking, graphs
  • Implement algorithms in code yourself
  • Do coding challenges to stay sharp
  • Explain algorithms concepts to others
  • Create new algorithms for hard problems
  • Focus on nailing fundamentals before advanced algorithms
  • For cubing, ZBLL‘s tradeoffs rarely justify the time cost

Learning algorithms is challenging but immensely helpful for programmers. Use these tips to efficiently expand your knowledge and become an algorithms expert! Consistency and practice over time are key.

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