Mastering Time Complexity: From O(n) to O(1)

I've been studying Grokking Algorithms, and in the chapter about Big O notation, I had some trouble understanding the different notations. By coincidence, Augusto Galego (a YouTuber I really like), released a video explaining Big O, and it helped me a lot. Here’s what I learned: Time complexity refers to how long an algorithm takes to run, and space complexity refers to how much memory it uses. O(1) means constant complexity. The algorithm performs a fixed number of operations, no matter the size of the input. For example, accessing an element in an array by its index is O(1) because you know exactly where the element is, so the operation happens once. O(n) means the running time grows linearly with the input size n. If you have to go through an entire list to find an item, the number of operations depends on how many elements are in the list. O(log n) is a classic case for algorithms like binary search. Even as the input grows, the running time increases much more slowly proportional to the logarithm of the input size because the problem is divided in half at each step. O(n log n) is typical of efficient sorting algorithms like Merge Sort, Heap Sort, and Quick Sort. They divide the problem into smaller parts (log n times) and process all elements (n) in each division. O(n²) appears in algorithms with two nested loops, such as Bubble Sort. Each element is compared with every other element, so the number of operations grows quadratically with the input size. Because of that, these algorithms are recommended only for small lists. I’ve just finished the first chapter of the book, and it’s been a great start to understanding how algorithms really work. #BigO #AlgorithmComplexity #Programming #SoftwareDevelopment #Tech #ComputerScience

Time Complexity vs Space Complexity When writing efficient code, understanding time complexity and space complexity is essential. Time Complexity measures how the execution time of an algorithm grows as the size of the input increases. It helps us understand how fast or slow a program runs. Example: Linear search → O(n) Binary search → O(log n) Space Complexity measures how much memory an algorithm uses as the input size increases. It includes variables, data structures, and recursion stacks. Example: Storing an array → O(n) Constant variables → O(1) In short: Time complexity = How long it takes to run Space complexity = How much memory it consumes Efficient algorithms balance both — fast execution with minimal memory use. #Programming #DataStructures #Algorithms #Coding #SoftwareEngineering #Developer #BigO #TimeComplexity #SpaceComplexity #TechLearning

🌀 “Recursion: When Code Learns to Think Like Humans” Ever had a problem so big that you didn’t know where to start? So… you broke it down — one step at a time — until it made sense. That’s recursion in computer science. It’s not just a concept — it’s how your code learns to think smarter, not harder. Every time a function calls itself, it’s like saying — “Let me handle this small piece first, I’ll come back for the rest.” 💭 And just like that, massive problems dissolve into simple steps. 💡 Why Recursion Feels Magical: It teaches clarity in complexity. It powers algorithms like Tree Traversals, DFS, and Factorial Calculations. It mirrors how humans solve problems — step by step, layer by layer. 🔥 Life + Code Tip: Don’t try to solve everything at once. Break it down. Solve a smaller part. Then another. That’s recursion — in code and in life. 💫 #Recursion #Programming #DSA #SoftwareDevelopment #CodeJourney #TechEducation #LearningInPublic #Developers #MotivationForDevelopers

Mastering Problem-Solving Patterns in DSA! 💡 When it comes to Data Structures & Algorithms, recognizing patterns can turn a complex problem into an easy one. Here’s a visual that beautifully connects real-life analogies with algorithmic techniques — making it easier to remember when and why to use each one. Whether it’s: 🔹 Sliding Window → “Peeking through a moving window” 🔹 Two Pointers → “Two fingers walking toward each other” 🔹 DFS/BFS → “Go deep vs. Go wide” 🔹 or Dynamic Programming → “Why re-solve what’s already solved?” Each pattern teaches a way of thinking smarter, not harder. 🧠 If you’re preparing for coding interviews or competitive programming, this cheat sheet is a gem! 💎 ✨ Keep learning. Keep solving. Keep growing. #DSA #Coding #ProblemSolving #DataStructures #Algorithms #Programming #TechLearning #InterviewPreparation #LeetCode #CompetitiveProgramming #Developers #SoftwareEngineering #100DaysOfCode

Solving X problems on LeetCode doesn’t automatically make you a great problem solver. 1️⃣ Quality > Quantity It’s not about how many you solved. It’s about how deeply you understood each one. 2️⃣ Pattern Recognition Wins Once you start seeing the hidden link between problems, you stop memorising and start visualising. 3️⃣ Everyone’s Curve Is Different For some, 100 problems = strong foundation. For others, even 500 feels shaky. And that’s perfectly fine problem-solving is personal, not mechanical. 4️⃣ Random Solving = Random Growth Jumping from topic to topic might feel productive, But pattern-based learning builds real intuition. 5️⃣ The Goal Isn’t Solving More, It’s Thinking Better The best coders don’t just solve problems. They break them, analyse them, and rebuild them better. 💡 Stop counting problems. Start connecting patterns. I share enlightening and helpful content here. https://lnkd.in/d9xfHX6h

🧩 Understanding Bubble Sort — The Classic Sorting Algorithm Made Simple! Bubble Sort is one of the most fundamental sorting algorithms in computer science — perfect for understanding comparison-based logic and how iterative processes work. It repeatedly compares adjacent elements and swaps them if they’re in the wrong order. With each pass, the largest element “bubbles up” to its correct position — just like air bubbles rising to the top! While it’s not the most efficient algorithm (O(n²) time complexity), Bubble Sort remains a great learning tool for beginners to grasp the core concepts of loops, conditionals, and data manipulation. At GSW Infotech, we believe in building a strong foundation in both core logic and modern technologies. Every great developer starts by mastering the basics — and that’s where true innovation begins. #Programming #Coding #Algorithms #BubbleSort #ComputerScience #DataStructures #SoftwareDevelopment #TechEducation #LearnToCode #WebDevelopment #GSWInfotech #DeveloperCommunity #TechLearning #Innovation #CodeLogic #CodingBasics #SortingAlgorithm #ProgrammersLife

🔵 Understanding Circular Linked Lists This image beautifully illustrates the concept of a Circular Linked List, a unique variation of a linked list where the last node points back to the first node, forming a continuous loop. In the diagram: Each block (A, B, C, D) represents a node, containing two parts — Data and a Next pointer. The Head node (A) is the starting point of the list. Unlike a singly linked list that ends with a null pointer, the Next pointer of the last node (D) connects back to the head node, creating a circular connection. This structure is particularly useful in applications like: Round-robin scheduling, where tasks are managed cyclically. Buffer management, where continuous data flow is required. Implementation of queues, that reuse memory efficiently. Circular linked lists are a great example of how data structures optimize memory use and enhance traversal efficiency by eliminating null ends. 💡 Takeaway: Understanding and mastering linked list variations like circular linked lists helps build a strong foundation for solving complex programming and algorithmic challenges. #DataStructures #CircularLinkedList #LinkedList #ProgrammingConcepts #Coding #ComputerScience #SoftwareEngineering #LearnToCode #TechEducation #DSA #Developers #ProblemSolving

🔥 Day 21 of My DSA Journey — LeetCode 62: Unique Paths Today’s problem was a classic combinatorics and dynamic programming question — finding how many unique paths exist for a robot moving only right or down in an m x n grid. 🤖➡️⬇️ 🧮 Brute Force Approach Explore every path recursively by moving right and down from each cell until reaching the destination. Base case: when the robot reaches (m-1, n-1). ❌ Time complexity: O(2^(m+n)) — exponential and inefficient for larger grids. ⚙️ Better Approach — Combinatorics Every path consists of a total of (m−1) downward moves and (n−1) rightward moves. So, total moves = (m + n − 2). We just need to choose positions for one of them (say, downs). 🧠 Formula: Unique Paths=(m+n−2/m−1)=(m+n−2)!/(m−1)!(n−1)! We compute this efficiently without overflow using iterative multiplication and division. ⏱️ Complexity Time: O(min(m, n)) Space: O(1) ✨ Key Takeaway This problem beautifully connects math (combinations) with programming logic. It’s a great reminder that sometimes the best optimization is understanding the mathematical structure behind a problem. 💡 #DSAJourney #Day21 #LeetCode62 #UniquePaths #Combinatorics #DynamicProgramming #MathInCode #CPlusPlus #CodingChallenge #ProblemSolving #DSA #InterviewPrep #100DaysOfCode #Algorithms #GridPath #TechLearning #BruteForceToOptimal #OptimizedApproach #CodingCommunity #ProgrammerLife #DSAMastery #LearnDSA #CodeEveryday

𝐏𝐫𝐨𝐠𝐫𝐚𝐦𝐦𝐢𝐧𝐠 𝐋𝐚𝐧𝐠𝐮𝐚𝐠𝐞𝐬 𝐋𝐢𝐞, 𝐚𝐧𝐝 𝐈𝐭’𝐬 𝐓𝐢𝐦𝐞 𝐖𝐞 𝐀𝐝𝐦𝐢𝐭 𝐈𝐭. Every time you write 𝒊𝒏𝒕 𝒙 = 42;, you’re telling yourself a beautiful lie. You think you’re creating an 𝐢𝐧𝐭𝐞𝐠𝐞𝐫. But you’re 𝐧𝐨𝐭. You’re labeling a pattern of 𝐛𝐢𝐭𝐬, a sequence of 0s and 1s that could just as easily be a 𝐟𝐥𝐨𝐚𝐭, a 𝐜𝐡𝐚𝐫𝐚𝐜𝐭𝐞𝐫, or even a 𝐛𝐨𝐨𝐥𝐞𝐚𝐧. Your CPU doesn’t know what “𝐝𝐚𝐭𝐚 𝐭𝐲𝐩𝐞𝐬” are. It only moves 𝐞𝐥𝐞𝐜𝐭𝐫𝐢𝐜𝐢𝐭𝐲. 𝐎𝐧 and 𝐨𝐟𝐟. Voltage high, voltage low. In my latest blog, I broke this illusion by running a simple C 𝐞𝐱𝐩𝐞𝐫𝐢𝐦𝐞𝐧𝐭 using one universal container: → 𝒖𝒊𝒏𝒕32_𝒕 𝒈𝒆𝒏𝒆𝒓𝒊𝒄𝑪𝒐𝒏𝒕𝒂𝒊𝒏𝒆𝒓; With that 𝐬𝐢𝐧𝐠𝐥𝐞 𝐯𝐚𝐫𝐢𝐚𝐛𝐥𝐞, I printed an integer, a float, a char, a string, and a boolean, without changing memory. Just 𝐫𝐞𝐢𝐧𝐭𝐞𝐫𝐩𝐫𝐞𝐭𝐚𝐭𝐢𝐨𝐧. What happened was mind-bending. The 𝐬𝐚𝐦𝐞 32 bits, when viewed through different lenses, produced entirely 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭 meanings. It wasn’t conversion. It was 𝐩𝐞𝐫𝐬𝐩𝐞𝐜𝐭𝐢𝐯𝐞. That’s when it hit me: Types aren’t real. They’re 𝐜𝐨𝐧𝐯𝐞𝐧𝐭𝐢𝐨𝐧𝐬. Stories we tell ourselves to make sense of binary chaos. The machine doesn’t care. It just follows 𝐢𝐧𝐬𝐭𝐫𝐮𝐜𝐭𝐢𝐨𝐧𝐬. We’re the ones adding meaning, creating order out of electricity. Here’s the takeaway: Understanding this illusion changes how you think about code. → 𝐌𝐚𝐜𝐡𝐢𝐧𝐞 𝐥𝐞𝐚𝐫𝐧𝐢𝐧𝐠? Tensors are just bits with metadata. → 𝐍𝐞𝐭𝐰𝐨𝐫𝐤𝐢𝐧𝐠? Packets are bytes until a protocol gives them meaning. → 𝐒𝐲𝐬𝐭𝐞𝐦𝐬 𝐩𝐫𝐨𝐠𝐫𝐚𝐦𝐦𝐢𝐧𝐠? One wrong interpretation of bits, and you’ve got a vulnerability. When you see through the 𝐚𝐛𝐬𝐭𝐫𝐚𝐜𝐭𝐢𝐨𝐧, you stop treating programming as syntax, and start seeing it as 𝐭𝐫𝐚𝐧𝐬𝐥𝐚𝐭𝐢𝐨𝐧. Between meaning and binary truth. And once you 𝐬𝐞𝐞 it, you can’t 𝐮𝐧𝐬𝐞𝐞 it. 👉 𝘙𝘦𝘢𝘥 𝘵𝘩𝘦 𝘧𝘶𝘭𝘭 𝘣𝘳𝘦𝘢𝘬𝘥𝘰𝘸𝘯 𝘩𝘦𝘳𝘦: https://lnkd.in/g-GbhVU3 #Programming #ComputerScience #BackendDevelopment #SystemsProgramming #Binary #CProgramming #Learning