Demystifying Dynamic Programming with Intelligent Brute Force

🚀 𝐇𝐨𝐰 𝐜𝐚𝐧 𝐲𝐨𝐮 𝐢𝐦𝐩𝐥𝐞𝐦𝐞𝐧𝐭 𝐚𝐧 𝐞𝐱𝐩𝐨𝐧𝐞𝐧𝐭𝐢𝐚𝐥 𝐟𝐮𝐧𝐜𝐭𝐢𝐨𝐧 𝐢𝐧 𝐂 ( 𝐞^𝐦 ) 𝐰𝐢𝐭𝐡𝐨𝐮𝐭 𝐮𝐬𝐢𝐧𝐠 𝐦𝐚𝐭𝐡.𝐡? This question came up while working on a low-level C implementation—and it revealed a surprising compiler behavior that many developers and students miss. 👀 I initially wrote my own function and named it exp(). Even without including math.h, my code was not calling my function. 😐 After renaming it to my_exp(), everything worked perfectly. ✔️ 𝑺𝒐 𝒘𝒉𝒂𝒕 𝒘𝒂𝒔 𝒉𝒂𝒑𝒑𝒆𝒏𝒊𝒏𝒈? 🔍 𝑻𝙝𝒆 𝒓𝙚𝒂𝙡 𝙧𝒆𝙖𝒔𝙤𝒏 Modern compilers (GCC/Clang) often treat exp() as a built-in function. That means the compiler may silently replace calls to exp(double) with its own optimized version—even if you define your own function and don’t include math.h. 🤯 🛠️ 𝙏𝒉𝙚 𝙨𝒐𝙡𝒖𝙩𝒊𝙤𝒏 ✅ Avoid naming collisions (my_exp() instead of exp()) ✅ Use a Taylor series expansion for ( e^x ) ✅ Control accuracy by limiting terms or error tolerance 📌 𝑾𝒉𝒚 𝒕𝒉𝒊𝒔 𝒎𝒂𝒕𝒕𝒆𝒓𝒔 This is more than a coding trick—it’s a powerful real-world lesson in: • Compiler optimizations • Numerical approximation • Low-level C behavior • Mathematics behind standard libraries 📚 Perfect discussion material for students, educators, and systems programmers alike. #CProgramming #NumericalMethods #MathematicsInCS #SystemsProgramming #CompilerBehavior #MathWithoutLibraries #STEMEducation #LearningByDoing

That handshake between brute force and optimization is Dynamic Programming. Most people try to learn DP directly. That’s why it feels hard. First, brute force teaches you the structure of the problem. Then optimization shows you the repeated work. DP simply remembers and reuses those results. No new magic. No shortcuts. Just fewer mistakes repeated. [Brute Force, Optimization, Dynamic Programming, Algorithms, Problem Solving] #ComputerScience #Algorithms #DynamicProgramming #ProblemSolving #SoftwareEngineering

I've found this analogy super helpful when teaching or learning: DP is fundamentally about recognizing patterns and caching results. It's not some mystical algorithmic magic—it's structured problem-solving.

🧠 Discovering the Magic of Bit Manipulation Today I explored one of the most elegant and powerful concepts in computer science — bit manipulation. What started as curiosity turned into a deep appreciation for how simple binary tricks can solve problems in an incredibly efficient way. A few problems that really changed how I think about low-level optimization: 🔹 LeetCode 191 – Number of 1 Bits Learned the classic n & (n - 1) trick to remove the lowest set bit and count ones efficiently. 🔹 LeetCode 231 – Power of Two A beautiful one-liner using bit logic to check if a number has exactly one set bit. 🔹 LeetCode 338 – Counting Bits Using dynamic programming + bit manipulation to build bit counts in linear time. What surprised me most is how these small binary tricks: Improve time complexity Reduce memory usage Reveal how computers really represent numbers Bit manipulation taught me that elegant solutions often come from understanding problems at the binary level. One of my biggest takeaways: what looks like “magic” at first becomes logical once you understand how binary numbers and two’s complement really work. These patterns are not just academic — they show up frequently in interviews and help build intuition for writing optimal code. #BitManipulation #LeetCode #DSA #ProblemSolving #ComputerScience

You asked: "Which paradigm should I learn first?" Here is the strict hierarchy. Do not jump ahead. Recursion (The Engine): You must be comfortable calling a function inside itself. This is the foundation. Backtracking (The Navigation): This is organized recursion. It is "Brute Force with a Brain." It explores all possibilities (like a maze) but knows how to turn back when it hits a dead end. Dynamic Programming (The Memory): This is just Backtracking + Memoization (Caching). If you can't backtrack, you can't DP. Greedy (The Shortcut): This is an optimization where you prove you don't need to backtrack. It’s the hardest to prove but easiest to code.

That’s what engineering programs should feel like. Not just theory, but learning new tools, new languages, and new ways to think. From Python to C#, from Scratch to visual programming, this is what hands-on engineering looks like. Real skills. Real projects. Real-world problem solving from day one. #eVTOLStudentTeam #futuremadeinAustralia #ManufacturingExcellenceForum #MEFSC #MEF

*** Problem of the Day: Minimum Deletions to Make String Balanced One of the classic DP problems I recently solved. The goal Given a string containing only 'a' and 'b', remove the minimum number of characters so that all 'a's appear before all 'b's. 🔹 Approach I used (DP + Greedy logic): 1. Traverse the string recursively. 2. Keep track of 'b's seen so far (cntb). 3. For each character: 1. If 'a' appears after some 'b', delete it. 2. If 'b' appears before any 'b', either delete it or count it for future comparison. 4. Use memoization to avoid recomputation. Check out my solution here!👇 https://lnkd.in/gcVFdHei The solution essentially decides greedily whether to delete 'a' or 'b' at each step to minimize total deletions. A classic example where DP meets greedy thinking. #Coding #Programming #DataStructures #Algorithms #DynamicProgramming #DP #GreedyAlgorithms #ProblemSolving #LeetCode #CompetitiveProgramming #Tech #SoftwareEngineering #CodeDaily #LearningToCode #CodingChallenge #CodeOptimization #AlgorithmDesign #LinkedInLearning

Sweep Line Technique – Part 2! Optimize Event Processing & Interval Queries Like a Pro I’ve published Part-2 of my Sweep Line Technique series where I focus more on practical problem ideas. In this part, I covered : - Union of Intervals – how overlapping ranges merge - Intersection of Intervals – using max(Li) & min(Ri) intuition - Event Priority Logic (Insert / Query / Remove) - Inclusive vs Exclusive interval handling - Efficient C++ implementations with examples Part-1 explained the foundations and event processing basics, and Part-2 dives into thinking patterns and real problem approaches. Read the full blog here : https://lnkd.in/deM8hJbH If you’re preparing for coding interviews, DSA rounds, or competitive programming, mastering Sweep Line can transform brute-force solutions into efficient O(N log N) strategies Would love to hear your feedback and suggestions! #DSA #Algorithms #CompetitiveProgramming #SweepLine #CPP #CodingJourney #TechBlog #LearningInPublic #Programming

DP on string 🚀 Intuition If the current characters of both strings match, include them in the LCS and move forward. If they don’t match, try both possibilities by skipping one character at a time and take the maximum result. Approach Used Recursion + Memoization (Top-Down DP) Defined state solve(i, j) as the LCS length starting from index i in text1 and j in text2 If characters match → 1 + solve(i+1, j+1) Else → max(solve(i+1, j), solve(i, j+1)) Stored results in a DP table to avoid recomputation Time Complexity: O(n × m) Space Complexity: O(n × m) 📌 Key takeaway: Dynamic Programming works best when problems have overlapping subproblems and optimal substructure. #Day4 #DynamicProgramming #LCS #LeetCode #DSA #Coding #Cplusplus #LearningInPublic

I create a fair amount of code/software in my spare time. The thing is, to publicly release this code (or some of it) I am required to submit my code for review, which has typically meant creating a pdf with all source files concatenated into one. And because I don’t like doing this, I created a utility that does this for me: Paper Cut. Paper Cut is a highly configurable tool that takes multiple source files (technically just any text-based files) and concatenates them and then generates a pdf (without external dependencies such as latex). It includes syntax highlighting for a bunch of popular programming languages and the output can be tweaked using a yaml configuration file (e.g., to add a title page with a description, author, etc.). I created it using Claude Code over the course of a weekend and it is written in #Rust (why not?). Why is it called Paper Cut? Because doing this task without the utility is about as much fun as a paper cut. I understand this might be a niche tool. The documentation in the repo was AI generated and it tries really hard to point out “real” world use cases. I consider many of them sort of laughable. One use case I could see for students is to bundle up their source code for a homework submission. Having said that, this solves a real world problem for me and on the off chance that this is useful to someone else, I decided to open source it. The repo can be found at: https://lnkd.in/gTpRvZYm