Mastering Dynamic Programming with Brute Force and Optimization

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.

ATLAS v0.1 — Released I’ve released ATLAS v0.1, a correctness-first programming language for modeling explicit state machines. ATLAS enforces correctness before execution through a strict AST-based compiler: exactly one explicit initial state explicit state declarations explicit transitions explicit termination full reachability validation If an ATLAS program runs, its structure has already been proven valid. ATLAS is not a general-purpose language. It is a deliberately constrained language for modeling systems with explicit state, transition, and termination. The architecture and semantics of v0.1 are locked. Only bug fixes are allowed. Any new capability will target v0.2 or later. Source (Apache 2.0): 👉 https://lnkd.in/g_eprVF2 ATLAS models reality through explicit state, transition, and termination — nothing more, nothing less.

15 LeetCode patterns Instead of memorizing hundreds of problems, focus on patterns. Once a pattern clicks, the solution often reveals itself naturally. These patterns reshape how you think, not just what you solve. Some of the most high-impact ones: • Prefix Sum. • Sliding Window. • Two Pointers. • Fast & Slow Pointers. • Monotonic Stack. • Modified Binary Search. • DFS & BFS. • Backtracking. • Dynamic Programming. #LeetCode #DataStructures #Algorithms #DSA

DSA Practice – Day 11 | Difficulty-Balanced Set Solved on LeetCode and GFG, focusing on backtracking, recursion, combinatorics, and dynamic programming: Medium • LC 40 – Combination Sum II — Backtracking, Duplicate Handling • LC 46 – Permutations — Backtracking • LC 78 – Subsets — Backtracking, Bit Manipulation • LC 377 – Combination Sum IV — Dynamic Programming GFG • Rat Maze With Multiple Jumps — Backtracking, Matrix Traversal, Recursion Core topics covered: Backtracking, Recursion, Dynamic Programming, Combinatorics, Matrix Traversal #DSA #LeetCode #GeeksforGeeks #Algorithms #DataStructures #ProblemSolving

Solved the “Symmetric Tree” problem using a recursive mirror-check algorithm in C++. Algorithm (Mirror Recursion Approach): Define a helper function check(left, right) to compare two nodes. Base cases: • If both nodes are NULL → return true (symmetric at this level). • If one is NULL and the other is not → return false. Check current nodes: • Values must be equal. • Recursively compare left->left with right->right. • Recursively compare left->right with right->left. Start by calling check(root->left, root->right). Time Complexity: O(n) — each node is visited once. Space Complexity: O(h) — recursion stack where h is tree height. #DataStructures #Algorithms #BinaryTree #Recursion #CPP #Programming #CodingInterview #ProblemSolving #LeetCode #SoftwareEngineering

Day -9 DSA Progress Update Focused on strengthening matrix traversal, binary search, and dynamic programming concepts through LeetCode problems. Problems Solved: 378. Kth Smallest Element in a Sorted Matrix (Medium) Practiced binary search on value range and heap-based thinking in sorted matrices. 74. Search a 2D Matrix (Medium) Reinforced binary search by treating a 2D matrix as a flattened sorted array. 54. Spiral Matrix (Medium) Improved control over matrix traversal and boundary management. 1312. Minimum Insertion Steps to Make a String Palindrome (Hard) Strengthened understanding of dynamic programming on strings and optimal substructure. Key Takeaways: Better handling of matrix-based problems Improved confidence with binary search variations Deeper understanding of DP on strings #DSA #LeetCode #ProblemSolving #Algorithms #Consistency

Day 50 – List Partitioning and Deep Copy with Random Pointers 🔗🎯🧬 Reaching the halfway milestone with two intricate linked list challenges each demanding precise pointer manipulation and structural ingenuity to transform lists under complex constraints. 🎯 Partition List Segregated a linked list into two partitions nodes less than a target value x followed by nodes greater than or equal to x while preserving relative order. Used two dummy headed lists to collect nodes from each partition during traversal, then merged them in O(n) time with O(1) space. A clean exercise in conditional node redirection without restructuring values. 🧬 Copy List with Random Pointer Constructed a deep copy of a linked list where each node contains an additional random pointer to any node (or null). Created cloned nodes interleaved with originals Assigned random pointers using next relationships Separated the lists to extract the deep copy. Achieved O(n) time with O(1) extra space (excluding output) a masterclass in pointer manipulation and structural mirroring. #LeetCode #Coding #Algorithms #DataStructures #LinkedList #TwoPointers #DeepCopy #RandomPointer #ProblemSolving #SoftwareEngineering #Programming #100DaysOfCode

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

Day 68 of #100DaysOfDSA | Recursion Today I solved the Subset Sum Problem using a recursive approach in C++. The problem follows a clear decision-based pattern: at each step, we either include the current element or exclude it while tracking the remaining sum. Key learnings from today: • Applying the subsets/backtracking pattern with constraints • Importance of well-defined base cases • Understanding why naive recursion has exponential complexity This problem serves as a natural transition point from recursion to dynamic programming concepts like memoization and tabulation. 📌 Code and explanation available on GitHub:https://lnkd.in/gViBVfmk #100DaysOfDSA #SubsetSum #Recursion #Backtracking #DataStructures #Algorithms #Cplusplus #ProblemSolving #SoftwareEngineering #CSFundamentals #LearningInPublic #DeveloperJourney #Consistency

Day 69 of #100DaysOfDSA | Recursion Today I worked on the Target Sum Combination problem using recursion and backtracking in C++. The key idea was to explore all valid combinations by choosing to include or exclude elements while adjusting the remaining target value. Key learnings from today: • How index control enables element reuse • Effective use of pruning when the target becomes negative • Writing clean backtracking code with clear base cases This pattern appears frequently in problems related to combinations, coin change, and dynamic programming. 📌 Code and explanation available on GitHub: https://lnkd.in/gRtRSXSt #100DaysOfDSA #Backtracking #Recursion #TargetSum #CombinationSum #DataStructures #Algorithms #Cplusplus #ProblemSolving #SoftwareEngineering #LearningInPublic #DeveloperJourney #Consistency #CSFundamentals