Dynamic Programming Decoding Ways Problem

🚀 DSA Deep Dive – Day 30 Solved Longest Increasing Subsequence today. And I realized… Dynamic Programming is not about continuous subarrays. It’s about controlled choices over time. 🤯 The problem sounds simple: Given an array, find the length of the longest strictly increasing subsequence. Not subarray. Subsequence. That one word changes everything. 👀 You’re allowed to skip elements. But you must maintain order. Here’s what I learned 👇 • Define dp[i] = length of LIS ending at index i • Every element can start a subsequence (minimum length = 1) • For every i, check all j < i • If nums[j] < nums[i] → extend subsequence • Take the maximum possible extension This is classic DP state building. At every index, you ask: 👉 Can I extend a previous increasing chain? 👉 Or do I start fresh from here? Brute force recursion: Exponential 💀 Optimized DP (nested loops): O(n²) ⚡ Even better approach exists: O(n log n) with binary search 🚀 But the mindset is what matters. The powerful shift? Instead of asking “What is the longest sequence overall?” Ask “What is the longest sequence ending HERE?” That’s dynamic programming thinking. Local decisions → Global answer. Lesson: DP is not about memorizing patterns. It’s about defining the right state. Once the state is clear, the transition becomes obvious. 30 days in. Graphs ✅ 1-D DP almost done 🚀 Consistency compounds. Follow for more DSA breakdowns 🔥 #LeetCode #DSA #DynamicProgramming #InterviewPrep #CodingJourney #ProblemSolving #100DaysOfCode #SoftwareEngineering #TechGrowth

🚀 DSA Deep Dive – Day 32 Solved Longest Common Subsequence today. And I realized… Dynamic Programming is not about matching characters. It’s about managing choices between two paths. 🤯 The problem looks simple: Given two strings, find the length of their longest common subsequence. Not substring. Subsequence. That means you can skip characters — but order must remain the same. 👀 Here’s what I learned 👇 • Define dp[i][j] = LCS length till text1[0..i-1] and text2[0..j-1] • If characters match → extend previous answer • If they don’t match → take max of two possibilities • Either skip from first string • Or skip from second string This is pure decision-based DP. At every cell, you decide: 👉 If text1[i-1] == text2[j-1] → 1 + dp[i-1][j-1] 👉 Else → max(dp[i-1][j], dp[i][j-1]) Every state depends on smaller prefixes. Brute force recursion: Exponential 💀 Optimized DP: O(n × m) time ⚡ Space optimized possible 🚀 The powerful shift? Instead of asking “What is the longest common sequence overall?” Ask “What is the answer for these two prefixes?” Small answers build the big one. That’s dynamic programming. Lesson: When two strings are involved, DP is usually hiding behind prefixes. Define the right state. Trust the transitions. Build step by step. 2-D DP getting stronger 💪 Consistency continues. Follow for more DSA breakdowns 🚀 #LeetCode #DSA #DynamicProgramming #InterviewPrep #CodingJourney #ProblemSolving #100DaysOfCode #SoftwareEngineering #TechGrowth

Efficient Range Queries Using Sqrt Decomposition : Ever faced problems where you need to answer multiple range queries like sum, min, or max efficiently?  That’s where Sqrt Decomposition comes into play! Core Idea :- Divide the array into blocks of size √N and precompute values (like sum/min/max) for each block. Why it’s powerful? Query Time → O(√N) Update Time → O(1) Perfect for online queries where answers are needed instantly Best Use Cases :- Range Sum Queries Range Minimum/Maximum Frequency / Count problems How it works :- Break array into √N blocks Precompute block values For each query → combine :- Left partial block Full blocks  Right partial block Bonus : Updates are super easy! Just adjust the affected block — no need to recompute everything. Comparison :- Brute Force → O(N) Sqrt Decomposition → O(√N) Segment Tree → O(logN) I recently wrote a detailed breakdown with examples and code to make this concept beginner-friendly. Blog Link : https://lnkd.in/ghECuvRB If you're learning DSA or competitive programming, this is a must-know technique! #DSA #CompetitiveProgramming #Algorithms #Coding #DataStructures #SqrtDecomposition #LearningInPublic

DSA Starts Making Sense When You Learn It Pattern-Wise Many developers approach DSA by jumping between random problems. The result? Progress often feels slow and inconsistent. Effective DSA preparation comes from recognizing that most problems are built around repeating patterns. Once you understand the pattern behind a problem, solving similar questions becomes significantly easier. A Practical Preparation Strategy- • Identify core DSA patterns • Focus on mastering one pattern at a time • Solve multiple problems that follow the same logic • Move to the next pattern only after gaining confidence Fundamental DSA Patterns Every Learner Should Know 1) Sliding Window 2) Two Pointers 3) Hashing & Frequency Map 4) Prefix Sum 5) Binary Search (on array & answer) 6) Recursion & Backtracking 7) Linked List Patterns 8) Stack & Monotonic Stack 9) Heap / Priority Queue 10) Greedy 11) Dynamic Programming 12) Graph Traversal (BFS / DFS) 13) Tree Traversal 14) Bit Manipulation When you prepare DSA pattern-wise: ✔ Problem recognition becomes faster. ✔ Solutions become more structured and confident. ✔ Learning shifts from memorization to understanding. Strong DSA skills are rarely about volume. They come from mastering foundational patterns. 📌 Save this as a structured DSA preparation roadmap. hashtag #DSA #CodingInterview #Python #PlacementPreparation #LeetCode #PatternBasedDSA #PythonDeveloper #SoftwareEngineering

🚀 #100DaysOfCode – Day 10 | DSA Practice Continuing my 100 Days Data Structures and Algorithms challenge, today I worked on a problem based on bit manipulation and dynamic programming. 📌 Problem: Counting Bits Given an integer n, return an array ans where each index i (0 ≤ i ≤ n) contains the number of 1’s in the binary representation of i. Example: Input: n = 5 Output → [0,1,1,2,1,2] 🧠 Approach / Logic: 1️⃣ Initialize a result array of size n + 1. 2️⃣ Start from i = 1 and go till n. 3️⃣ For each number i, divide it by 2 → i / 2 (this removes the last bit). 4️⃣ Check if the last bit is 1 using i % 2. 5️⃣ Use the relation: ans[i] = ans[i / 2] + (i % 2) 6️⃣ This helps reuse previously computed results → making it efficient. 📊 Time Complexity: O(n) 📦 Space Complexity: O(n) 🎯 Key Learning: This problem shows how bit manipulation + dynamic programming can optimize solutions from brute force to linear time. Consistency is the key to growth. Let’s keep improving step by step! 💪 #100DaysOfCode #DSA #CodingJourney #ProblemSolving #CPP #LearningInPublic

This One Trick Can Turn O(N) Queries into O(log N) Imagine this  You are given an array and multiple queries :  - “Find sum from L to R”  - “Update an element” Brute force? Too slow Segment Tree? Complex for beginners Here’s where Fenwick Tree (Binary Indexed Tree) comes in This simple yet powerful data structure helps you : - Answer range sum queries in O(log N) - Update elements in O(log N) - Write code with much less complexity than Segment Trees The best part? It works using a beautiful bit manipulation trick : i & (-i) This tiny operation helps navigate the tree efficiently If you’re into DSA or Competitive Programming,Fenwick Tree is a MUST-KNOW concept. I’ve explained it step-by-step : https://lnkd.in/ghjAFydx I’ll be sharing more such concepts in a simple way. Follow along #DSA #CompetitiveProgramming #FenwickTree #Coding #LearnInPublic

Start solving at least ONE DSA question a day. Not 50 in one weekend. Not random problems from everywhere. Just one question. Every day. Because consistency beats intensity in DSA preparation. But here’s the mistake many people make. They solve random problems without a clear roadmap. Arrays today. Graphs tomorrow. Dynamic Programming next week. And after months, it still feels like nothing is clicking. That’s why a structured roadmap like this 8-week DSA plan is extremely helpful. :contentReference[oaicite:0]{index=0} Instead of guessing what to study next, it organizes the most important topics week by week. Week 1 starts with Arrays and Basic Hashing. You learn patterns like: • Prefix Sum • Two Pointers • Sliding Window • HashMap based problems With classic questions like: • Two Sum • Kadane’s Algorithm • Subarray Sum Equals K • Product of Array Except Self :contentReference[oaicite:1]{index=1} Week 2 moves to Sorting and Searching. Here you practice: • Binary Search • Search space problems • Rotated array problems • Kth largest element patterns :contentReference[oaicite:2]{index=2} Week 3 focuses on Strings. You practice patterns like: • Sliding Window • HashMap counting • Palindromes and anagrams With problems like: • Longest Substring Without Repeating Characters • Group Anagrams • Minimum Window Substring :contentReference[oaicite:3]{index=3} Then comes Linked Lists, where you learn: • Fast and slow pointers • Reversal techniques • Cycle detection • Merging linked lists :contentReference[oaicite:4]{index=4} And the later weeks cover important interview topics like: • Stack and Queue • Trees and BST • Recursion and Backtracking • Dynamic Programming • Graph basics like BFS, DFS, and Topological Sort :contentReference[oaicite:5]{index=5} This is the kind of structure that makes DSA preparation much easier. Instead of solving hundreds of random questions, you follow patterns step by step. Save this roadmap so you can follow it week by week. #dsa

DSA Starts Making Sense When You Learn It Pattern-Wise Many developers approach DSA by jumping between random problems. The result? Progress often feels slow and inconsistent. Effective DSA preparation comes from recognizing that most problems are built around repeating patterns. Once you understand the pattern behind a problem, solving similar questions becomes significantly easier. A Practical Preparation Strategy- • Identify core DSA patterns • Focus on mastering one pattern at a time • Solve multiple problems that follow the same logic • Move to the next pattern only after gaining confidence Fundamental DSA Patterns Every Learner Should Know 1) Sliding Window 2) Two Pointers 3) Hashing & Frequency Map 4) Prefix Sum 5) Binary Search (on array & answer) 6) Recursion & Backtracking 7) Linked List Patterns 8) Stack & Monotonic Stack 9) Heap / Priority Queue 10) Greedy 11) Dynamic Programming 12) Graph Traversal (BFS / DFS) 13) Tree Traversal 14) Bit Manipulation When you prepare DSA pattern-wise: ✔ Problem recognition becomes faster. ✔ Solutions become more structured and confident. ✔ Learning shifts from memorization to understanding. Strong DSA skills are rarely about volume. They come from mastering foundational patterns. 📌 Save this as a structured DSA preparation roadmap. #DSA #CodingInterview #Python #PlacementPreparation #LeetCode #PatternBasedDSA #PythonDeveloper #SoftwareEngineering

😱 Most beginners solve this problem in O(N²) or O(N³) But experienced programmers solve it in O(N). The trick? Sliding Window Technique. Let’s understand it with a simple example. Array : 1 2 3 4 5 Window size = 3 Instead of recalculating every subarray like this: [1 2 3] [2 3 4] [3 4 5] We simply slide the window. Old window : [1 2 3] Slide → [2 3 4] Instead of recomputing everything we just : • Remove 1 • Add 4 That’s it. Time Complexity improves from O(N²) → O(N). Key Idea New Window = Previous Window - element leaving + element entering I wrote a detailed explanation with code and visuals here : https://lnkd.in/gKRuKHy8 If you're learning DSA or Competitive Programming, this technique is extremely useful. Follow me for more simple explanations of algorithms  #DSA #CompetitiveProgramming #Algorithms #CodingInterview #SlidingWindow #LeetCode #Programming

🚀 Cracked a Powerful LIS Variant Today While practicing Dynamic Programming (LIS patterns), I came across a really interesting problem that pushed me to think beyond the standard approach. The twist? Instead of applying LIS directly on the whole array, the problem required: * Splitting the array into **k independent subsequences** * Solving each subsequence separately * And optimizing using **Longest Non-Decreasing Subsequence (LNDS)** with binary search Key Insight: When constraints are large, a naive DP (O(n²)) won’t work. You need to switch to an **O(n log n)** approach using the patience sorting technique. What I learned: * How to **identify hidden LIS patterns** * Difference between **LIS vs LNDS (strict vs non-decreasing)** * Importance of **problem transformation (splitting into k groups)** * Writing **efficient, contest-ready code** This kind of question is a great example of how: > A classic DP concept + smart observation = optimized solution Really enjoying diving deeper into CP patterns for upcoming contests like HackWithInfy #DataStructures #Algorithms #DynamicProgramming #LIS #CompetitiveProgramming #CodingJourney #HackWithInfy