LeetCode 3129: Find All Stable Binary Arrays with Dynamic Programming

🚀 DSA Day 47 – LeetCode Problem 300: Longest Increasing Subsequence (LIS) Today’s problem was a classic and super important one in Dynamic Programming 📈 🔍 Problem Insight: Given an array of integers, the goal is to find the length of the longest strictly increasing subsequence. 💡 Key Approaches: 1️⃣ Dynamic Programming (O(n²)) For each element, check all previous elements Build a dp[] array where dp[i] stores LIS ending at index i 2️⃣ Optimized Binary Search Approach (O(n log n)) Maintain a temporary list (tails) Use binary search to replace elements and keep the list sorted Length of this list = LIS length ⚡ Why optimization works? We don’t need the actual subsequence — just the length. So we maintain the smallest possible tail for increasing subsequences of each length. 🧠 What I Learned: Difference between brute DP and optimized approach Using binary search in unexpected ways Importance of LIS in many advanced problems 💻 Time Complexity: DP: O(n²) Optimized: O(n log n) 📦 Space Complexity: O(n) Slowly building strong fundamentals 💪 — consistency > intensity! #DSA #LeetCode #DynamicProgramming #BinarySearch #CodingJourney #100DaysOfCode #TechGrowth

HI CONNECTIONS I recently tackled LeetCode 474, a problem that perfectly illustrates how to extend basic Dynamic Programming to handle multiple dimensions. 🔍 The Challenge Given an array of binary strings strs and two integers m (max zeros) and n (max ones), find the size of the largest subset of strs such that there are at most m zeros and n ones in the subset. 🛠️ My Approach: 2D Space-Optimized DP This is a variation of the 0/1 Knapsack Problem. For each string, we have a choice: either include it in our subset or skip it. Preprocessing: For every string in the input, count its number of zeros (c0) and ones (c1). Defining the State: Let dp[i][j] be the maximum number of strings we can form using exactly i zeros and j ones. The Transitions: For each string (c0, c1): We iterate backwards through our DP table (from m down to c0 and n down to c1). The update rule: dp[i][j] = max(dp[i][j], dp[i - c0][j - c1] + 1) Why backwards? This ensures that we use each string only once (0/1 property) without needing a full 3D table. The Result: After processing all strings, dp[m][n] holds the maximum subset size. 📊 Efficiency Time Complexity: O(L \cdot m \cdot n) — Where L is the number of strings. We iterate through the DP table for every string. Space Complexity: O(m \cdot n) — By using the 2D space-optimization trick, we only need to store the current state of the "bag." 💡 Key Takeaway This problem highlights the flexibility of Dynamic Programming. By adding a second dimension to the standard Knapsack array, we can represent multiple constraints. The "looping backwards" trick is a vital tool for optimizing space from O(L \cdot m \cdot n) to O(m \cdot n), which is crucial when memory is a bottleneck. #LeetCode #DynamicProgramming #KnapsackProblem #Algorithms #SoftwareEngineering #Optimization

🚀 Day 23/50 – LeetCode Challenge 🧩 Problem: Pascal’s Triangle Today’s problem focused on generating Pascal’s Triangle, a classic example that strengthens understanding of patterns and dynamic programming concepts. 📌 Problem Summary: Given an integer numRows, generate the first numRows of Pascal’s Triangle. Each element in the triangle is the sum of the two elements directly above it. Example: [1] [1,1] [1,2,1] [1,3,3,1] 🔍 Approach Used ✔ Started with the first row [1] ✔ For each new row: First and last elements are always 1 Middle elements = sum of two elements from previous row ✔ Built the triangle row by row ⏱ Time Complexity: O(n²) 📦 Space Complexity: O(n²) 💡 Key Learning ✔ Identifying patterns in problems ✔ Building solutions step by step ✔ Understanding dynamic programming intuition ✔ Working with nested loops effectively A simple problem that builds strong foundational thinking for more complex DP problems. Consistency is the key to improvement 🚀 🔗 Problem Link: https://lnkd.in/gjVfC6Kf #50DaysOfLeetCode #LeetCode #DSA #DynamicProgramming #Arrays #ProblemSolving #CodingJourney #FutureAIEngineer #Consistency

🚀 Back to Basics: The Trap of Integer Overflow I was revisiting some DSA problems today and got a quick reality check on a problem I’ve definitely solved before: Plus One. The logic seems simple: take an array representing a large integer, add 1, and return the new array. My first instinct? Convert the array to an integer, add 1, and convert it back. The Result: 🛑 Runtime Error: signed integer overflow. In the world of competitive programming, a standard int or even long long can’t always handle an array with 50+ digits. It was a great reminder that when dealing with large number arithmetic, Simulation is your best friend. 💡 The Takeaway: Instead of trying to force the array into a primitive data type, simulate the addition process manually from the least significant digit (the end of the array) and handle the carry logic. Step 1: Iterate from the end. Step 2: If the digit is less than 9, just increment and return. Step 3: If it's a 9, set it to 0 and move to the next digit. Step 4: Handle the edge case where all digits are 9 (e.g., [9, 9, 9] becomes [1, 0, 0, 0]). Sometimes "forgetting" a solution is the best way to truly understand the why behind the optimal approach. #DSA #LeetCode #CPP #CodingLife #SoftwareDevelopment #ProblemSolving #ContinuousLearning

Today’s LeetCode POTD really humbled me, but it also introduced me to one of the most brilliant code optimizations I have ever seen. 🤯 Problem: Find All Possible Stable Binary Arrays I 🔗 https://lnkd.in/gYXAAYku My initial thought process: I spotted a few patterns early on and immediately tried to force a Greedy approach. I spent a good amount of time on it but ultimately hit a wall. Instead of giving up, I looked for resources and stumbled upon a video by Mazhar Imam Khan. His explanation was an absolute masterclass—taking the logic from a beginner-friendly breakdown all the way to advanced DP state transitions. 🎥 Video link: https://lnkd.in/ggzzrkNh Even though I didn’t solve it entirely on my own today, the insights I gained from this optimized code are insane: ✅ Time Complexity: Optimized down to O(zero x one). Instead of a 3rd nested loop for the limit, it uses a sliding window concept to subtract out-of-bound states in O(1)time! ✅ Space Complexity: Compressed to O(limit x min(zero, one)). By conditionally swapping zero and one and using a deque to store only the strictly necessary previous states (limit + 1), it completely avoids the memory overhead of a 3D DP matrix. Sometimes, the best way to level up your problem-solving intuition is to study code that is leagues ahead of your current approach. Huge thanks to Mazhar for the crazy insights today! #LeetCode #DynamicProgramming #Algorithms #DataStructures #PlacementPrep #LearningJourney #C++

Day 70 of #100DaysOfCode Today I solved "Unique Binary Search Trees" on LeetCode using Recursion + Dynamic Programming (Memoization). Key Idea: For n nodes, we try every value as the root. If a value root is chosen: Left subtree can be formed using (root − 1) nodes Right subtree can be formed using (n − root) nodes The total number of BSTs for that root becomes: left_subtrees × right_subtrees By summing this for all possible roots, we get the total number of unique BSTs. To avoid recomputing the same subproblems, I used memoization. Concepts Used: • Recursion • Dynamic Programming • Memoization • Binary Search Tree properties Time Complexity: O(n²) Space Complexity: O(n) This problem is a classic example of the Catalan Number pattern in dynamic programming. Step by step, building stronger intuition for DP and tree-based problems. #100DaysOfCode #DSA #LeetCode #DynamicProgramming #BinaryTree #Cpp #CodingJourney

🔥 Day 532 of #750DaysOfCode 🔥 ✅ Solved: 1622. Fancy Sequence (Hard) Today’s problem was a tough one! This question required designing an API that supports multiple operations on a sequence efficiently using modular arithmetic, lazy updates, and modular inverse. Instead of updating every element for each operation, I used a mathematical transformation approach with two variables to keep track of multiplication and addition globally. This helped achieve O(1) per operation. 💡 Key Concepts Used: Modular Arithmetic (10^9 + 7) Fast Power (Binary Exponentiation) Modular Inverse Lazy Transformation Technique Design Data Structure 🚀 Approach: Maintain two variables a and b to represent transformation Store values in normalized form Use modular inverse while appending Compute actual value during getIndex 💻 Language: Java 💻 Topic: Design + Math + Hashing + Modular Arithmetic Hard problems like this really improve problem-solving skills and understanding of mathematical optimizations. 🔗 LeetCode Problem: Fancy Sequence #leetcode #java #datastructures #algorithms #codingchallenge #100daysofcode #programming #softwareengineer #backenddeveloper #dsa #750daysofcode

Day 61 on LeetCode — Contiguous Array (Find Max Length of Equal 0s and 1s) ⚖️✅ This problem is a classic application of prefix sum + hashmap technique. 🔹 Idea Behind the Solution The key trick is to convert the problem into a prefix sum problem: • Treat 0 as -1 and 1 as +1 • Maintain a running sum (sum) • If the same sum appears again at two indices, it means the subarray between them has equal number of 0s and 1s 🔹 How the HashMap Helps • Store the first occurrence of each prefix sum • If a prefix sum repeats at index i and was previously seen at index j, then:   i - j gives a balanced subarray length 🔹 Initialization Trick • seen{{0, -1}} ensures that subarrays starting from index 0 are correctly handled ⚡ Complexity: • Time: O(n) • Space: O(n) 💡 Key Takeaways: • Converting binary problems into prefix sum transformations simplifies logic • Hashmaps are powerful for tracking previous states of cumulative sums • Recognizing patterns where equal values → zero sum subarray is very useful 🔥 This is a very important pattern for array + hashmap + prefix sum problems! #LeetCode #DSA #Algorithms #DataStructures #PrefixSum #HashMap #Arrays #ProblemSolving #Coding #Programming #Cpp #STL #SoftwareEngineering #ComputerScience #CodingPractice #DeveloperLife #TechJourney #CodingDaily #100DaysOfCode #AlgorithmPractice #CodingSkills #Developers #TechCommunity #SoftwareDeveloper #EngineeringJourney

🚀 Day 535 of #750DaysOfCode 🚀 ✅ Solved: Count Submatrices with Top-Left Element and Sum ≤ k (LeetCode 3070) Today’s problem was a great example of using 2D Prefix Sum to optimize matrix queries. Instead of checking every possible submatrix, we can observe that the question only allows submatrices that include the top-left element (0,0). This means every valid submatrix is just a prefix rectangle, so we can compute the sum efficiently using prefix sums. 💡 Key Learning: Used 2D Prefix Sum technique Reduced brute force complexity to O(m × n) Learned how to handle matrix range sum problems efficiently 📌 Approach: Build prefix sum for each cell Check if sum from (0,0) to (i,j) ≤ k Count valid submatrices This problem improved my understanding of: ✔️ Prefix Sum ✔️ Matrix DP patterns ✔️ Optimization from brute force to efficient solution Consistency continues 🔥 On to Day 536 tomorrow. #leetcode #java #datastructures #algorithms #codingchallenge #prefixsum #matrix #programming #softwareengineering #750daysofcode