Counting Square Submatrices with All Ones using DP

Day 9 of #30DaysOfCode 📐 From Brute Force to Ultra-Optimized: Maximum Rectangle Area Problem Just cracked an interesting geometric problem that taught me the power of micro-optimizations in competitive programming! The Challenge: Find the largest axis-aligned rectangle from a set of points where no other points lie inside or on the borders. The Journey: Started with O(n⁴) brute force approach Optimized to O(n³) using diagonal-pair strategy Applied competitive programming micro-optimizations Key Optimizations That Made the Difference: - unordered_set with reserve() → 3-5x faster lookups vs set - Bit packing coordinates → (x,y) into single 64-bit integer for faster hashing - Const references → Reduced array access overhead - Early break/continue → Eliminated wasted iterations - Direct comparison → Avoided max() function overhead The Results: ⚡ 6-8x performance improvement 💾 Same O(n) space complexity 🎯 Runs in ~100-200 operations for n ≤ 10 Key Takeaway: For small constraints, the right data structure + micro-optimizations matter more than asymptotic complexity. Sometimes it's not about changing the algorithm, but making every operation count! #CompetitiveProgramming #CPP #AlgorithmOptimization #DSA #ProblemSolving #SoftwareEngineering #CodingInterview #PerformanceOptimization Educative #educative

1526. Minimum Number of Increments on Subarrays to Form a Target Array 1526. Minimum Number of Increments on Subarrays to Form a Target Array Difficulty: Hard Topics: Array, Dynamic Programming, Stack, Greedy, Monotonic Stack, Biweekly Contest 31 You are given an integer array target. You have an integer array initial of the same size as target with all elements initially zeros. In one operation you can choose any subarray from initial and increment each value by one. Return the minimum number of operations to form a target array from initial. The test cases are generated so that the answer fits in a 32-bit integer. Example 1: Input: target = [1,2,3,2,1] Output: 3 Explanation: We need at least 3 operations to form the target array from the initial array. [0,0,0,0,0] increment 1 from index 0 to 4 (inclusive). [1,1,1,1,1] increment 1 from index 1 to 3 (inclusive). [1,2,2,2,1] increment 1 at index 2. [1,2,3,2,1] target array is formed. Example 2: Input: target = [3,1,1,2] Output: 4 Explanation: [0,0,0,0] -> [1,1,1,1] -> [1,1,1,2] -> [2,1,1,2] -> [3,1,1,2] https://lnkd.in/geCSn5Fq

🎯 LeetCode Daily – Unique Paths (Day 110) Today’s challenge was a classic Dynamic Programming grid problem - Unique Paths ✅ My Approach: 🔹 The goal was to count the total distinct paths from the top-left corner to the bottom-right corner of an n x m grid, moving only right or down. 🔹 Implemented two approaches:   • Memoization: Recursively explored all paths while caching overlapping subproblems in a 2D dp array.   • Tabulation: Built the solution bottom-up, where each cell’s value represents the sum of paths from the top and left cells. 🔹 Base case: Only one path exists when starting at the origin (0, 0). 🧠 Key Insight: This problem highlights the power of Dynamic Programming on grids - transforming recursive exploration into efficient tabular computation. It’s a perfect foundation for advanced path-based DP problems like Unique Paths II and Minimum Path Sum. 📊 Time Complexity: O(N × M) 📦 Space Complexity: O(N × M)

🔹 Day 39 of #100DaysOfCode Topic: Pointer Arithmetic and Array Manipulation in C Today I practiced accessing and modifying array elements using pointers. Here's a breakdown of what the code does: 🧠 Code Summary: Array Declaration: An integer array arr[] is initialized with values {10, 20, 30, 40, 50}. Pointer Initialization: A pointer ptr is assigned to point to the first element of the array (arr). Accessing Elements via Pointer Arithmetic: Using *(ptr + i), each element is accessed by moving the pointer i steps forward. This demonstrates how pointers can traverse arrays without using traditional indexing. Modifying Elements via Pointer Arithmetic: Each element is incremented by 5 using *(ptr + i) += 5. This shows how pointers can directly modify array values. 🖥️ Output: The program first prints the original array values, then prints the updated values after adding 5 to each. #CProgramming #PointersInC #ArrayManipulation #CodeNewbie #LearnToCode 

🎯 LeetCode Daily – Partition Equal Subset Sum (Day 119) Today I revisited one of the classic Dynamic Programming problems - Partition Equal Subset Sum, and focused on space optimization techniques. ✅ My Approach: • The goal is to determine if an array can be split into two subsets with equal sum. • After calculating the total sum, I reduced the problem to a Subset Sum check using DP. • Initially implemented it with a 2D DP table, but today I optimized it to use just two 1D arrays (prev and curr) - cutting space complexity from O(N × Target) to O(Target). • Each element’s inclusion/exclusion decision depends only on the previous row’s state. 🧠 Key Insight: Space optimization in DP is all about recognizing dependency patterns - when a solution relies only on the previous computation, we can safely compress dimensions without losing correctness. 📊 Time Complexity: O(N × Target) 📦 Space Complexity: O(Target) #LeetCode #DSA #DynamicProgramming #ProblemSolving #Optimization #DailyCoding #LearningInPublic #Day119

🚀 Day 60 of #100DaysOfLeetCodeHard — LeetCode 3725: Count Ways to Choose Coprime Integers from Rows (Hard) My Submission:https://lnkd.in/gFY6Yg_f Today’s problem was a Dynamic Programming + GCD challenge — a great exercise in combining mathematical reasoning with state-based recursion. The task was to count the number of ways to select exactly one integer from each row of a given matrix such that the GCD of all chosen integers equals 1, with results taken modulo 109+710^9 + 7109+7. 💡 Approach: I used recursive DP with memoization where each state represents: ind: current row index gcdNum: current running GCD value At each step, we iterate through all numbers in the current row and recursively compute the number of valid combinations leading to a final GCD of 1. A 2D DP array dp[ind][gcdNum] stores intermediate results to avoid recomputation. 📘 Key Concepts Used: Dynamic Programming over GCD states Modulo arithmetic for large result handling Efficient bottom-up recursion with pruning ⏱️ Time Complexity: O(n × m × log(maxValue)) 💾 Space Complexity: O(n × maxValue) This problem beautifully highlights how mathematical insight (GCD) and DP optimization come together to handle complex combinatorial counting problems. 💪 #LeetCode #DynamicProgramming #Math #GCD #ProblemSolving #C++ #100DaysOfCode #LearningEveryday #CodingChallenge

🚀 Day 74 – 75 Days DSA Challenge 💻 # Today, I focused on strengthening one of the most important problem-solving techniques in algorithms - Dynamic Programming (DP). # I revised all core DP concepts and successfully solved a classic LeetCode problem: Fibonacci Number. 📘 Concepts Covered: 🔹 What is Dynamic Programming? # A technique to solve problems by breaking them into overlapping subproblems. # Uses optimal substructure and memoization/tabulation to avoid repeated work. # Helps convert exponential solutions into polynomial-time ones. 🔹 DP Approaches I Practiced: # Recursive (Top-Down) with memoization # Iterative (Bottom-Up) tabulation # Space-Optimized DP for efficient memory usage # Understanding when DP is applicable by identifying patterns and recurrence relations 🔹 Problem Solved – Fibonacci Number: # Implemented the Fibonacci series using space-optimized DP (O(n) time, O(1) space). # Observed how DP transforms a slow exponential solution into an efficient linear one. # Reinforced my understanding of subproblems, transitions, and base cases. 💡 Key Takeaway: # Dynamic Programming is not just a technique - it’s a mindset. # Today’s practice helped me become more comfortable recognizing DP patterns and building efficient solutions for complex problems. #Day74 #75DaysDSAChallenge #DynamicProgramming #DP #LeetCode #Fibonacci #Algorithms #DataStructures #ProblemSolving #CodingJourney #TechLearning #Programming