Junaid Arshad’s Post

Min Stack: Parallel Stack Tracks Running Minimum in O(1) Finding minimum naively requires O(n) scan. Solution: maintain parallel stack where each position stores minimum of all elements at/below it. Push/pop synchronize both stacks. getMin becomes O(1) lookup of minStack top. Auxiliary Stack Pattern: For O(1) access to aggregate property (min, max, sum) at any depth, maintain parallel stack tracking that property. Space doubles but all operations stay O(1). Time: O(1) all ops | Space: O(n) #Stack #AuxiliaryStructure #MinTracking #ConstantTime #Python #DataStructureDesign #SoftwareEngineering

Today I took a break to continue working on my master’s final project. A day ago, I thought the next step was simple: write Python code for V&V. But the real question turned out to be different. Not only how to build the POC or simulation, but what it should actually prove or disprove. For me, a good POC or simulation is not just a technical exercise. It should support or challenge design decisions, provide evidence that the architecture is moving in the right direction, and expose weak assumptions before they become expensive mistakes. Sometimes, proving that a direction is wrong early is more valuable than proving that it is right. How often do you use a POC or simulation to validate design choices in your systems? #SystemsEngineering #Architecture #Validation #Simulation #Engineering

🚀 Day 17 of #DSAStreak 📌 Problem: Longest Common Prefix 🧠 Problem Summary: Given an array of strings, find the longest common prefix shared among all strings. If no common prefix exists → return "" 💡 Approach: Vertical Scanning 🔥 Instead of comparing entire strings (slow ❌), we optimize using: ✔ Take first string as reference ✔ Compare characters index by index ✔ Check across all strings ✔ Stop immediately at first mismatch ⚙️ Key Logic: Take first string → iterate over each character Compare with same index in other strings If mismatch or index out of bound → return prefix till that point 📌 Example: Input: ["flower","flow","flight"] Output: "fl" Explanation: First mismatch at index 2 → "o" ≠ "i" ⏱ Time Complexity: O(N × M) 💾 Space Complexity: O(1) 🔥 Key Learnings: 👉 Nested loops ≠ always O(n²) 👉 Early stopping saves time 👉 Compare character-wise, not string-wise 👉 Prefix must be common in ALL strings #Python #DSA #Strings #CodingJourney #100DaysOfCode #ProblemSolving #LeetCode #Tech

LCA of BST: Exploiting Order Property for O(h) Space-Free Search Generic tree LCA needs full traversal. BST ordering enables iterative solution — LCA is where paths to p and q diverge. If both values smaller than current, go left; both larger, go right; otherwise, current node is split point = LCA. BST Advantage: Ordering enables O(h) iterative solution without recursion stack. Divergence point is guaranteed LCA by BST property. This pattern applies to any problem where BST ordering simplifies logic. Time: O(h) | Space: O(1) #BST #LCA #OrderProperty #IterativeSearch #Python #AlgorithmDesign #SoftwareEngineering

LeetCode Problem 155 "Min Stack": Design a stack that supports push, pop, top, and retrieving the minimum element in constant time. Implement the MinStack class: MinStack() initializes the stack object. void push(int val) pushes the element val onto the stack. void pop() removes the element on the top of the stack. int top() gets the top element of the stack. int getMin() retrieves the minimum element in the stack. You must implement a solution with O(1) time complexity for each function. Approach: we can implement a single stack and store values as tuples (current element, min so far). But wait ... consider edge case when we pop and the stack becomes empty, so to handle this we consider two conditions- one when stack becomes empty, we set min so far to +ve infinity again, second whenever we pop elements, if stack is not empty, we update min so far to the top of the stack's min so far. In this way we can keep track of the minimum element upto a specific stack level. Time complexity of all the operations: O(1) #Python #LeetCode #ProblemSolving #DSA #InterviewPrep #DataStructures #Algorithms #Programming

LCA of BST: Exploiting Order Property for O(1) Space Generic tree LCA needs full traversal. BST ordering enables iterative solution — LCA is where paths diverge. Both values smaller? Go left. Both larger? Go right. Otherwise, current node is split point = LCA. BST Advantage: Ordering enables O(h) iterative solution without recursion stack. Divergence point is guaranteed LCA by BST property. This demonstrates how data structure properties simplify algorithms. Time: O(h) | Space: O(1) #BST #LCA #OrderProperty #IterativeSearch #Python #AlgorithmDesign #SoftwareEngineering

📌 Problem: Product of Array Except Self 💡 Approach: Instead of using division, compute the result using prefix and suffix products. First, traverse from left to right to store prefix products in the result array. Then, traverse from right to left to multiply with suffix products. This ensures each index contains the product of all elements except itself. ⚙️ Key Insight: Avoid division to handle zero cases efficiently Use prefix and suffix multiplication in a single result array Optimized space usage (no extra arrays needed) ⏱️ Time Complexity: O(n) 📦 Space Complexity: O(1) (excluding output array) 📚 What I learned: Prefix & suffix technique for array problems Space optimization strategies #LeetCode #DSA #Algorithms #Coding #ProblemSolving #Python #InterviewPreparation #Array #CodingJourney

Daily Temperatures: Monotonic Stack for Next Warmer Day Checking future temperatures for each day is O(n²). Monotonic decreasing stack reduces to O(n) — stack holds indices waiting for warmer days. When warmer temperature arrives, resolve all waiting cooler temperatures via stack pops. Monotonic Stack: Elements waiting for "next greater/smaller" use monotonic stacks. Each element pushed/popped once = amortized O(n). Pattern appears in stock span, histogram area, next greater problems. Time: O(n) amortized | Space: O(n) #MonotonicStack #NextGreaterElement #AmortizedAnalysis #StackOptimization #Python #AlgorithmDesign #SoftwareEngineering

Product Except Self: Prefix-Postfix Eliminates Division Division fails with zeros. Two-pass prefix-postfix avoids division — first pass stores product of all left elements, second multiplies by product of all right elements. Reusing output array achieves O(1) auxiliary space. Prefix-Postfix Pattern: Powerful technique for transformations where each element depends on surrounding elements. Appears in cumulative sums, range queries, sliding aggregations. Combining left and right passes solves many "except self" problems. Time: O(n) | Space: O(1) excluding output #PrefixPostfix #ArrayTransformation #DivisionFree #SpaceOptimization #Python #AlgorithmDesign #SoftwareEngineering

LeetCode 200. Number of Islands: "Given an m x n 2D binary grid grid which represents a map of '1's (land) and '0's (water), return the number of islands. An island is surrounded by water and is formed by connecting adjacent lands horizontally or vertically. You may assume all four edges of the grid are all surrounded by water." Approach: Using Depth-first-search, traverse the grid, if '1' is encountered, mark is '0' and explore its 4-side neighbors, for this create a function that recursively explores the neighbors forming an island of '1'. Count the number of islands formed. time complexity: O(N*M) #Python #LeetCode #DSA #CompetitiveProgramming #Graphs #OptimalSolution