Greedy Bill Change Algorithm Simulation

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

Plus One: Digit Addition with Carry Propagation Add 1 to number represented as digit array. Reverse for easier processing (rightmost = index 0). Propagate carry: 9 becomes 0 with carry, else increment and stop. If carry remains after all digits, append it (e.g., 999 → 1000). Simpler Approach: Process from right without reversing using for i in range(len(digits) - 1, -1, -1). Your reversing works but adds extra operations. Both O(n) time though. Time: O(n) | Space: O(1) excluding output #DigitArithmetic #CarryPropagation #ArrayManipulation #Simulation #Python #AlgorithmDesign #SoftwareEngineering

Product Except Self: Prefix-Postfix Pattern Avoids Division Division-based solution fails with zeros. Two-pass prefix-postfix eliminates division — first pass stores product of all left elements, second pass multiplies by product of all right elements. Reusing output array achieves O(1) auxiliary space. Prefix-Postfix Technique: Powerful pattern for array transformations where each element depends on surrounding elements. Appears in: cumulative sums, range queries, sliding aggregations. Time: O(n) | Space: O(1) excluding output #PrefixPostfix #ArrayTransformation #DivisionFree #SpaceOptimization #Python #AlgorithmDesign #SoftwareEngineering

A lot of systems today are built to be “responsive.” I care more about systems that are bounded. That is part of why I made atlas-kvd-demo: a tiny Python toy where state evolves through: K — what the system carries  V — what the world pushes onto it  Δ — what a local event changes The point is simple: instead of jumping from 0 to 100 every time something happens, a system can update in a way that is legible, constrained, and stable. https://lnkd.in/e8WFcFPv Tiny demo. Bigger direction. #Python #SystemsDesign #Simulation #AIEngineering #GitHub #BuildInPublic #Tech

Validate BST: Boundary Tracking for Global Ordering Checking only immediate children misses violations. Solution: pass valid range bounds down recursion. Each node must satisfy not just local constraint (left < node < right) but global constraint — all ancestors' bounds. Boundaries narrow as we recurse. Boundary Propagation: Each recursive call narrows allowable range. Left subtree inherits lower bound but gets node value as upper bound. This ensures all descendants respect ancestors' ordering requirements. Time: O(n) | Space: O(h) #BST #BoundaryTracking #TreeValidation #RecursiveConstraints #Python #AlgorithmDesign #SoftwareEngineering

🚀 Day 33 – LeetCode Journey Today’s problem: Move Zeroes ✔️ Used two-pointer technique for in-place modification ✔️ Moved all non-zero elements forward efficiently ✔️ Maintained relative order of elements 💡 Key Insight: By keeping a pointer for non-zero elements, we can swap values in a single pass and avoid extra space — making the solution both clean and optimal. This problem improved my understanding of array manipulation and in-place algorithms. Consistency is building confidence day by day 💪🔥 #LeetCode #Day33 #Arrays #TwoPointers #Python #ProblemSolving #CodingJourney #100DaysOfCode

Evaluate RPN: Stack for Postfix Expression Evaluation Postfix notation (Reverse Polish Notation) places operators after operands. Stack naturally handles this — push numbers, on operator pop two operands, compute, push result. No precedence rules needed unlike infix notation. Postfix Advantage: No parentheses or precedence handling needed. Linear stack evaluation is simple and efficient. This makes RPN ideal for calculators and expression engines. Time: O(n) | Space: O(n) #Stack #RPN #ExpressionEvaluation #PostfixNotation #Python #AlgorithmDesign #SoftwareEngineering

Tired of crappy static heat maps on R or Python? Check out @ZeynepHG and Osho's most recent pre print about a new scalable interactive and gpu accelerated heat map visualization tool! arxiv.org/abs/2602.08280. @IcahnMountSinai #bioinformatics

Tribonacci: Space-Optimized Triple-Window DP Tribonacci extends Fibonacci to three predecessors: f(n) = f(n-1) + f(n-2) + f(n-3). Instead of storing all values, maintain sliding window of last three. Shift window left, compute new value as sum. Fixed-Window DP: When recurrence depends on fixed k previous states, maintain k-sized window instead of full array. Reduces O(n) space to O(k) — here O(3) = O(1). Time: O(n) | Space: O(1) #DynamicProgramming #Tribonacci #SlidingWindow #SpaceOptimization #Python #AlgorithmDesign #SoftwareEngineering

Top K Frequent: Bucket Sort Beats Heap with O(n) Time Heap-based solution costs O(n log k). Bucket sort achieves O(n) by leveraging frequency bounds — frequencies can't exceed array length. Index = frequency, value = list of elements with that frequency. Traverse buckets high-to-low, collecting k elements. Bucket Sort Advantage: When value range is bounded and known (frequencies ≤ n), bucket sort beats comparison-based O(n log k). Exploiting constraints transforms complexity. Time: O(n) | Space: O(n) #BucketSort #TopK #FrequencyAnalysis #ComplexityReduction #Python #AlgorithmOptimization #SoftwareEngineering