Notes .

Building Zunexis: Engineering a Modern Multi-Language Browser IDE with Monaco, Next.js & Server-Side Execution

A deep technical breakdown of how I built Zunexis — a browser-based multi-language IDE featuring Monaco Editor, workspace management, backend-powered execution, custom autocomplete, and an IDE-like developer experience using Next.js and TypeScript.

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18 min read

Strings

Ordering Matters: Solving Count the Number of Special Characters II

A deep dive into one of the most deceptive string problems on LeetCode — where existence is not enough, and positional ordering completely changes the logic.

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10 min read

Graph Patterns: The Matrix Traversal (Island) Pattern

A definitive guide to solving 2D grid problems using DFS/BFS without building complex adjacency lists.

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12 min read

Graph Patterns: Resolving Dependencies with Topological Sort

Master Kahn's Algorithm to solve task scheduling and prerequisite problems using Directed Acyclic Graphs.

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7 min read

Graph Patterns: Connectivity and Union-Find

Bypass expensive graph traversals and determine network connectivity in near O(1) time using the Disjoint Set data structure.

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8 min read

Graph Patterns: Unweighted Shortest Path (BFS)

When edges have no weight, Breadth-First Search guarantees the shortest path by radiating outward in concentric levels.

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6 min read

Graph Patterns: Weighted Shortest Path (Dijkstra's)

Upgrade your BFS to handle weighted edges using a Priority Queue to always traverse the cheapest path first.

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8 min read

Graph Patterns: Cycle Detection in Directed Graphs

Tracking the active recursion stack to accurately detect circular dependencies and deadlocks in directed graphs.

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7 min read

Graph Patterns: Cycle Detection in Undirected Graphs

Detecting structural loops in undirected graphs by tracking parent pointers to avoid false cycle positives.

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5 min read

Graph Patterns: Minimum Spanning Tree (Prim's Algorithm)

Connect all nodes in a graph with the absolute minimum total edge cost using a Greedy Priority Queue.

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7 min read

Graph Patterns: Minimum Spanning Tree (Kruskal's Algorithm)

An edge-centric approach to building an MST by sorting edges and leveraging Union-Find.

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7 min read

Graph Patterns: Bipartite Graph Verification

Determine if a graph can be split into two mutually exclusive sets using graph coloring and BFS.

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7 min read

Graph Patterns: Strongly Connected Components (Kosaraju's)

Find clusters in a directed graph where every node can reach every other node using a two-pass DFS approach.

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8 min read

Graph Patterns: All-Pairs Shortest Path (Floyd-Warshall)

Find the shortest path between every single pair of nodes simultaneously using an elegant 3D Dynamic Programming matrix.

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7 min read

Graph Patterns: Shortest Path with Negative Weights (Bellman-Ford)

Detect negative weight cycles and find shortest paths when edge relaxation requires multiple passes.

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7 min read

The Sliding Window Pattern: Taming Contiguous Subarrays

Stop using nested loops for subarray problems. Learn how the Sliding Window technique reduces O(N^2) time complexity to a single O(N) pass.

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7 min read

Tortoise and Hare: Cycle Detection with Fast & Slow Pointers

How two pointers moving at different speeds can detect infinite loops and find the middle of a Linked List in O(1) space.

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6 min read

Backtracking: The Art of Exploring Every Possibility

A deep dive into the Backtracking pattern. Learn how to systematically build solutions and undo state changes to traverse complex decision trees.

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8 min read

Data Structures

Top K Elements: Mastering Priority Queues

When asked to find the 'Kth largest' or 'Top K most frequent', sorting the whole array is a trap. Priority Queues are the ultimate optimization.

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7 min read

Dynamic Programming

1D Dynamic Programming: Breaking Down the House Robber

Transitioning from recursive guessing to tabulated mastery. Learn how to optimize 1D Dynamic Programming problems down to O(1) space.

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9 min read

Mastering Two Sum: The Gateway to Algorithmic Thinking

A clear, beginner-friendly breakdown of LeetCode #1, exploring how moving from Brute Force to an optimized Hash Map slashes execution times from O(N^2) to O(N).

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6 min read