Implicit Graph (Grids) Introduction скачать в хорошем качестве

Implicit Graph (Grids) Introduction

📌 BFS on Grids — Key Takeaways (Telegram-style) 🔹 Problem focus Using Breadth-First Search (BFS) to find the shortest path on a grid 🧩 Why grids matter Many problems can be modeled as graphs A grid is an implicit graph (neighbors are determined by position) 🧭 Typical grid problems Maze solving Pathfinding with obstacles (trees, rivers, rocks) “Number of Islands”–style problems 🔗 Classic approach (not optimal) Convert grid → adjacency list / adjacency matrix Label each cell as a node Works, but inefficient in time & memory ⚡️ Better approach Do NOT convert the grid Traverse the grid directly using its structure 📐 Grid assumptions Unweighted grid Movement: ⬅️ ➡️ ⬆️ ⬇️ (no diagonals by default) 🧮 Core idea: direction vectors Use vectors to represent moves: up, down, left, right Mathematically clean & scalable 🔁 Traversal logic From cell (r, c) generate neighbors via direction vectors Check bounds (stay inside the grid) Push neighbors into queue (BFS) or recurse (DFS) 🚀 Why this technique is powerful Cleaner, more readable code No copy-paste logic Easy to extend to:   • Diagonal movement   • 3D / higher dimensions 🧠 Educational insight Writing manual transitions is discouraged Direction vectors = professional & scalable solution 🔜 What’s next Applying BFS on grids to find the shortest path with obstacles 💡 Bottom line Treat grids as graphs Traverse them directly Use direction vectors + BFS for optimal shortest paths 🚀