Breadth First Search (BFS) Algorithm
The Lee Algorithm is a breadth-first search (BFS) algorithm that is used to find the shortest path between two points in a grid-like structure, such as a maze. It is an unweighted grid-based algorithm, meaning that all cells in the grid have the same traversal cost, and it finds the shortest path in terms of the number of steps.
Key Characteristics:
The algorithm is well-suited for solving shortest path problems in mazes or grids, where movement is typically limited to four or eight directions (up, down, left, right, or diagonals).
It works by expanding the search layer by layer, ensuring that the first time it reaches the target, it has found the shortest path.
It guarantees finding the shortest path in an unweighted grid if one exists.
Lee Algorithm Overview:
Input: A 2D grid (or maze) with cells representing either open paths or obstacles (walls), a starting point, and an ending point.
Output: The shortest path from the start to the end, if one exists.
Approach: Uses BFS to explore the maze. The BFS approach ensures that all cells at a certain distance from the starting point are processed before moving on to cells at a greater distance.
Real-World Applications of the Lee Algorithm:
Robotics Navigation: The Lee algorithm can be used in robotic navigation systems where the robot needs to find the shortest path in a grid-like environment with obstacles.
Maze Solving: It is commonly used for solving mazes where the goal is to find the shortest route between two points, typically used in games, AI puzzles, or escape room designs.
Routing in Computer Networks: Although less common in weighted graphs, the algorithm can be adapted for simple routing protocols in network grids, where routers or nodes need to find the shortest path across a network.
Grid-Based Pathfinding in Video Games: Games often use the Lee algorithm for pathfinding on grid-like maps, where characters or agents need to navigate around obstacles in the shortest possible way.