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A maze is a path or collection of paths, typically from an entrance to a goal. The word is used to refer both to branching tour puzzles through which the solver must find a route, and to simpler non-branching ("unicursal") patterns that lead unambiguously through a convoluted layout to a goal.
Robot in a wooden maze. A maze-solving algorithm is an automated method for solving a maze.The random mouse, wall follower, Pledge, and Trémaux's algorithms are designed to be used inside the maze by a traveler with no prior knowledge of the maze, whereas the dead-end filling and shortest path algorithms are designed to be used by a person or computer program that can see the whole maze at once.
The animation shows the maze generation steps for a graph that is not on a rectangular grid. First, the computer creates a random planar graph G shown in blue, and its dual F shown in yellow. Second, the computer traverses F using a chosen algorithm, such as a depth-first search, coloring the path red.
The Lee algorithm is one possible solution for maze routing problems based on breadth-first search. It always gives an optimal solution, if one exists, but is slow and requires considerable memory. It always gives an optimal solution, if one exists, but is slow and requires considerable memory.
In this specialized usage, maze refers to a complex branching multicursal puzzle with choices of path and direction, while a unicursal labyrinth has only a single path to the center. A labyrinth in this sense has an unambiguous route to the center and back and presents no navigational challenge. [6] [7] [8] [9]
Historically, a turf maze is a labyrinth made by cutting a convoluted path into a level area of short grass, turf or lawn. Some had names such as Mizmaze, Troy Town, The Walls of Troy, Julian's Bower, or Shepherd's Race. This is the type of maze referred to by William Shakespeare in A Midsummer Night's Dream (Act 2, Scene 2) when Titania says:
A* pathfinding algorithm navigating around a randomly-generated maze Illustration of A* search for finding a path between two points on a graph. From left to right, a heuristic that prefers points closer to the goal is used increasingly.
Input: A graph G and a starting vertex root of G. Output: Goal state.The parent links trace the shortest path back to root [9]. 1 procedure BFS(G, root) is 2 let Q be a queue 3 label root as explored 4 Q.enqueue(root) 5 while Q is not empty do 6 v := Q.dequeue() 7 if v is the goal then 8 return v 9 for all edges from v to w in G.adjacentEdges(v) do 10 if w is not labeled as explored then 11 ...