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Our First Random Mazes

Who Should Take This Course and Why?

Getting Started

Preparing the Grid

The Binary Tree Algorithm

Digging Deeper into the Binary Tree Algorithm

The Sidewinder Algorithm

Quiz Yourself on Random Mazes Algorithms

Exercise: Upside-down Sidewinder

Automating and Displaying our Mazes

Introducing Our Basic Grid Implementing the Grid Class Implementing the Binary Tree Algorithm Displaying a Maze on the Console Implementing the Sidewinder Algorithm Rendering a Maze as an Image Quiz Yourself on Automating and Displaying Mazes Exercise: Interactive Fiction Display Solution: Interactive Fiction Display

Solving Mazes

Dijkstra's Algorithm Implementing Dijkstra's Algorithm Displaying the Dijkstra's Matrix Finding the Shortest Path Making Challenging Mazes Coloring Our Mazes Displaying Colored Mazes Quiz Yourself on Dijkstra's Algorithm Exercise: Coloring Cells by Shortest Distance Solution: Coloring Cells by Shortest Distance

Avoiding Bias with Random Walks

Understanding Biases The Aldous-Broder Algorithm Implementing the Aldous-Broder Algorithm Wilson's Algorithm Implementing Wilson's Algorithm Quiz Yourself on Avoiding Bias with Random Walks Exercise: Optimizing Aldous-Broder Solution: Optimizing Aldous-Broder

Adding Constraints to Random Walks

Introduction to Random Walks (the Hunt-and-Kill Algorithm)Implementing the Hunt-and-Kill algorithm Counting Dead Ends The Recursive Backtracker Algorithm Implementing the Recursive Backtracker Algorithm Quiz Yourself on Adding Constraints to Random Walks Exercise: Recursive Recursive Backtracker Solution: Recursive Recursive Backtracker

Fitting Mazes to Shapes

Introducing Masking Implementing a Mask ASCII Masks Image Masks Quiz Yourself on Fitting Mazes to Shapes Exercise: Generating Geometric Masks Solution: Generating Geometric Masks

Going in Circles

Understanding Polar Grids Drawing Polar Grids Adaptively Subdividing the Grid Implementing a Polar Grid Testing and Tweaking Quiz Yourself on Polar Grids Exercise: Polar Grids with Uneven Row Heights Solution: Polar Grids with Uneven Row Heights

Exploring Other Grids

Implementing a Hex Grid Displaying a Hex Grid Making Hexagon (Sigma) Mazes Implementing a Triangle Grid Displaying a Triangle Grid Making Triangle (Delta) Mazes Quiz Yourself on Hexagon and Triangle Grids and Mazes Exercise: Zeta Mazes Solution: Zeta Mazes

Braiding and Weaving Our Mazes

Braiding Mazes Cost vs. Distance Implementing a Cost-Aware Dijkstra's Algorithm Introducing Weaves and Insets Getting Deep into Weaves and Insets Generating Weave Mazes Implementing the OverCell and UnderCell Class Implementing the WeaveGrid Class Quiz Yourself on Braiding and Weaving Mazes Exercise: Sparse Mazes Solution: Sparse Mazes

Improving Our Weaving

Introducing Kruskal's Algorithm Implementing Randomized Kruskal’s Algorithm Better Weaving with Kruskal Implementing Better Weaving Quiz Yourself on Kruskal's Algorithm Exercise: Masking Weave Mazes Solution: Masking Weave Mazes

Growing With Prim's

Introducing Prim's Algorithm Understanding the Simplified Version of Prim's Algorithm Understanding the True Version of Prim's Algorithm Understanding the Growing Tree Algorithm Quiz Yourself on Prim's Algorithm Exercise: Modified Prim's Algorithm Solution: Modified Prim's Algorithm

Combining, Dividing

Understanding Eller’s Algorithm Implementing Eller's Algorithm Recursive Division Implementing Recursive Division In-Depth Analysis of the Recursive Division Algorithm Quiz Yourself on the Recursive Division and Eller's Algorithms Exercise: Aldous-Broder as a Wall Adder Solution: Aldous-Broder as a Wall Adder

Extending Mazes into Higher Dimensions

Understanding Dimensions Introducing 3D Mazes Implementing a Third Dimension Displaying a 3D Maze Representing Four Dimensions Quiz Yourself on Extending Mazes into Higher Dimensions Exercise: Shuffled 2D Mazes Solution: Shuffled 2D Mazes

Bending and Folding Our Mazes

Cylinder Mazes Möbius Mazes Introducing Cube Mazes More Methods for Cube Mazes Displaying the Cube Grid Introducing Sphere Mazes Implementing POV-Ray on Sphere Mazes Quiz Yourself on Bending and Folding Mazes Exercise: Linking Worlds Solution: Linking Worlds

Conclusion

Summary of Maze Algorithms Final Word

Mazes for Programmers/

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Preparing the Grid

Preparing the Grid

Draw mazes using a piece of paper or a napkin.

We'll cover the following...

Perfect maze
Braid maze

Perfect maze

We’re going to start by drawing a grid—just a regular crosshatching of perpendicular lines. This scaffolding will form the skeleton of the maze, the bones, and the sinews that will give structure and stability to our final product.

Here’s what we'll do.

We'll get a piece of paper. It doesn’t have to be fancy—a napkin would also work. We'll want something to write with, too, and having something to erase with will be a plus.

On this piece of paper, ...