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Mazes for Programmers

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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

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

Exercise: Sparse Mazes

Learn to draw sparse mazes.

We'll cover the following

A sneak peek into sparse mazes
Problem statement
Coding challenge

A sneak peek into sparse mazes

The mazes we've generated to this point have been dense mazes, filling the available grid. Not all mazes need to do so, however. For example, if we wanted to represent a cave system with a random maze, we probably wouldn't want the passages packed in as tightly as possible.

For this exercise, we want a sparse maze. We do this by cutting dead ends back, trimming them down, and leaving gaps in our maze like this:

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