MATLAB Assignment for ENGR 133. Generates a maze of variable size and difficulty. Depth-first search idea found from wikipedia.

This program uses a randomized version of the depth-first search algorithm to generate a maze of size n and difficulty d. The main function controls the rest of this program, so this is the only function that needs to be called in order to generate a maze. Descriptions of the created functions are listed below.

To use this program, simply navigate to the directory that holds all files listed below. Open main.m and press run. The program will ask for user input for the size and difficulty of the maze. The size input can be any number larger than 5. The difficulty must be 1 - 10.
To do: Include screenshots and example parameters along with expected outputs

A reference to where each requirement can be found in the list below:

1. User input: main function lines 29 - 37
2. Functions: One main function with five subfunctions, setup, move, validateMove, adjustEnd, checkNodes, dispMaze
3. For loop: validateMove function lines 36 - 40
4. While loop: main function lines 33 - 37
5. Embedded loops: validateMove function lines 42 - 48
6. Matrix: main function lines 40 - 50
7. Conditional structure: adjustEnd function lines 35 - 45
8. 100 lines of code: Current code is about 300 lines without the function headers at the top

Inputs: None
Outputs: None (Note: displays maze with dispMaze function)
This is the main function of the maze generation program. This uses the setup function to create an empty maze. Then, it uses the move function while there are no more nodes listed in the nodes list. The adjustEnd function is used to link the exit to the rest of the maze. Lastly, dispMaze function is called to format the maze to a viewable format.

Inputs: size
Outputs: maze, nodes, startPos, endPos
This function takes a size parameter and generates a nxn matrix of that size. Next, the function creates a border of 8's around the outside edges. It then randomly generates a start and end point (which will be returned at the end of the function). The start point will be located at some point along the bottom row (where it will replace one of the 8's). The end point will be located at some point along the top row (where it will replace one of the 8's). A 1 (path) will be generated directly above the start point, and a node will be created at that point. The function then returns the created maze, a list of nodes, and the start/end positions of the maze.

Inputs: maze, position
Outputs: maze, position, nodes
This function takes a maze and generates one new point along its current path. This function is recursively called within the main function until there are zero nodes. This function first calls validateMove to get a list of possible directions the function can go. If there are 0 possible directions and the current position is a node, the node is removed and the current position is set to the last node on the list. If there are 0 possible directions and the current position is not a node, the current position is set to the last node on the list. If there are 1, 2, 3, or 4 possible directions, the function does a couple of things. It first finds a random direction using the weighting described in the movement section of this README. It then finds the position of the previous position (whatever point was created just before this one). It then calls the checkNodes function. If it returns true, then add the current point to the node list. Regardless, the currentPoint is set equal to the futurePoint and that point in the maze is set to 1. maze, pos, and nodes are all returned in order to make this function easy to be called recursively.

Inputs: maze, position
Outputs: position
The purpose of this function is to tell the move function where the current position could possibly go. This function will return a matrix called directions that will return either a 1 or a 0 for each direction. The format for directions is up, down, left, right. Valid movements are checked using a valid movement matrix outlined below.

Inputs: maze, endPos
Outputs: maze
This function connects the end piece to the rest of the maze. Because the movement constraints are set to not directly touch the border (8's), a connection must be made to the generated maze. This is done by traversing straight down from the end position until a connection has been made to the rest of the maze. This is indicated by looking left, right, and down to see if there is a 1 next to it. This outputs the adjusted maze at the end of this function.

Credit to Bailey Keel for helping me come up with this idea.
Inputs: futurePoint, previousPoint
Outputs: result
This function checks to see if the movement would result in the creation of a node. Most simply, a node is created when there is a change in the direction of a path. In all cases, the generated point (futurePoint) will be in a different row and column than the last point (previousPoint, not currentPoint). If a node is found, returns true.

Inputs: maze
Outputs: None (Note: displays maze)
This function formats the matrix to be graphed via heatmap. This is a two dimensional graph in which there are different colors based on the value in the matrix. That way, the walls can be grey, paths blue, and start/end orange.

Point class
Properties: row, col
Methods: point(a, b), adjust(maze, position, value), mazeValue(maze, position, a, b), same(a, nodes)
The purpose of this class is to prevent the need for x and y components for all points throughout the maze. These functions are mostly one liners whos purpose is to make adjustments to the maze and positions simpler.

The difficulty input allows for a user to adjust the tendency for the maze to traverse upwards versus side to side. When a random number is generated (1-100), the different directions are given different weightings (based on difficulty). By default, the difficulty is 5, meaning all directions have a tendency to travel upwards. The higher the difficulty, the higher the tendency for the path to traverse side to side. The lower the difficulty, the higher the tendency for the path to traverse upwards. This is represented by the following code sequence:

% Possible directions: [Up, down, left, right]
locations = directions .* floor(100/sum(directions));
% Percentage based increase
locations(1) = locations(1) * (1 - ((difficulty - 5.0)/14));
locations(2) = locations(2) * (1 + ((difficulty - 5.0)/14));
locations(3) = locations(3) * (1 + ((difficulty - 5.0)/14));
locations(4) = locations(4) * (1 + ((difficulty - 5.0)/14));
if sum(locations) ~= 100
locations(1) = locations(1) + 100 - sum(locations);
end

During the validateMove function, a series of surrounding points are checked to see if the maze can move in that direction. Below is a matrix that indicates which directions are not valid if there is a point there. The current point is marked with an O. If there is a point where an X is, then the directions the arrows point in are now marked as an invalid direction.