Maze generation: Difference between revisions

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</pre>

In the following, a maze is represented by a matrix, each of whose elements

is in turn a ~~boolean~~ ~~array~~ representing the bounding box:

is in turn a JSON object representing the bounding box:

$box[$i] is true iff ~~edge~~ $i open,

$box["N"] is true iff the northern edge open, and similarly for the

other points of the compass.

where $i is:

⚫

Note that in the following, the "walk" always starts at the (0,0)

0 for the top (north) side,

cell; this is just to make it clear that walk starts at the top left of the

1 bottom (south)

display.

2 right (east)

3 left (west)

⚫

Note that ~~for simplicity,~~ in the following the "walk" always starts at the (0,0) ~~cell.~~

# Output: a prn in range(0;$n) where $n is .

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| .a

end;

# Arrays wherein `false` and `null` are the only falsey values.

# The input array and $y need not be of the same length.

def lor($y): [., $y] | transpose | map(.[0] or .[1]);

def falsey: all(.[]; IN(false, null) );

# Create an array such that .[$n] is true, and .[$i] is null for $i < $n

def bit($n): [] | .[$n] = true;

# Compass is a JSON object {n,s,e,w} representing the four possible

# directions in which to move, i.e. to open a gate.

# For example, Compass.n corresponds to a move north (i.e. dx is 0, dy is 1),

# and Compass.n.gates[0] is true indicating that the "northern" gate should be opened.

# and Compass.n.gates["N"] is true indicating that the "northern" gate should be opened.

def Compass:

{n: { gates: ~~bit(0)~~, dx: 0, dy: -1},

{n: { gates: {"N": true}, dx: 0, dy: -1},

s: { gates: ~~bit(1)~~, dx: 0, dy: 1},

s: { gates: {"S": true}, dx: 0, dy: 1},

e: { gates: ~~bit(2)~~, dx: 1, dy: 0},

e: { gates: {"E": true}, dx: 1, dy: 0},

w: { gates: ~~bit(3)~~, dx:-1, dy: 0} }

w: { gates: {"W": true}, dx:-1, dy: 0} }

| .n.opposite = .s

| .s.opposite = .n

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# Produce a matrix representing an $x x $y maze.

# .[$i][$j] represents the box in row $i, column $j.

# Initially, all the gates of all the boxes are closed ~~(falsey)~~.

# Initially, all the gates of all the boxes are closed.

def MazeMatrix($x; $y):

[range(0;$x) | [] ] as $v | [range(0;$y) | $v];

[range(0;$x) | {} ] as $v | [range(0;$y) | $v];

# Input: a MazeMatrix

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($cx + $v.dx) as $nx

| ($cy + $v.dy) as $ny

| if interior($nx; $x) and interior($ny; $y) and (.[$nx][$ny]~~|falsey)~~

| if interior($nx; $x) and interior($ny; $y) and .[$nx][$ny] == {}

then .[$cx][$cy] |= ~~lor(~~$v.gates)

then .[$cx][$cy] += $v.gates

| .[$nx][$ny] |= ~~lor(~~$v.opposite.gates)

| .[$nx][$ny] += $v.opposite.gates

| generate($nx; $ny)

end );

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# draw the north edge

| ([range(0;$x) as $j

| if $maze[$j][$i][0] then "+ " else "+---" end] | join("")) + "+",

| if $maze[$j][$i]["N"] then "+ " else "+---" end] | join("")) + "+",

# draw the west edge

([range(0;$x) as $j

| if $maze[$j][$i][3] then " " else "| " end] | join("")) + "|" ),

| if $maze[$j][$i]["W"] then " " else "| " end] | join("")) + "|" ),

# draw the bottom line

($x * "+---") + "+"

;

# ~~Always~~ ~~start~~ at ~~(0,0)~~

# Start the walk at the top left

def amaze($x;$y):

MazeMatrix($x; $y)