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jsmaze7.html
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<!doctype html>
<html lang="en">
<head>
<title>Maze</title>
<meta charset="utf-8">
<style type="text/css" id="maze-style">
body, div, table, tr, th, td { margin: 0; padding: 0; border: 0; }
input[type="range"] { width: 90vw; }
div#wrap { width: 90vw; height: 90vh; min-height: 90vh; padding: 10px; margin: auto auto; background: white; position: relative; }
table.maze { width: 100%; height: 100%; border: none;}
table.maze td { border-width: 1px; border-style: none; border-color: black; }
table.maze td { padding: 0; font-size: 12px; min-height: 1em; min-width: 1em; background-repeat: no-repeat; background-position: center; background-origin: padding-box; background-clip: padding-box; background-size: 50%;}
table.maze td.wall_0 { border-top-style: solid; }
table.maze td.wall_1 { border-right-style: solid; }
table.maze td.wall_2 { border-bottom-style: solid; }
table.maze td.wall_3 { border-left-style: solid; }
table.maze td.wall_0.wall_1.wall_2.wall_3 { background: black; }
table.maze td.solution { background-color: lightgreen; }
table.maze td.no-solution { background-color: #eee; }
table.maze td.current { background-color: cyan; }
/*
table.maze td.backtrack_0 { background-image: url(images/arrow-up.svg); }
table.maze td.backtrack_1 { background-image: url(images/arrow-right.svg); }
table.maze td.backtrack_2 { background-image: url(images/arrow-down.svg); }
table.maze td.backtrack_3 { background-image: url(images/arrow-left.svg); }
*/
table.maze td.testing { background-image: url(images/question-lg.svg); }
</style>
<script type="text/javascript">
// This function will add an onload handler to the body. It's fine to
// add a bunch of handlers, this keeps track of all of them.
function add_body_onload(func) {
var old_body_onload=window.onload;
window.onload=function() {
if (old_body_onload) { old_body_onload(); }
func();
}
}
// Get query parameters from the url. This returns an object like this:
// ?param => args['param']=true
// ?param=value => args['param']=value
// ?param[]=value => args['param']=[value,...]
function get_args() {
var args = new Object();
var query_string=location.search.slice(1);
if (!query_string) return args;
var query_pairs = query_string.split('&');
var pname, pvalue;
for (var i=0 ; i<query_pairs.length ; i++) {
var equal_position=query_pairs[i].indexOf('=');
if (equal_position<0) {
args[my_uri_decoder(query_pairs[i])]=true;
} else {
pname=my_uri_decoder(query_pairs[i].slice(0,equal_position));
pvalue=my_uri_decoder(query_pairs[i].slice(equal_position+1));
// If a name is followed by [], then we'll create an array of
// values. This is good for a multiple-select box
if (pname.match(/\[\]$/)) {
pname=pname.slice(0,-2);
if (!args[pname]) args[pname]=new Array();
args[pname].push(pvalue);
} else {
args[pname]=pvalue;
}
}
}
return args;
}
function my_uri_decoder(v) {
return decodeURIComponent(v.replace(/\+/g,'%20'));
}
var args=get_args();
// Basically, this array "converts" any number 0-15 to its
// binary equivalent as a string, which is useful for the use
// with the above stylesheet.
var to_bin=['0000', '0001', '0010', '0011', '0100', '0101', '0110', '0111', '1000', '1001', '1010', '1011', '1100', '1101', '1110', '1111'];
// Dir: 0 1 2 3
// N E S W
var deltax=[0,1,0,-1];
var deltay=[-1,0,1,0];
var reverse_dirs=[2,3,0,1];
// walls are horizontal or vertical
var wall_offsets={
h: { x: [0,0,0,0], y: [0,0,1,0] },
v: { x: [0,1,0,0], y: [0,0,0,0] }
};
var wall_types=['h','v','h','v'];
// perms array has these indices:
// 1. direction of entering square
// 2. a perm #
// 3. a direction #
// 4. sequence #
//
// Note that the perm# is broken down as follows:
// 0 - go straight first
// 1 - go straight second
// 2 - go straight last
//
// Direction # is:
// 0 - left first
// 1 - right first
//
// Therefore:
//
// 0,0 - straight,right,left
// 0,1 - straight,left,right
// 1,0 - right,straight,left
// 1,1 - left,straight,right
// 2,0 - right,left,straight
// 2,1 - left,right,straight
var perms = [[[[0,1,3],[0,3,1]],[[1,0,3],[3,0,1]],[[1,3,0],[3,1,0]]],
[[[1,2,0],[1,0,2]],[[2,1,0],[0,1,2]],[[2,0,1],[0,2,1]]],
[[[2,3,1],[2,1,3]],[[3,2,1],[1,2,3]],[[3,1,2],[1,3,2]]],
[[[3,0,2],[3,2,0]],[[0,3,2],[2,3,0]],[[0,2,3],[2,0,3]]]];
// These are the solver directions to follow right wall
var right_solve_directions = [[1,0,3], [2,1,0], [3,2,1], [0,3,2]];
// These are the solver directions to follow left wall
var left_solve_directions = [[3,0,1], [0,1,2], [1,2,3], [2,3,0]];
var xsize=parseInt(args['xsize']);
var ysize=parseInt(args['ysize']);
if (!xsize) xsize=10;
if (!ysize) ysize=10;
// We'll add some empty cells around the outside for bounding
xsize += 2;
ysize += 2;
var right_preference=args['r'];
if (right_preference) {
right_preference = parseFloat(right_preference);
} else {
right_preference = 0.5;
}
if (right_preference<0.0) {
right_preference=0.0;
} else if (right_preference>1.0) {
right_preference=1.0;
}
var straight_preference=args['s'];
if (straight_preference) {
straight_preference = parseFloat(straight_preference);
} else {
straight_preference = 0.0;
}
if (straight_preference<-1.0) {
straight_preference=-1.0;
} else if (straight_preference>1.0) {
straight_preference=1.0;
}
var show_backtracks=args['b'];
// For each cell, we need to keep state. Walls are booleans,
// and consist of horizontal walls and vertical walls. We can
// determine which walls belong to a cell using wall_offsets
// and wall_types.
// For each cell position we'll keep the following information:
// 1. entry direction
// 2. permutation
// 3. current sequence
// 4. depth
// Only depth needs to be kept in an array for later use
var depths = new Array(xsize);
var backtracks = new Array(xsize);
var walls = { h: new Array(xsize), v: new Array(xsize+1) }
var startx=1;
var starty=0;
var start_direction=2;
var endx=xsize-2;
var endy=ysize-1;
var end_direction=0;
var maxdepth=0;
function may_solve(x,y,dir) {
return !get_wall(x,y,dir);
}
function* solve_maze(x,y,dir,goalx,goaly) {
yield { action: 'solve', x: x, y: y, dir: dir };
if (x==goalx && y==goaly) {
yield { action: 'solve-done' };
return true;
} else {
for (var new_dir of right_solve_directions[dir]) {
if (may_solve(x, y, new_dir)) {
var i=x+deltax[new_dir];
var j=y+deltay[new_dir];
if (yield* solve_maze(x+deltax[new_dir], y+deltay[new_dir], new_dir, goalx, goaly)) {
return true;
}
}
}
yield { action: 'solve-backtrack', x: x, y: y, dir: dir };
return false;
}
}
function* make_maze(x,y,depth,dir) {
yield { action: 'move', x: x, y: y, dir: dir };
// remove the wall where we entered
remove_wall(x,y,reverse_dirs[dir]);
// record backtracking
backtracks[x][y] = reverse_dirs[dir];
// update max depth
if (depth>maxdepth) maxdepth=depth;
depths[x][y]=depth;
var i,j,k,new_dir,straightness;
var lr=(Math.random()>=right_preference ? 0 : 1);
// straightness is a number from 0 to 2, with "0" being
// straight first, "1" straight second, and "2" straight
// last. straight_preference is between -1 and 1, with
// -1 being very straight, 0 being neutral, and 1 being
// very curvy. We'll use the beta function to come up
// with some numbers for this.
if (straight_preference < 0.0) {
straightness=get_straightness(-straight_preference);
} else if (straight_preference > 0.0) {
straightness=2-get_straightness(straight_preference);
} else {
straightness=Math.floor(Math.random()*2.999999);
}
for (new_dir of perms[dir][straightness][lr]) {
i=x+deltax[new_dir];
j=y+deltay[new_dir];
// it should always be in bounds, this is a sanity check
if (in_bounds(i,j)) {
if (unvisited(i,j)) {
yield* make_maze(i,j,depth+1,new_dir);
yield { action: 'backtrack', x: x, y: y };
} else {
//yield { action: 'try', x: i, y: j };
}
}
}
}
function in_bounds(x,y) {
return (x>=0 && x<xsize && y>=0 && y<ysize);
}
function four_walls(x,y) {
var ret = new Array(4);
for (var dir=0; dir<4; dir++) {
ret[dir] = get_wall(x,y,dir);
}
return ret;
}
function four_walls_as_integer(x,y) {
var ret = 0;
var fw_arr = four_walls(x,y);
for (var dir=0; dir<4; dir++) {
if (fw_arr[dir]) ret |= 1<<dir;
}
return ret;
}
function unvisited(x,y) {
return four_walls(x,y).every(t => t);
}
function get_wall(x,y,dir) {
wall_type = wall_types[dir];
return walls[wall_type][x+wall_offsets[wall_type]['x'][dir]][y+wall_offsets[wall_type]['y'][dir]];
}
function set_wall(x,y,dir,val) {
wall_type = wall_types[dir];
walls[wall_type][x+wall_offsets[wall_type]['x'][dir]][y+wall_offsets[wall_type]['y'][dir]] = val;
}
function remove_wall(x,y,dir) {
set_wall(x,y,dir,false);
}
// seed is 0 -> 1. At 0, we have a regular distribution and at 1
// we have a distribution completely weighted toward 0. Simply, at
// 0 the cutoffs are at 1/3 and 2/3, since 2/3 is half way between
// 1/3 and 1. At .5, the first cutoff is 2/3 and the second is
// 11/12.
// cutoff2 is .5 of remaining space when seed is 0 and 0 of
// remaining space when seed is 1.
function get_straightness(seed) {
var cutoff1 = .333333333 + seed*.666666666
var rnd = Math.random();
if (rnd<cutoff1) {
return 0;
} else {
var cutoff2 = 1.0 - (1.0 - cutoff1) * (.5-seed*.5);
if (rnd<cutoff2) {
return 1;
} else {
return 2;
}
}
}
function test_get_straightness() {
var counts = new Array(11);
for (var seed=0; seed<=10; seed++) {
these_counts = [0,0,0];
for (var x=0; x<50000; x++) {
var straightness = get_straightness(seed/10.0);
these_counts[straightness] += 1;
}
counts[Math.floor(seed)] = these_counts;
}
console.log(counts);
}
function create_table_cells(table, xsize, ysize) {
for (var y=0; y<ysize; y++) {
var tr = document.createElement('tr');
tr.id = 'row_' + y;
tr.className = 'row_' + y;
for (var x=0; x<xsize; x++) {
var td = document.createElement('td');
td.id = 'cell_' + x + '_' + y;
td.className = 'row_' + y + ' col_' + x;
for (var dir=0; dir<4; dir++) {
if (get_wall(x,y,dir)) {
td.classList.add('wall_' + dir);
}
}
tr.appendChild(td);
}
table.appendChild(tr);
}
}
function td_at(x,y) {
return document.getElementById('cell_' + x + '_' + y);
}
function display_maze(table, xsize, ysize, walls, backtracks, depths) {
for (var x=0; x<xsize; x++) {
for (var y=0; y<ysize; y++) {
var td = td_at(x,y);
for (var dir=0; dir<4; dir++) {
if (get_wall(x,y,dir)) {
td.classList.add('wall_' + dir);
}
}
if (show_backtracks) {
td.classList.add('backtrack_' + backtracks[x][y]);
}
}
}
}
function clear_walls() {
// Create the horizontal walls, all set to "true" except
// first and last
walls = { 'h': false, 'v': false };
walls['h'] = new Array(ysize+1);
for (var x=0 ; x<xsize ; x++) {
walls['h'][x] = new Array(ysize+1).fill(false);
}
// Create the vertical walls, all set to "true" except first
walls['v'] = new Array(xsize+1);
// and last
for (var x=0 ; x<xsize+1 ; x++) {
walls['v'][x] = new Array(ysize).fill(false);
}
}
function set_initial_walls() {
// horizontal walls
for (var x=1 ; x<xsize-1 ; x++) {
for (var y=1 ; y<ysize ; y++) {
walls['h'][x][y] = true;
}
}
// vertical walls
for (var x=1 ; x<xsize ; x++) {
for (var y=1 ; y<ysize-1 ; y++) {
walls['v'][x][y] = true;
}
}
}
function* make_and_solve_maze_generator() {
yield* make_maze(startx, starty, 0, start_direction);
yield {action: 'open_end', x: endx, y: endy, dir: end_direction};
yield {action: 'solve', x: endx, y: endy, dir: end_direction};
yield* solve_maze(endx+deltax[end_direction], endy+deltay[end_direction], end_direction, startx, starty);
}
function init() {
maxdepth=0;
for (var x=0 ; x<xsize ; x++) {
depths[x] = new Array(ysize);
}
for (var x=0 ; x<xsize ; x++) {
backtracks[x] = new Array(ysize);
}
clear_walls();
set_initial_walls();
var table = document.getElementById('maze');
create_table_cells(table, xsize, ysize);
var last_x=null, last_y=null;
var last_try_x=null, last_try_y=null;
var completely_done = false;
var maze_generator = make_and_solve_maze_generator();
var interval_id = null;
var delay = 100.0;
function stop_interval() {
if (interval_id !== null) {
clearInterval(interval_id);
interval_id = null;
}
}
function change_interval(delay) {
stop_interval();
interval_id = setInterval(do_next, delay);
}
function do_next() {
var next_item = maze_generator.next();
if (next_item.done) {
if (interval_id) {
stop_interval();
}
} else {
var action = next_item.value;
handle_action(action);
}
}
function handle_action(action) {
//console.log(action);
switch(action.action) {
case 'move':
remove_outbound_wall(last_x, last_y, action.dir);
remove_inbound_wall(action.x, action.y, action.dir);
set_backtrack(action.x, action.y, action.dir);
update_current(action.x, action.y);
break;
case 'try':
update_try(action.x, action.y);
break;
case 'backtrack':
update_current(action.x, action.y);
break;
case 'open_end':
remove_try();
remove_current();
remove_outbound_wall(action.x, action.y, action.dir);
remove_inbound_wall(action.x+deltax[action.dir], action.y+deltay[action.dir], action.dir);
break;
case 'solve':
set_solution(action.x, action.y);
break;
case 'solve-done':
remove_current();
break;
case 'solve-backtrack':
set_no_solution(action.x, action.y);
break;
}
function remove_outbound_wall(x,y,dir) {
if (x!==null && y!==null) {
var td = td_at(x,y);
td.classList.remove('wall_' + dir);
}
}
function remove_inbound_wall(x,y,dir) {
remove_outbound_wall(x,y,reverse_dirs[dir]);
}
function set_backtrack(x,y,dir) {
var td = td_at(x,y);
td.classList.add('backtrack_' + reverse_dirs[dir]);
}
function remove_try() {
if (last_try_x!==null && last_try_y!==null) {
var last_try_td = td_at(last_try_x, last_try_y);
last_try_td.classList.remove('testing');
last_try_x=null;
last_try_y=null;
}
}
function update_try(x,y) {
remove_try();
last_try_x=x;
last_try_y=y;
var td = td_at(x,y);
td.classList.add('testing');
}
function remove_current() {
if (last_x!==null && last_y!==null) {
var last_td = td_at(last_x, last_y);
last_td.classList.remove('current');
last_x = null;
last_y = null;
}
}
function update_current(x,y) {
remove_try();
remove_current();
last_x=x;
last_y=y;
var td = td_at(x,y);
td.classList.add('current');
}
function set_solution(x,y) {
remove_current();
last_x=x;
last_y=y;
var td = td_at(x,y);
td.classList.add('current');
td.classList.add('solution');
}
function set_no_solution(x,y) {
remove_current();
last_x=x;
last_y=y;
var td = td_at(x,y);
td.classList.add('current');
td.classList.remove('solution');
td.classList.add('no-solution');
}
}
var speeder = document.getElementById('speed');
speeder.addEventListener('input', function(ev) {
var speed = parseFloat(speeder.value);
//console.log("Speed: " + speed);
if (speed > 0.0) {
delay = 1000.0 / speed;
change_interval(delay);
} else {
stop_interval();
}
});
}
add_body_onload(init);
</script>
</head>
<body>
<div id="wrap">
<p>
This is a recursive backtracker demonstration.
The maze is set in a square grid using an HTML table
for display. Parameters are xsize, ysize, l for left/right
preference (0 left, 1 right), and s for straightness preference
(-1 really straight, 0 normal, 1 really curvy).
</p>
<input type="range" id="speed" min="0" max="1000.0" step="1" value="0" list="tickmarks">
<datalist id="tickmarks">
<option value="0" label="0"></option>
<option value="250" label="250"></option>
<option value="500" label="500"></option>
<option value="750" label="750"></option>
<option value="1000" label="1000"></option>
</datalist>
<table id="maze" class="maze" cellspacing="0">
</table>
</div>
</body>
</html>