This maze is generated using random traversal, and then solved using “better-only search”, a variation of best-first search that only considers passages that move monotonically towards the goal (North and East). This algorithm typically fails.
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February 9, 2016 01:55
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license: gpl-3.0 |
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<!DOCTYPE html> | |
<meta charset="utf-8"> | |
<style> | |
body { | |
background: #000; | |
} | |
</style> | |
<body> | |
<script src="//d3js.org/d3.v3.min.js"></script> | |
<script> | |
var width = 960, | |
height = 500; | |
var N = 1 << 0, | |
S = 1 << 1, | |
W = 1 << 2, | |
E = 1 << 3; | |
var cellSize = 4, | |
cellSpacing = 4, | |
cellWidth = Math.floor((width - cellSpacing) / (cellSize + cellSpacing)), | |
cellHeight = Math.floor((height - cellSpacing) / (cellSize + cellSpacing)), | |
cells = generateMaze(cellWidth, cellHeight), // each cell’s edge bits | |
parent = new Array(cellHeight * cellWidth), // path tracking | |
minScore = Infinity, | |
minIndex = (cellHeight - 1) * cellWidth, | |
goalX = cellWidth - 1, | |
goalY = 0, | |
frontier = minHeap(function(a, b) { return score(a) - score(b); }); | |
frontier.push(minIndex); | |
parent[minIndex] = null; | |
var canvas = d3.select("body").append("canvas") | |
.attr("width", width) | |
.attr("height", height); | |
var context = canvas.node().getContext("2d"); | |
context.translate( | |
Math.round((width - cellWidth * cellSize - (cellWidth + 1) * cellSpacing) / 2), | |
Math.round((height - cellHeight * cellSize - (cellHeight + 1) * cellSpacing) / 2) | |
); | |
context.fillStyle = "#fff"; | |
for (var y = 0, i = 0; y < cellHeight; ++y) { | |
for (var x = 0; x < cellWidth; ++x, ++i) { | |
fillCell(i); | |
if (cells[i] & S) fillSouth(i); | |
if (cells[i] & E) fillEast(i); | |
} | |
} | |
context.fillStyle = "#777"; | |
d3.timer(function() { | |
for (var i = 0; i < 10; ++i) { | |
if (exploreFrontier()) { | |
return true; | |
} | |
} | |
}); | |
function exploreFrontier() { | |
var i0 = frontier.pop(), | |
i1, | |
s0 = score(i0); | |
fillCell(i0); | |
if (s0 < minScore) { | |
fillPath(minIndex); | |
context.fillStyle = "magenta"; | |
minScore = s0, minIndex = i0; | |
fillPath(minIndex); | |
context.fillStyle = "#777"; | |
if (!s0) return true; | |
} | |
if (cells[i0] & E && isNaN(parent[i1 = i0 + 1])) parent[i1] = i0, fillEast(i0), frontier.push(i1); | |
// if (cells[i0] & W && isNaN(parent[i1 = i0 - 1])) parent[i1] = i0, fillEast(i1), frontier.push(i1); | |
// if (cells[i0] & S && isNaN(parent[i1 = i0 + cellWidth])) parent[i1] = i0, fillSouth(i0), frontier.push(i1); | |
if (cells[i0] & N && isNaN(parent[i1 = i0 - cellWidth])) parent[i1] = i0, fillSouth(i1), frontier.push(i1); | |
} | |
function fillPath(i1) { | |
while (true) { | |
fillCell(i1); | |
var i0 = parent[i1]; | |
if (i0 == null) break; | |
(Math.abs(i0 - i1) === 1 ? fillEast : fillSouth)(Math.min(i0, i1)); | |
i1 = i0; | |
} | |
} | |
function score(i) { | |
var x = goalX - (i % cellWidth), y = goalY - (i / cellWidth | 0); | |
return x * x + y * y; | |
} | |
function fillCell(i) { | |
var x = i % cellWidth, y = i / cellWidth | 0; | |
context.fillRect(x * cellSize + (x + 1) * cellSpacing, y * cellSize + (y + 1) * cellSpacing, cellSize, cellSize); | |
} | |
function fillEast(i) { | |
var x = i % cellWidth, y = i / cellWidth | 0; | |
context.fillRect((x + 1) * (cellSize + cellSpacing), y * cellSize + (y + 1) * cellSpacing, cellSpacing, cellSize); | |
} | |
function fillSouth(i) { | |
var x = i % cellWidth, y = i / cellWidth | 0; | |
context.fillRect(x * cellSize + (x + 1) * cellSpacing, (y + 1) * (cellSize + cellSpacing), cellSize, cellSpacing); | |
} | |
function generateMaze(cellWidth, cellHeight) { | |
var cells = new Array(cellWidth * cellHeight), | |
frontier = [], | |
startIndex = (cellHeight - 1) * cellWidth; | |
cells[startIndex] = 0; | |
frontier.push({index: startIndex, direction: N}); | |
frontier.push({index: startIndex, direction: E}); | |
while ((edge = popRandom(frontier)) != null) { | |
var edge, | |
i0 = edge.index, | |
d0 = edge.direction, | |
i1 = i0 + (d0 === N ? -cellWidth : d0 === S ? cellWidth : d0 === W ? -1 : +1), | |
x0 = i0 % cellWidth, | |
y0 = i0 / cellWidth | 0, | |
x1, | |
y1, | |
d1, | |
open = cells[i1] == null; // opposite not yet part of the maze | |
if (d0 === N) x1 = x0, y1 = y0 - 1, d1 = S; | |
else if (d0 === S) x1 = x0, y1 = y0 + 1, d1 = N; | |
else if (d0 === W) x1 = x0 - 1, y1 = y0, d1 = E; | |
else x1 = x0 + 1, y1 = y0, d1 = W; | |
if (open) { | |
cells[i0] |= d0, cells[i1] |= d1; | |
if (y1 > 0 && cells[i1 - cellWidth] == null) frontier.push({index: i1, direction: N}); | |
if (y1 < cellHeight - 1 && cells[i1 + cellWidth] == null) frontier.push({index: i1, direction: S}); | |
if (x1 > 0 && cells[i1 - 1] == null) frontier.push({index: i1, direction: W}); | |
if (x1 < cellWidth - 1 && cells[i1 + 1] == null) frontier.push({index: i1, direction: E}); | |
} | |
} | |
return cells; | |
} | |
function minHeap(compare) { | |
var heap = {}, | |
array = [], | |
size = 0; | |
heap.empty = function() { | |
return !size; | |
}; | |
heap.push = function(value) { | |
up(array[size] = value, size++); | |
return size; | |
}; | |
heap.pop = function() { | |
if (size <= 0) return; | |
var removed = array[0], value; | |
if (--size > 0) value = array[size], down(array[0] = value, 0); | |
return removed; | |
}; | |
function up(value, i) { | |
while (i > 0) { | |
var j = ((i + 1) >> 1) - 1, | |
parent = array[j]; | |
if (compare(value, parent) >= 0) break; | |
array[i] = parent; | |
array[i = j] = value; | |
} | |
} | |
function down(value, i) { | |
while (true) { | |
var r = (i + 1) << 1, | |
l = r - 1, | |
j = i, | |
child = array[j]; | |
if (l < size && compare(array[l], child) < 0) child = array[j = l]; | |
if (r < size && compare(array[r], child) < 0) child = array[j = r]; | |
if (j === i) break; | |
array[i] = child; | |
array[i = j] = value; | |
} | |
} | |
return heap; | |
} | |
function popRandom(array) { | |
if (!array.length) return; | |
var n = array.length, i = Math.random() * n | 0, t; | |
t = array[i], array[i] = array[n - 1], array[n - 1] = t; | |
return array.pop(); | |
} | |
</script> |
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