This maze is generated using random traversal, and then solved using best-first search. Compare to random search. See best-first search on a maze generated using Wilson’s algorithm.
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Best-First Search
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| license: gpl-3.0 | |
| redirect: https://observablehq.com/@mbostock/best-first-search |
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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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