Random Search II

This maze is generated using Wilson’s algorithm and then solved using random search. Compare to best-first search. See random search on a maze generated using random traversal.

<!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 = [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 = popRandom(frontier),
      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(width, height) {
  var cells = new Array(width * height), // each cell’s edge bits
      remaining = d3.range(width * height), // cell indexes to visit
      previous = new Array(width * height); // current random walk

// Add the starting cell.
  var start = remaining.pop();
  cells[start] = 0;

// While there are remaining cells,
  // add a loop-erased random walk to the maze.
  while (!loopErasedRandomWalk());

return cells;

function loopErasedRandomWalk() {
    var direction,
        index0,
        index1,
        i,
        j;

// Pick a location that’s not yet in the maze (if any).
    do if ((index0 = remaining.pop()) == null) return true;
    while (cells[index0] >= 0);

// Perform a random walk starting at this location,
    previous[index0] = index0;
    while (true) {
      i = index0 % width;
      j = index0 / width | 0;

// picking a legal random direction at each step.
      direction = Math.random() * 4 | 0;
      if (direction === 0) { if (j <= 0) continue; --j; }
      else if (direction === 1) { if (j >= height - 1) continue; ++j; }
      else if (direction === 2) { if (i <= 0) continue; --i; }
      else { if (i >= width - 1) continue; ++i; }

// If this new cell was visited previously during this walk,
      // erase the loop, rewinding the path to its earlier state.
      // Otherwise, just add it to the walk.
      index1 = j * width + i;
      if (previous[index1] >= 0) eraseWalk(index0, index1);
      else previous[index1] = index0;
      index0 = index1;

// If this cell is part of the maze, we’re done walking.
      if (cells[index1] >= 0) {

// Add the random walk to the maze by backtracking to the starting cell.
        // Also erase this walk’s history to not interfere with subsequent walks.
        while ((index0 = previous[index1]) !== index1) {
          direction = index1 - index0;
          if (direction === 1) cells[index0] |= E, cells[index1] |= W;
          else if (direction === -1) cells[index0] |= W, cells[index1] |= E;
          else if (direction < 0) cells[index0] |= N, cells[index1] |= S;
          else cells[index0] |= S, cells[index1] |= N;
          previous[index1] = NaN;
          index1 = index0;
        }

previous[index1] = NaN;
        return;
      }
    }
  }

function eraseWalk(index0, index1) {
    var index;
    while ((index = previous[index0]) !== index1) previous[index0] = NaN, index0 = index;
    previous[index0] = NaN;
  }
}

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>

https://d3js.org/d3.v3.min.js