Breadth-First Search

1Queue<Integer> queue = new ArrayDeque<>();  // Frontier of cells to visit2queue.add(start); visited[start] = true;  // Seed with the start cell3while (!queue.isEmpty()) {  // Until frontier is empty4  int node = queue.poll();  // Take oldest queued cell5  if (node == goal) return buildPath();  // Goal found — trace path6  for (int neighbor : neighbors(node))  // Scan passable neighbors7    if (!visited[neighbor]) {  // Skip already-seen cells8      visited[neighbor] = true; parent[neighbor] = node;  // Mark and record parent9      queue.add(neighbor);  // Enqueue for later10    }11}12 13List<Integer> neighbors(int cell) {  // Passable 4-neighbors14  int r = cell / COLS, c = cell % COLS;15  int[][] dirs = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};16  List<Integer> out = new ArrayList<>();17  for (int[] d : dirs) {18    int nr = r + d[0], nc = c + d[1];19    if (nr < 0 || nr >= ROWS || nc < 0 || nc >= COLS) continue;20    int nbr = nr * COLS + nc;21    if (!walls.contains(nbr)) out.add(nbr);22  }23  return out;24}25 26List<Integer> buildPath() {  // Walk parent back from goal27  List<Integer> path = new ArrayList<>();28  for (int at = goal; at != -1; at = parent[at]) path.add(at);29  Collections.reverse(path);30  return path;31}