Bound the frontier. I.e., do beam search.

[slidingtile] / sliding_tile_lib.cc

diff --git a/sliding_tile_lib.cc b/sliding_tile_lib.cc
index 6b42f284690069e13f0f2371aeb6525018fa0674..5a4114bd89c6ab621ddec79db2476ef8e0665494 100644 (file)
--- a/sliding_tile_lib.cc
+++ b/sliding_tile_lib.cc
@@ -2,11 +2,18 @@
 
 #include <cstdlib>
 #include <istream>
+#include <map>
 #include <memory>
 #include <ostream>
+#include <queue>
+#include <set>
+#include <sstream>
 #include <stdexcept>
 #include <vector>
 
+#include <iostream>
+
+int Step::count = 0;
 signed char Step::adjacent[BOARD_SIZE][5] = {
   1,   4,   -1,  -1,  -1,
   0,   2,   5,   -1,  -1,
@@ -62,6 +69,17 @@ bool Board::operator!=(const Board& o) const {
   return !operator==(o);
 }
 
+bool Board::operator<(const Board& o) const {
+  for (int i = 0; i < BOARD_SIZE; i++) {
+    if (board[i] < o.board[i]) {
+      return true;
+    } else if (board[i] > o.board[i]) {
+      return false;
+    }
+  }
+  return false;
+}
+
 std::istream& operator>>(std::istream& is, Board& board) {
   for (int i = 0; i < BOARD_SIZE; i++) {
     if (!is.good()) {
@@ -116,22 +134,43 @@ int Board::distance(const Board& o) const {
 int Board::distance(const InvertedBoard& invo) const {
   int dist = 0;
   for (int i = 0; i < BOARD_SIZE; i++) {
-    dist += std::abs(i % BOARD_DIM - invo.pos[board[i]] % BOARD_DIM) +
-            std::abs(i / BOARD_DIM - invo.pos[board[i]] / BOARD_DIM);
+    if (board[i] != 0) {
+      dist += std::abs(i % BOARD_DIM - invo.pos[board[i]] % BOARD_DIM) +
+              std::abs(i / BOARD_DIM - invo.pos[board[i]] / BOARD_DIM);
+    }
   }
   return dist;
 }
 
-std::vector<Step*> Step::successors(std::shared_ptr<Step> shared_this) {
-  std::vector<Step*> suc;
+Step::Step(Board board, std::shared_ptr<Step> prev) : board(board), prev(prev) {
+  count++;
+}
+
+Step::~Step() {
+  count--;
+}
+
+std::vector<std::shared_ptr<Step>> Step::successors(std::shared_ptr<Step> shared_this) const {
+  std::vector<std::shared_ptr<Step>> suc;
   signed char hole_pos = board.hole();
-  for (int i = 0; adjacent[hole_pos][i] > 0; i++) {
-    suc.emplace_back(new Step{board, shared_this});
+  for (int i = 0; adjacent[hole_pos][i] >= 0; i++) {
+    suc.emplace_back(std::make_shared<Step>(board, shared_this));
     std::swap(suc.back()->board.board[hole_pos], suc.back()->board.board[adjacent[hole_pos][i]]);
   }
   return suc;
 }
 
+int Step::length() const {
+  if (prev.get() == nullptr) {
+    return 0;
+  }
+  return 1 + prev->length();
+}
+
+int Step::cost(const InvertedBoard& invgoal) const {
+  return length() + board.distance(invgoal) / 2;
+}
+
 std::ostream& operator<<(std::ostream& os, const Step& step) {
   if (step.prev != nullptr) {
     os << *step.prev;
@@ -149,3 +188,51 @@ std::ostream& operator<<(std::ostream& os, const Step& step) {
   }
   return os;
 }
+
+std::shared_ptr<Step> find_path(const std::string& start, const std::string& goal, unsigned max_frontier) {
+  std::istringstream iss_start{start}, iss_goal{goal};
+  Board board_start, board_goal;
+  iss_start >> board_start;
+  iss_goal >> board_goal;
+  if (iss_start.fail() || !iss_start.eof()) {
+    throw std::runtime_error("Could not parse the start board: " + start);
+  }
+  if (iss_goal.fail() || !iss_goal.eof()) {
+    throw std::runtime_error("Could not parse the goal board: " + goal);
+  }
+  return find_path(board_start, board_goal, max_frontier);
+}
+
+std::shared_ptr<Step> find_path(const Board& start, const Board& goal, unsigned max_frontier) {
+  InvertedBoard invgoal = goal.invert();
+  std::multimap<int, std::shared_ptr<Step>> todo;
+  std::set<Board> seen;
+
+  seen.insert(start);
+  auto start_step = std::make_shared<Step>(start, nullptr);
+  todo.emplace(start_step->cost(invgoal), start_step);
+  while (!todo.empty()) {
+    auto cur = todo.begin()->second;
+    todo.erase(todo.begin());
+    if (cur->board == goal) {
+      return cur;
+    }
+    std::vector<std::shared_ptr<Step>> successors = cur->successors(cur);
+    for (const std::shared_ptr<Step>& s : successors) {
+      if (seen.find(s->board) == seen.end()) {
+        seen.insert(s->board);
+        todo.emplace(s->cost(invgoal), s);
+        if (seen.size() % 10000 == 0) {
+          std::cerr << "Examined " << seen.size() << " boards.  Tracking "
+                    << Step::count << " steps.  " << todo.size()
+                    << " waiting.  Considering paths of length "
+                    << cur->cost(invgoal) << std::endl;
+        }
+      }
+    }
+    while (todo.size() > max_frontier) {
+      todo.erase(--todo.end());
+    }
+  }
+  throw std::runtime_error("No path from start to goal");
+}