趣味编程：用IDA*算法求解八数码问题
#include <iostream> #include <list> #include <string> #include <tuple> #include <algorithm> #include <boost/foreach.hpp> using namespace std; typedef pair<int, int> Position; inline Position operator+(const Position& p1, const Position& p2) { return Position(p1.first + p2.first, p1.second + p2.second); } inline unsigned int myabs(int i) { return static_cast<unsigned int>(i < 0 ? -i : i); } Position offset[] = { Position(0, -1), Position(0, 1), Position(-1, 0), Position(1, 0), }; struct puz_game { Position m_size; string m_start, m_goal; Position m_space; puz_game(int r, int c, const string& start, const string& goal); int rows() const {return m_size.first;} int cols() const {return m_size.second;} }; puz_game::puz_game(int r, int c, const string& start, const string& goal) : m_size(r, c) , m_start(start) , m_goal(goal) { int n = m_start.find(' '); m_space = Position(n / cols(), n % cols()); } struct puz_state : string { puz_state() {} puz_state(const puz_game& g) : string(g.m_start), m_game(&g), m_space(g.m_space), m_move(0) {} int rows() const {return m_game->rows();} int cols() const {return m_game->cols();} char cell(int r, int c) const {return at(r * cols() + c);} char& cell(const Position& p) {return (*this)[p.first * cols() + p.second];} bool is_valid(const Position& p) const { return p.first >= 0 && p.first < rows() && p.second >= 0 && p.second < cols(); } void make_move(const Position& p, char move){ cell(m_space) = cell(p); cell(m_space = p) = ' '; m_move = move; } //puz_solver_idastar interface bool is_goal_state() const {return *this == m_game->m_goal;} void gen_children(list<puz_state>& children) const; unsigned int get_heuristic() const; unsigned int get_distance(const puz_state& child) const {return 1;} const puz_game* m_game; Position m_space; char m_move; }; void puz_state::gen_children(list<puz_state> &children) const { char* moves = "wens"; for(int i = 0; i < 4; ++i){ Position p = m_space + offset[i]; if(is_valid(p)){ children.push_back(*this); children.back().make_move(p, moves[i]); } } } unsigned int puz_state::get_heuristic() const { unsigned int md = 0; for(size_t i = 0; i < size(); ++i) { size_t j = m_game->m_goal.find(at(i)); md += myabs(j / cols() - i / cols()) + myabs(j % cols() - i % cols()); } return md; } ostream& operator<<(ostream& out, const puz_state& s) { if(s.m_move) out << "move: " << s.m_move << endl; for(int r = 0; r < s.rows(); ++r) { for(int c = 0; c < s.cols(); ++c) out << s.cell(r, c) << ' '; out << endl; } return out; } template<class puz_state> class puz_solver_idastar { static bool dfs(unsigned int start_cost, const puz_state& cur, unsigned int cost_limit, unsigned int& next_cost_limit, list<puz_state>& spath, size_t& examined) { ++examined; unsigned int minimum_cost = start_cost + cur.get_heuristic(); if(minimum_cost > cost_limit) return next_cost_limit = min(next_cost_limit, minimum_cost), false; if(cur.is_goal_state()) return next_cost_limit = cost_limit, true; list<puz_state> children; cur.gen_children(children); BOOST_FOREACH(const puz_state& child, children){ // full cycle checking if(find(spath.begin(), spath.end(), child) != spath.end()) continue; unsigned int new_start_cost = start_cost + cur.get_distance(child); spath.push_back(child); bool found = dfs(new_start_cost, child, cost_limit, next_cost_limit, spath, examined); if(found) return true; spath.pop_back(); } return false; } public: static pair<bool, size_t> find_solution(const puz_state& sstart, list<puz_state>& spath) { unsigned int inf = numeric_limits<unsigned int>::max(); unsigned int cost_limit = sstart.get_heuristic(), next_cost_limit = inf; size_t examined = 0; spath.assign(1, sstart); for(;;){ bool found = dfs(0, sstart, cost_limit, next_cost_limit, spath, examined); if(found) return make_pair(true, examined); if(next_cost_limit == inf) return make_pair(false, examined); cost_limit = next_cost_limit, next_cost_limit = inf; } } }; int main() { // start state // 2 8 3 // 1 6 4 // 7 5 // goal state // 1 2 3 // 8 4 // 7 6 5 puz_game g(3, 3, "2831647 5", "1238 4765"); list<puz_state> spath; bool found; size_t examined; tie(found, examined) = puz_solver_idastar<puz_state>::find_solution(g, spath); if(found){ cout << "Sequence of moves: " << endl; BOOST_FOREACH(const puz_state& s, spath) cout << s; cout << "Number of moves: " << spath.size() - 1 << endl; } cout << "Number of states examined: " << examined << endl; } /* Sequence of moves: 2 8 3 1 6 4 7 5 move: n 2 8 3 1 4 7 6 5 move: n 2 3 1 8 4 7 6 5 move: w 2 3 1 8 4 7 6 5 move: s 1 2 3 8 4 7 6 5 move: e 1 2 3 8 4 7 6 5 Number of moves: 5 Number of states examined: 19 */