趣味编程：用BGL求解八数码问题（A*）
代码
#include <algorithm> #include <iostream> #include <list> #include "nonconst_bfs.hpp" // so we can modify the graph #include <boost/graph/astar_search.hpp> #include <boost/graph/adjacency_list.hpp> #include <boost/bimap.hpp> #include <boost/foreach.hpp> #include <boost/optional.hpp> using namespace boost; using namespace std; class pstate_t : public vector<int> { public: int m_r, m_c; optional<char> m_dir; pstate_t() {} pstate_t(int rows, int cols) : vector<int>(m_r * m_c), m_r(rows), m_c(cols) {} template <class I> pstate_t(int rows, int cols, I beg, I end) : vector<int>(beg, end), m_r(rows), m_c(cols) {} inline int get(int r, int c) const { return operator[](cell(r, c)); } inline void move(int i, int j, char dir) { int tmp = operator[](i); operator[](i) = operator[](j); operator[](j) = tmp; m_dir = dir; } // find offset of coordinates inline int cell(int r, int c) const { return r * m_c + c; } // find coordinates of an offset inline void coords(int i, int &r, int &c) const { r = i / m_c; c = i % m_c; } }; ostream & operator<<(ostream &out, const pstate_t &p) { if(p.m_dir) out << "move: " << *p.m_dir << endl; for(int i = 0; i < p.m_r; ++i) { for(int j = 0; j < p.m_c; ++j) { if(p.get(i, j) > 0) out << p.get(i, j) << " "; else out << " "; } out << endl; } return out; } void gen_children(const pstate_t &p, list<pstate_t> &children) { pstate_t::const_iterator i = find(p.begin(), p.end(), 0); int sr, sc, soff = i - p.begin(); p.coords(soff, sr, sc); if(sc > 0) { // move tile to left of space children.push_back(p); children.back().move(soff, p.cell(sr, sc - 1), 'w'); } if(sc < p.m_c - 1) { // move tile to right of space children.push_back(p); children.back().move(soff, p.cell(sr, sc + 1), 'e'); } if(sr > 0) { // move tile above space children.push_back(p); children.back().move(soff, p.cell(sr - 1, sc), 'n'); } if(sr < p.m_r - 1) { // move tile below space children.push_back(p); children.back().move(soff, p.cell(sr + 1, sc), 's'); } } typedef property<vertex_color_t, default_color_type, property<vertex_rank_t, unsigned int, property<vertex_distance_t, unsigned int, property<vertex_predecessor_t, unsigned int> > > > vert_prop; typedef property<edge_weight_t, unsigned int> edge_prop; typedef adjacency_list<listS, vecS, undirectedS, vert_prop, edge_prop> mygraph_t; typedef mygraph_t::vertex_descriptor vertex_t; typedef mygraph_t::vertex_iterator vertex_iterator_t; typedef bimap<vertex_t, pstate_t> StateMap; typedef property_map<mygraph_t, edge_weight_t>::type WeightMap; typedef property_map<mygraph_t, vertex_predecessor_t>::type PredMap; typedef property_map<mygraph_t, vertex_distance_t>::type DistMap; struct found_goal {}; template <class VisitorType> class puz_visitor : public VisitorType { public: puz_visitor(pstate_t &goal, list<vertex_t> &seq, StateMap &smap) : m_goal(goal), m_seq(seq), m_smap(smap) {} template <class Vertex, class Graph> void examine_vertex(Vertex u, Graph& g) { m_seq.push_back(u); VisitorType::examine_vertex(u, g); DistMap dmap = get(vertex_distance_t(), g); // check for goal const pstate_t& cur = m_smap.left.at(u); if(cur == m_goal) throw found_goal(); // add successors of this state list<pstate_t> children; gen_children(cur, children); BOOST_FOREACH(pstate_t& child, children) { // make sure this state is new try{ vertex_t v = m_smap.right.at(child); //add_edge(u, v, edge_prop(1), g); } catch(out_of_range&) { vertex_t v = add_vertex(vert_prop(white_color), g); m_smap.insert(StateMap::relation(v, child)); dmap[v] = numeric_limits<unsigned int>::max(); add_edge(u, v, edge_prop(1), g); } } } private: pstate_t &m_goal; list<vertex_t> &m_seq; StateMap &m_smap; }; // manhattan distance heuristic class manhattan_dist : public astar_heuristic<mygraph_t, unsigned int> { public: manhattan_dist(pstate_t &goal, StateMap &smap) : m_goal(goal), m_smap(smap) {} unsigned int operator()(vertex_t u) { unsigned int md = 0; pstate_t::const_iterator i, j; int ir, ic, jr, jc; const pstate_t& cur = m_smap.left.at(u); for(i = cur.begin(); i != cur.end(); ++i) { j = find(m_goal.begin(), m_goal.end(), *i); cur.coords(i - cur.begin(), ir, ic); m_goal.coords(j - m_goal.begin(), jr, jc); md += myabs(jr - ir) + myabs(jc - ic); } return md; } private: pstate_t &m_goal; StateMap &m_smap; inline unsigned int myabs(int i) { return static_cast<unsigned int>(i < 0 ? -i : i); } }; int main(int argc, char **argv) { mygraph_t g; list<vertex_t> examine_seq; StateMap smap; vertex_t start = add_vertex(vert_prop(white_color), g); //int sstart[] = {2, 8, 3, 1, 6, 4, 7, 0, 5}; // 5 steps //int sstart[] = {2, 1, 6, 4, 0, 8, 7, 5, 3}; // 18 steps //int sgoal[] = {1, 2, 3, 8, 0, 4, 7, 6, 5}; int sstart[] = {7, 5, 6, 8, 3, 2, 4, 0, 1}; // 23 steps int sgoal[] = {1, 2, 3, 4, 5, 6, 7, 8, 0}; smap.insert(StateMap::relation(start, pstate_t(3, 3, &sstart[0], &sstart[9]))); pstate_t psgoal(3, 3, &sgoal[0], &sgoal[9]); cout << "Start state:" << endl << smap.left.at(start) << endl; cout << "Goal state:" << endl << psgoal << endl; try { puz_visitor<default_astar_visitor> vis(psgoal, examine_seq, smap); astar_search(g, start, manhattan_dist(psgoal, smap), visitor(vis).color_map(get(vertex_color, g)). rank_map(get(vertex_rank, g)). distance_map(get(vertex_distance, g)). predecessor_map(get(vertex_predecessor, g))); } catch(found_goal&) { PredMap p = get(vertex_predecessor, g); list<vertex_t> shortest_path; for(vertex_t v = examine_seq.back();; v = p[v]) { shortest_path.push_front(v); if(p[v] == v) break; } cout << "Sequence of moves:" << endl; BOOST_FOREACH(vertex_t v, shortest_path) cout << smap.left.at(v) << endl; cout << "Number of moves: " << shortest_path.size() - 1 << endl; cout << "Number of vertices examined: " << examine_seq.size() << endl; } return 0; }