趣味编程：用BGL求解八数码问题（A*）

 

A* Graph Search Within the BGL Framework

 

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 coordinatesinline int cell(int r, int c) const {return r * m_c + c;}// find coordinates of an offsetinline 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) << " ";elseout << " ";}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 spacechildren.push_back(p);children.back().move(soff, p.cell(sr, sc - 1), 'w');}if(sc < p.m_c - 1) { // move tile to right of spacechildren.push_back(p);children.back().move(soff, p.cell(sr, sc + 1), 'e');}if(sr > 0) { // move tile above spacechildren.push_back(p);children.back().move(soff, p.cell(sr - 1, sc), 'n');}if(sr < p.m_r - 1) { // move tile below spacechildren.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 goalconst pstate_t& cur = m_smap.left.at(u);if(cur == m_goal)throw found_goal();// add successors of this statelist<pstate_t> children;gen_children(cur, children);BOOST_FOREACH(pstate_t& child, children) {// make sure this state is newtry{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 heuristicclass 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 stepsint 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;}