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updated honeycomb-rule-generator to work with 353, and also heavily commented it
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Zeno Rogue
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@ -7,11 +7,27 @@ Usage:
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./hyper -geo 534h -gen-rule honeycomb-rules-534.dat -quit
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./hyper -geo 535h -gen-rule honeycomb-rules-535.dat -quit
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./hyper -geo 435h -gen-rule honeycomb-rules-435.dat -quit
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./hyper -geo 353h -gen-rule honeycomb-rules-353.dat -quit
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You need to change the value of XS7 to 6 (for 435) or 12 (for others)
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You also need to select 'fp used for rules'
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This algorithm works as follows:
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- We use a DFS-like algorithm to identify all the required states. To tell whether two cells
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c1 and c2 are in the same state, we compute its generate_ext_nei -- the same generate_ext_nei
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is the same state. To compute generate_ext_nei(c), we list all cells vertex-adjacent to c,
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and for each c' in this list, we compute FV(c')-FV(c), where dist is the distance from
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some central tile. It is crucial to identify the directions in unique way (in 2D we can simply
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use clockwise order, in 3D it is more difficult) -- we do this by using a regular pattern
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(see get_id).
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After all states are identified, we construct the tree of states -- every non-root state is
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attached to the first neighbor (according to the direction order) which has smaller FV.
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For non-tree directions, we construct a path going through nodes with smaller values of FV --
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this guarantees termination of the algorithm in amortized time O(1).
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*/
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#include "zlib.h"
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@ -21,16 +37,28 @@ namespace hr {
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map<string, map<string,int> > rules;
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#define XS7 12
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/** \brief S7 -- for efficiency this is a fixed constant */
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#define XS7 20
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/** \brief distance from the center */
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#define FV master->fiftyval
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/** \brief change i into a string containing a displayable character */
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auto dis = [] (int i, char init='a') { return s0 + char(init + i); };
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/** \brief we use a regular pattern to make sure that the directions are identified consistently.
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In {5,3,5} we can just use the Seifert-Weber space for this identification; otherwise,
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we use the field pattern. */
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int get_id(cell *c) {
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if(geometry == gSpace535) return 0;
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return c->master->fieldval;
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}
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/** \brief aux function for find_path which limits path length
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* the rule is that we make some moves which decrease FV, then we make some moves which increase FV
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*/
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string find_path(cell *x, cell *y, int steps) {
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if(x->FV != y->FV) {
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println(hlog, x, y, " steps=", steps, " d=", x->FV, " vs ", y->FV);
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@ -49,8 +77,51 @@ string find_path(cell *x, cell *y, int steps) {
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return "?";
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}
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/** \brief aux function for find_path which limits path length
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* the rule is that we keep to a fixed FV-level (this works better in {x,x,3})
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*/
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string find_path_side(cell *x, cell *y, int steps) {
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if(x->FV != y->FV) {
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println(hlog, x, y, " steps=", steps, " d=", x->FV, " vs ", y->FV);
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exit(3);
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}
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if(x == y) return "";
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if(steps == 0) return "?";
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for(int i=0; i<S7; i++)
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if(x->move(i) && x->move(i)->FV == x->FV) {
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string ch = find_path_side(x->move(i), y, steps-1);
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if(ch == "?") continue;
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return dis(i) + ch;
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}
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return "?";
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}
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/** \brief find the sequence of moves we need to take to get from y to x (x and y must be the same fv-level)
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* return '?' if nothing found
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*/
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string find_path(cell *x, cell *y) {
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if(x == y) return "";
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if(geometry == gSpace353) {
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static int max_steps = -1;
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for(int steps=0; steps<5; steps++) {
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string f = find_path_side(x, y, steps);
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if(f != "?") {
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if(steps > max_steps) {
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println(hlog, "found a sidepath with ", max_steps = steps, " steps");
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}
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return f;
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}
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}
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if(max_steps < 10) {
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max_steps = 10;
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println(hlog, "failed to find_path_side");
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}
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}
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for(int steps=0;; steps++) {
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string f = find_path(x, y, steps);
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@ -60,21 +131,22 @@ string find_path(cell *x, cell *y) {
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vector<array<string, XS7>> rule_list;
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/** a map of all the cells vertex-adjacent to c */
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struct ext_nei_rules_t {
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vector<int> from, dir, original;
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};
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/** ext_nei_rules_t need to be created only once for each get_id */
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map<int, ext_nei_rules_t> ext_nei_rules;
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set<cell*> visi;
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void listnear(cell *c, ext_nei_rules_t& e, const transmatrix& T, int id) {
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/** aux recursive function of construct_rules */
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void listnear(cell *c, ext_nei_rules_t& e, const transmatrix& T, int id, set<cell*>& visi) {
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visi.insert(c);
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int a = 0, b = 0;
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for(int i=0; i<S7; i++) {
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bool ok = false;
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transmatrix U = T * currentmap->adj(c, i);
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for(auto v: reg3::vertices_only) for(auto w: reg3::vertices_only)
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for(auto v: cgi.vertices_only) for(auto w: cgi.vertices_only)
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if(hdist(v, U*w) < 1e-3) ok = true;
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if(!ok) continue;
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cell *c1 = c->cmove(i);
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@ -85,22 +157,24 @@ void listnear(cell *c, ext_nei_rules_t& e, const transmatrix& T, int id) {
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e.original.push_back(!visi.count(c1));
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if(e.original.back()) {
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b++;
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listnear(c1, e, U, id1);
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listnear(c1, e, U, id1, visi);
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}
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}
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}
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/** \brief create ext_nei_rules_t for the given c */
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void construct_rules(cell *c, ext_nei_rules_t& e) {
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visi.clear();
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e.from = {-1};
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e.dir = {-1};
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e.original = {1};
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listnear(c, e, Id, 0);
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set<cell*> visi;
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listnear(c, e, Id, 0, visi);
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int orgc = 0;
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for(auto i: e.original) orgc += i;
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println(hlog, "id ", get_id(c), " list length = ", isize(e.original), " original = ", orgc);
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}
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/** \brief we learn that a and b are connected -- make sure that their FV's match */
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void fix_dist(cell *a, cell *b) {
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if(a->FV > b->FV+1) {
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a->FV = b->FV+1;
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@ -112,6 +186,8 @@ void fix_dist(cell *a, cell *b) {
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}
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}
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/** \brief compute ext_nei_rules_t for the given cell, and make it into a string form; also do fix_dist */
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string generate_ext_nei(cell *c) {
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int fv = get_id(c);
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auto& e = ext_nei_rules[fv];
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@ -128,15 +204,23 @@ string generate_ext_nei(cell *c) {
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return its(fv) + ":" + res;
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}
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/** cells become 'candidates' before their generate_ext_nei is checked in order to let them become states */
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set<cell*> candidates;
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vector<cell*> candidates_list;
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/** the state ID for a given string returned by generate_ext_nei */
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map<string, int> id_of;
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/** cell representing the given state ID */
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vector<cell*> rep_of;
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/** current number of states */
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int number_states = 0;
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/** \brief for state s, child_rules[s][i] is -1 if i-th neighbor not a child; otherwise, the state index of that neighbor */
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vector<array<int, XS7> > child_rules;
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/** \brief if child_rules[s][i] is -1, the rules to get to that neighbor */
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vector<array<string, XS7> > side_rules;
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void add_candidate(cell *c) {
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@ -145,6 +229,7 @@ void add_candidate(cell *c) {
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candidates_list.push_back(c);
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}
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/** the main function */
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void test_canonical(string fname) {
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if(S7 != XS7) { println(hlog, "fix XS7=", S7); exit(4); }
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stop_game();
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@ -155,24 +240,28 @@ void test_canonical(string fname) {
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vector<cell*> c0;
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/* we start from a 'center' in every get_id-type */
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if(geometry == gSpace535) {
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c0.resize(qc, cwt.at);
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}
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else {
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for(int fv=0; fv<qc; fv++) {
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cell *c = cwt.at;
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for(int i=0; i<100 || c->master->fieldval != fv; i++) c = c->cmove(hrand(S7));
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/* 100 to ensure that the FV-spheres around candidates do not interact */
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for(int i=0; i<100 || get_id(c) != fv; i++) c = c->cmove(hrand(S7));
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c->FV = 0;
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c0.push_back(c);
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}
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}
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for(cell* c: c0) add_candidate(c);
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array<int, XS7> empty;
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for(auto& e: empty) e = -1;
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println(hlog, "empty = ", empty);
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/** generate candidate_list using a BFS-like algorithm, starting from c0 */
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for(int i=0; i<isize(candidates_list); i++) {
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cell *c = candidates_list[i];
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string s = generate_ext_nei(c);
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@ -187,10 +276,17 @@ void test_canonical(string fname) {
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child_rules.resize(number_states, empty);
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println(hlog, "found ", its(number_states), " states");
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fflush(stdout);
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/** generate child_rules */
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for(int i=0; i<number_states; i++) {
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cell *c = rep_of[i];
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string st = generate_ext_nei(c);
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if(!id_of.count(st) || id_of[st] != i) {
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println(hlog, "error: ext_nei changed");
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}
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for(int a=0; a<S7; a++) {
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cell *c1 = c->move(a);
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if(c1->FV <= c->FV) continue;
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@ -198,17 +294,23 @@ void test_canonical(string fname) {
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cell *c2 = c1->move(b);
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if(c2->FV != c->FV) continue;
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if(c2 == c) {
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child_rules[i][a] = id_of[generate_ext_nei(c1)];
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string st = generate_ext_nei(c1);
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if(!id_of.count(st)) {
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println(hlog, "error: new state generated while generating child_rules");
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}
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child_rules[i][a] = id_of[st];
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}
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break;
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}
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continue;
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}
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}
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if(true) {
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println(hlog, "original rules: ", child_rules);
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if(true) {
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/* minimize the automaton */
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// println(hlog, "original rules: ", child_rules);
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fflush(stdout);
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vector<int> ih(number_states, 0);
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@ -227,14 +329,14 @@ void test_canonical(string fname) {
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}
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int qids = 0;
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for(auto hash: found) ids[hash] = qids++;
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println(hlog, "qids = ", qids);
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println(hlog, "minimization step: ", qids, " states");
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if(qids == lqids) break;
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lqids = qids;
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for(int i=0; i<number_states; i++)
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ih[i] = ids[v[i]];
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}
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println(hlog, "lqids = ", lqids);
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println(hlog, "reduced states to = ", lqids);
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vector<array<int, XS7> > new_child_rules;
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new_child_rules.resize(lqids, empty);
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for(int i=0; i<number_states; i++) {
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@ -251,14 +353,16 @@ void test_canonical(string fname) {
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fflush(stdout);
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}
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for(auto& a: child_rules) for(auto i:a) print(hlog, i, ",");
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// for(auto& a: child_rules) for(auto i:a) print(hlog, i, ",");
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println(hlog);
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/* generate side rules */
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side_rules.resize(number_states);
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for(int i=0; i<isize(candidates_list); i++) {
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cell *c = candidates_list[i];
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string s = generate_ext_nei(c);
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if(!id_of.count(s)) println(hlog, "error: MISSING");
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int id = id_of[s];
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cell *cpar = nullptr;
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@ -305,7 +409,7 @@ void test_canonical(string fname) {
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cell *r = rep_of[id];
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println(hlog, r, " at ", r->FV);
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cell *r1 = r->move(a);
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if(!r1) { println(hlog, "r1 missing"); continue; }
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if(!r1) { println(hlog, "error: r1 missing"); continue; }
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println(hlog, r1, " at ", r1->FV);
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for(int a=0; a<S7; a++) if(r1->move(a)) println(hlog, a, ":", r1->move(a), " at ", r1->move(a)->FV);
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fflush(stdout);
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@ -326,7 +430,7 @@ void test_canonical(string fname) {
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auto& sr = side_rules[id][a];
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if(sr != "" && sr != solu) {
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println(hlog, "conflict: ", solu, " vs ", sr);
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println(hlog, "conflict: ", solu, " vs ", sr, " FV = ", c->FV, " vs ", c1->FV);
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if(isize(sr) < isize(solu)) continue;
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}
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@ -335,8 +439,8 @@ void test_canonical(string fname) {
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continue;
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}
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}
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println(hlog, side_rules);
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// println(hlog, side_rules);
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string side_data;
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for(auto& a: side_rules) for(auto&b :a) if(b != "") side_data += b + ",";
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