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hyperrogue/expansion.cpp

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// Hyperbolic Rogue -- expansion analyzer
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file expansion.cpp
* \brief exponential growth of hyperbolic geometries
*
* Calculations related to this exponential growth.
* Screens which display this exponential growth (e.g. 'size of the world' in geometry experiments) are also implemented here.
*/
#include "hyper.h"
namespace hr {
int subtype(cell *c) {
return patterns::getpatterninfo(c, patterns::PAT_NONE, 0).id;
}
void canonicize(vector<int>& t) {
for(int i=2; i<isize(t); i++)
if((t[i] & 3) == 1 && (t[i-1] & 3) != 1)
std::rotate(t.begin()+1, t.begin()+i, t.end());
}
#if HDR
struct expansion_analyzer {
int sibling_limit;
vector<int> gettype(cell *c);
int N;
vector<cell*> samples;
map<vector<int>, int> codeid;
vector<vector<int> > children;
int rootid, diskid;
int coefficients_known;
#if CAP_GMP
vector<mpq_class> coef;
#else
vector<int> coef;
#endif
int valid_from, tested_to;
ld growth;
int sample_id(cell *c);
void preliminary_grouping();
void reduce_grouping();
vector<vector<bignum>> descendants;
bignum& get_descendants(int level);
bignum& get_descendants(int level, int type);
void find_coefficients();
void reset();
expansion_analyzer() { reset(); }
string approximate_descendants(int d, int max_length);
void view_distances_dialog();
ld get_growth();
private:
bool verify(int id);
int valid(int v, int step);
};
#endif
vector<int> expansion_analyzer::gettype(cell *c) {
vector<int> res;
res.push_back(subtype(c) * 4 + 2);
int d = celldist(c);
for(int i=0; i<c->type; i++) {
cell *c1 = c->cmove(i);
int bonus = 0;
if(bt::in()) bonus += 16 * (celldistAlt(c1) - celldistAlt(c));
res.push_back(bonus + subtype(c1) * 4 + celldist(c1) - d);
}
canonicize(res);
return res;
}
int expansion_analyzer::sample_id(cell *c) {
auto t = gettype(c);
if(codeid.count(t)) return codeid[t];
auto &cit = codeid[t];
cit = isize(samples);
samples.push_back(c);
return cit;
}
template<class T, class U> vector<int> get_children_codes(cell *c, const T& distfun, const U& typefun) {
vector<int> res;
int d = distfun(c);
cellwalker cw(c, 0);
if(d > 0) {
forCellCM(c2, c) if(celldist(cw.peek()) < d) break; else cw++;
}
for(int k=0; k<c->type; k++) {
cell *c1 = cw.cpeek();
cw++;
if(distfun(c1) != d+1) continue;
cell *c2 = cw.cpeek();
if(distfun(c2) != d+1) continue;
res.push_back(typefun(c1));
}
return res;
}
void expansion_analyzer::preliminary_grouping() {
samples.clear();
codeid.clear();
children.clear();
if(currentmap->strict_tree_rules()) {
N = isize(rulegen::treestates);
children.resize(N);
rootid = rulegen::rule_root;
for(int i=0; i<N; i++)
for(int v: rulegen::treestates[i].rules)
if(v >= 0) children[i].push_back(v);
}
else if(reg3::in_rule()) {
#if MAXMDIM >= 4
rootid = reg3::rule_get_root(0);
auto& chi = reg3::rule_get_children();
N = isize(chi) / S7;
children.resize(N);
int k = 0;
for(int i=0; i<N; i++) for(int j=0; j<S7; j++) {
int ck = chi[k];
if(ck < -1) ck += (1<<16);
if(ck >= 0)
children[i].push_back(ck);
k++;
}
#endif
}
else {
sample_id(currentmap->gamestart());
// queue for, do not change to range-based for
for(int i=0; i<isize(samples); i++)
children.push_back(get_children_codes(samples[i], celldist, [this] (cell *c) { return sample_id(c); }));
N = isize(samples);
rootid = 0;
}
diskid = N;
children.push_back(children[rootid]);
children[diskid].push_back(diskid);
N++;
}
void expansion_analyzer::reduce_grouping() {
if(reg3::in_rule()) return;
if(currentmap->strict_tree_rules()) return;
int old_N = N;
vector<int> grouping;
grouping.resize(N);
int nogroups = 1;
for(int i=0; i<N; i++) grouping[i] = 0;
while(true) {
vector< pair<vector<int>, int > > childgroups(N);
for(int i=0; i<N; i++) {
childgroups[i].second = i;
for(int j: children[i])
childgroups[i].first.push_back(grouping[j]);
// sort(childgroups[i].first.begin(), childgroups[i].first.end());
}
sort(childgroups.begin(), childgroups.end());
int newgroups = 0;
for(int i=0; i<N; i++) {
if(i == 0 || childgroups[i].first != childgroups[i-1].first) newgroups++;
grouping[childgroups[i].second] = newgroups - 1;
}
if(nogroups == newgroups) break;
nogroups = newgroups;
}
vector<int> groupsample(nogroups, -1);
for(int i=0; i<N; i++) {
int& g = groupsample[grouping[i]];
if(g == -1) g = i;
}
vector<int> reorder(nogroups);
for(int i=0; i<nogroups; i++) reorder[i] = i;
sort(reorder.begin(), reorder.end(), [&] (int i, int j) { return groupsample[i] < groupsample[j]; });
vector<int> inv_reorder(nogroups);
for(int i=0; i<nogroups; i++) inv_reorder[reorder[i]] = i;
for(int i=0; i<N; i++) grouping[i] = inv_reorder[grouping[i]];
for(int i=0; i<N; i++) groupsample[grouping[i]] = i;
vector<vector<int>> newchildren(nogroups);
for(int i=0; i<nogroups; i++)
for(int j: children[groupsample[i]])
newchildren[i].push_back(grouping[j]);
children = move(newchildren);
for(auto& p: codeid) p.second = grouping[p.second];
N = nogroups;
rootid = grouping[rootid];
diskid = grouping[diskid];
for(int g=0; g<old_N; g++) if(grouping[g] != g) descendants.clear();
}
template<class T> int size_upto(vector<T>& v, int s) {
int res = isize(v);
if(res < s) v.resize(s);
return res;
}
bignum& expansion_analyzer::get_descendants(int level) {
if(!N) preliminary_grouping(), reduce_grouping();
return get_descendants(level, rootid);
}
bignum& expansion_analyzer::get_descendants(int level, int type) {
if(!N) preliminary_grouping(), reduce_grouping();
auto& pd = descendants;
size_upto(pd, level+1);
for(int d=0; d<=level; d++)
for(int i=size_upto(pd[d], N); i<N; i++)
if(d == 0) pd[d][i].be(1);
else for(int j: children[i])
pd[d][i] += pd[d-1][j];
return pd[level][type];
}
bool expansion_analyzer::verify(int id) {
if(id < isize(coef)) return false;
#if CAP_GMP
mpq_class res = 0;
for(int t=0; t<isize(coef); t++)
res += coef[t] * get_descendants(id-t-1).as_mpq();
return res == get_descendants(id).as_mpq();
#else
long long res = 0;
for(int t=0; t<isize(coef); t++)
res += coef[t] * get_descendants(id-t-1).approx_ll();
return res == get_descendants(id).approx_ll();
#endif
}
int expansion_analyzer::valid(int v, int step) {
if(step < 0) return 0;
int more = reg3::in_rule() ? 1 : 5;
#if CAP_GMP == 0
if(get_descendants(step+v+v+more).approx_int() >= bignum::BASE) return 0;
typedef ld val;
const val unit = 1;
#else
typedef mpq_class val;
const val unit = 1;
#endif
val matrix[100][128];
for(int i=0; i<v; i++)
for(int j=0; j<v+1; j++)
#if CAP_GMP == 0
matrix[i][j] = get_descendants(step+i+j).approx_ll();
#else
matrix[i][j] = get_descendants(step+i+j).as_mpq();
#endif
for(int k=0; k<v; k++) {
int nextrow = k;
#if CAP_GMP == 0
while(nextrow < v && std::abs(matrix[nextrow][k]) < 1e-6)
nextrow++;
#else
while(nextrow < v && matrix[nextrow][k] == 0)
nextrow++;
#endif
if(nextrow == v) return 1;
if(nextrow != k) {
// printf("swap %d %d\n", k, nextrow);
for(int l=0; l<=v; l++) swap(matrix[k][l], matrix[nextrow][l]);
// display();
}
val divv = unit / matrix[k][k];
for(int k1=k; k1<=v; k1++) matrix[k][k1] *= divv;
// printf("divide %d\n", k);
// display();
for(int k1=k+1; k1<v; k1++) if(matrix[k1][k] != 0) {
val coef = -matrix[k1][k];
for(int k2=k; k2<=v; k2++) matrix[k1][k2] += matrix[k][k2] * coef;
}
// printf("zeros below %d\n", k);
// display();
}
for(int k=v-1; k>=0; k--)
for(int l=k-1; l>=0; l--)
if(matrix[l][k]) matrix[l][v] -= matrix[l][k] * matrix[k][v];
coef.resize(v);
#if CAP_GMP
for(int i=0; i<v; i++) coef[i] = matrix[v-1-i][v];
#else
for(int i=0; i<v; i++) coef[i] = int(floor(matrix[v-1-i][v] + .5));
#endif
for(int t=step+v; t<step+v+v+more; t++) if(!verify(t)) return 2;
tested_to = step+v+v+more;
while(tested_to < step+v+v+100) {
#if !CAP_GMP
if(get_descendants(tested_to).approx_ll() >= bignum::BASE2) break;
#endif
if(!verify(tested_to)) return 2;
tested_to++;
}
valid_from = step+v;
return 3;
}
void expansion_analyzer::find_coefficients() {
if(coefficients_known) return;
if(!N) preliminary_grouping(), reduce_grouping();
for(int v=1; v<25; v++)
for(int step=0; step<3 * v; step++) {
int val = valid(v, step);
if(val == 0) break;
if(val == 3) { coefficients_known = 2; return; }
}
coefficients_known = 1;
}
ld growth;
ld expansion_analyzer::get_growth() {
if(growth >= 1) return growth;
if(!N) preliminary_grouping(), reduce_grouping();
vector<ld> eigen(N, 1);
ld total;
for(int iter=0; iter<100000; iter++) {
total = 0;
vector<ld> neweigen(N, 0);
for(int i=0; i<N; i++) {
for(int j: children[i]) neweigen[i] += eigen[j];
total += neweigen[i];
}
for(int i=0; i<N; i++) eigen[i] = .1 * eigen[i] + .9 * neweigen[i] / total;
}
return growth = total;
}
void expansion_analyzer::reset() {
N = 0;
growth = 0;
coefficients_known = 0;
samples.clear();
codeid.clear();
children.clear();
coef.clear();
descendants.clear();
}
EX int type_in(expansion_analyzer& ea, cell *c, const cellfunction& f) {
if(!ea.N) ea.preliminary_grouping(), ea.reduce_grouping();
vector<int> res;
res.push_back(subtype(c) * 4 + 2);
int d = f(c);
for(int i=0; i<c->type; i++) {
cell *c1 = c->cmove(i);
int bonus = 0;
if(bt::in()) bonus += 16 * (celldistAlt(c1) - celldistAlt(c));
res.push_back(bonus + subtype(c1) * 4 + f(c1) - d);
}
canonicize(res);
if(ea.codeid.count(res)) return ea.codeid[res];
int ret = ea.N++;
ea.codeid[res] = ret;
ea.children.emplace_back();
ea.children[ret] = get_children_codes(c, f, [&ea, &f] (cell *c1) { return type_in(ea, c1, f); });
return ret;
}
int type_in_quick(expansion_analyzer& ea, cell *c, const cellfunction& f) {
vector<int> res;
res.push_back(subtype(c) * 4 + 2);
int d = f(c);
for(int i=0; i<c->type; i++) {
cell *c1 = c->cmove(i);
int dd = f(c1) - d;
if(dd < -1 || dd > 1) return -1;
res.push_back(subtype(c1) * 4 + dd);
}
canonicize(res);
if(ea.codeid.count(res)) return ea.codeid[res];
return -1;
}
EX bool sizes_known() {
if(reg3::in_rule()) return true;
if(closed_manifold) return false;
// Castle Anthrax is infinite
if(bt::in()) return false;
// not implemented
if(arcm::in()) return false;
if(kite::in()) return false;
if(currentmap->strict_tree_rules()) return true;
if(arb::in()) return false;
return true;
}
EX bool trees_known() {
return sizes_known() && !(BITRUNCATED && a4 && S7 <= 5);
}
string expansion_analyzer::approximate_descendants(int d, int max_length) {
auto t = SDL_GetTicks();
while(isize(descendants) <= d && SDL_GetTicks() < t + 100)
get_descendants(isize(descendants));
if(isize(descendants) > d)
return get_descendants(d).get_str(max_length);
int v = isize(descendants) - 1;
bignum& b = get_descendants(v);
if(b.digits.empty()) return "0";
ld log_10 = log(b.digits.back()) / log(10) + 9 * (isize(b.digits) - 1) + (d - v) * log(get_growth()) / log(10);
int more_digits = int(log_10);
return XLAT("about ") + fts(pow(10, log_10 - more_digits)) + "E" + its(more_digits);
}
enum eDistanceFrom { dfPlayer, dfStart, dfWorld };
EX string dfnames[3] = { "player", "start", "land" };
eDistanceFrom distance_from = dfPlayer;
#if HDR
enum eNumberCoding { ncNone, ncDistance, ncType, ncDebug, ncError };
#endif
EX string ncnames[5] = { "NO", "distance", "type", "debug", "error" };
EX eNumberCoding number_coding = ncDistance;
bool mod_allowed() {
return cheater || autocheat || arcm::in() || tour::on;
}
EX int curr_dist(cell *c) {
switch(distance_from) {
case dfPlayer:
return c->cpdist < INFD ? c->cpdist : celldistance(cwt.at, c);
case dfStart:
return celldist(c);
case dfWorld:
if(!mod_allowed() && !among(c->land, laOcean, laIvoryTower, laEndorian, laDungeon, laTemple, laWhirlpool, laCanvas))
return 0;
if((isCyclic(c->land) || among(c->land, laCanvas, laCaribbean, laStorms, laRlyeh))) {
if(eubinary || c->master->alt) return celldistAlt(c);
return UNKNOWN;
}
return inmirror(c) ? (c->landparam & 255) : c->landparam;
}
return 0;
}
int position;
EX int type_in_reduced(expansion_analyzer& ea, cell *c, const cellfunction& f) {
int a = ea.N;
int t = type_in(ea, c, f);
auto& expansion = get_expansion();
if(expansion.N != a) {
expansion.reduce_grouping();
t = type_in(ea, c, f);
}
return t;
}
// which=1 => right, which=-1 => left
EX int parent_id(cell *c, int which, const cellfunction& cf) {
int d = cf(c)-1;
for(int i=0; i<c->type; i++) {
if(cf(c->cmove(i)) == d) {
int steps = 0;
again:
if(!which || steps == c->type) return i;
int i2 = c->c.fix(i+which);
if(cf(c->cmove(i2)) == d) {
i = i2; steps++; goto again;
}
else return i;
}
}
return -1;
}
// set which=1,bonus=1 to get right neighbor on level
EX void generate_around(cell *c) {
forCellCM(c2, c) if(c2->mpdist > BARLEV) setdist(c2, BARLEV, c);
}
EX namespace ts {
EX cell *verified_add(cell *c, int which, int bonus, const cellfunction& cf) {
int id = parent_id(c, which, cf);
if(id == -1) return NULL;
return c->cmodmove(id + bonus);
}
EX cell *verified_add_gen(cell *c, int which, int bonus, const cellfunction& cf) {
return verified_add(c, which, bonus, cf);
}
EX cell *add(cell *c, int which, int bonus, const cellfunction& cf) {
int pid = parent_id(c, which, cf);
if(pid == -1) pid = 0;
return c->cmodmove(pid + bonus);
}
EX cell *left_of(cell *c, const cellfunction& cf) {
int pid = parent_id(c, 1, cf);
if(pid == -1) return c;
if(valence() == 3) return c->cmodmove(pid+1);
else return (cellwalker(c, pid) + wstep - 1).cpeek();
}
EX cell *right_of(cell *c, const cellfunction& cf) {
int pid = parent_id(c, -1, cf);
if(pid == -1) return c;
if(valence() == 3) return c->cmodmove(pid-1);
else return (cellwalker(c, pid) + wstep + 1).cpeek();
}
EX cell *child_number(cell *c, int id, const cellfunction& cf) {
int pid = parent_id(c, 1, cf);
if(pid == -1) return c->cmove(id);
return c->cmodmove(pid + (valence() == 3 ? 2 : 1) + id);
}
#if HDR
inline cell *left_parent(cell *c, const cellfunction& cf) { return verified_add(c, 1, 0, cf); }
inline cell *right_parent(cell *c, const cellfunction& cf) { return verified_add(c, -1, 0, cf); }
#endif
EX }
EX bool viewdists = false;
EX bool use_color_codes = true;
EX bool use_analyzer = true;
EX bool show_distance_lists = true;
int first_distance = 0, scrolltime = 0;
bool scrolling_distances = false;
EX map<int, color_t> expcolors;
color_t distribute_color(int id) {
if(expcolors.count(id)) return expcolors[id];
color_t v = forecolor; // 0xFFFFFF;
for(int z=0; z<24; z++) if(id & (1<<z)) part(v, (z%3)) ^= (1<<(7-(z/3)));
return v;
}
EX bool dist_label_colored = true;
EX color_t dist_label_color = 0;
void celldrawer::do_viewdist() {
if(behindsphere(V)) return;
int cd = (use_color_codes || number_coding == ncDistance || number_coding == ncDebug) ? curr_dist(c) : 0;
if(use_color_codes) {
int dc = distcolors[cd];
wcol = gradient(wcol, dc, 0, .4, 1);
fcol = gradient(fcol, dc, 0, .4, 1);
}
string label = "";
int dc = 0xFFD500;
switch(number_coding) {
case ncDistance: {
label = cd == UNKNOWN ? "?" : its(cd);
dc = distcolors[cd];
break;
}
case ncType: {
int t = -1;
if(reg3::in_rule()) switch(distance_from) {
case dfPlayer:
t = -1;
break;
case dfStart:
t = c->master->fiftyval;
break;
case dfWorld:
if(c->master->alt) t = c->master->alt->fiftyval;
break;
}
else if(currentmap->strict_tree_rules()) switch(distance_from) {
case dfPlayer:
t = -1;
break;
case dfStart:
t = c->master->fieldval;
break;
case dfWorld:
if(c->master->alt) t = c->master->alt->fieldval;
break;
}
else t = type_in_reduced(get_expansion(), c, curr_dist);
if(t >= 0) label = its(t), dc = distribute_color(t);
break;
}
case ncDebug: {
int d =
distance_from == dfStart && cwt.at == currentmap->gamestart() && c->cpdist < INFD ? c->cpdist :
celldistance(c, distance_from == dfPlayer ? cwt.at : currentmap->gamestart());
dc = (d != cd) ? 0xFF0000 : 0x00FF00;
label = its(d);
}
case ncError: {
if(pointer_indices.count(c)) label = index_pointer(c);
}
case ncNone: ;
}
if(!dist_label_colored) dc = dist_label_color;
// string label = its(fieldpattern::getriverdistleft(c)) + its(fieldpattern::getriverdistright(c));
/* queuepolyat(V, shFloor[ct6], darkena(gradient(0, distcolors[cd&7], 0, .25, 1), fd, 0xC0),
PPR::TEXT); */
if(label != "")
queuestr(V, (isize(label) > 1 ? .6 : 1), label, 0xFF000000 + dc, 1);
}
EX void viewdist_configure_dialog() {
dialog::init("");
cmode |= sm::SIDE | sm::MAYDARK | sm::EXPANSION;
gamescreen(0);
dialog::addSelItem(XLAT("which distance"), XLAT(dfnames[distance_from]), 'c');
dialog::add_action([] () { distance_from = mod_allowed() ? eDistanceFrom((distance_from + 1) % 3) : eDistanceFrom(2 - distance_from); });
dialog::addSelItem(XLAT("number codes"), XLAT(ncnames[number_coding]), 'n');
dialog::add_action([] () { number_coding = eNumberCoding((number_coding + 1) % (mod_allowed() ? 4 : 2)); });
dialog::addBoolItem_action(XLAT("color codes"), use_color_codes, 'u');
dialog::addSelItem(XLAT("display distances from"), its(first_distance), 'd');
dialog::add_action([] () {
scrolling_distances = false;
dialog::editNumber(first_distance, 0, 3000, 1, 0, XLAT("display distances from"), "");
dialog::bound_low(0);
});
dialog::addBoolItem(XLAT("strict tree maps"), currentmap->strict_tree_rules(), 's');
dialog::add_action_push(rulegen::show);
int id = 0;
using namespace linepatterns;
for(auto& lp: {&patTriTree, &patTriRings, &patTriOther}) {
dialog::addColorItem(XLAT(lp->lpname), lp->color, '1'+(id++));
dialog::add_action([&lp] () {
dialog::openColorDialog(lp->color, NULL);
dialog::dialogflags |= sm::MAYDARK | sm::SIDE | sm::EXPANSION;
});
}
if(!mod_allowed()) {
dialog::addItem(XLAT("enable the cheat mode for additional options"), 'C');
dialog::add_action(enable_cheat);
}
else
dialog::addBreak(100);
dialog::addBreak(100);
dialog::addItem(XLAT("disable"), 'x');
dialog::add_action([] () { viewdists = false; popScreen(); });
dialog::addItem(XLAT("move the player"), 'm');
dialog::add_action([] () { show_distance_lists = false; popScreenAll(); });
dialog::addItem(distance_from ? XLAT("show number of descendants by distance") : XLAT("show number of cells by distance"), 'l');
dialog::add_action([] () { show_distance_lists = true; popScreenAll(); });
dialog::display();
}
bool is_descendant(cell *c) {
if(c == cwt.at) return true;
if(curr_dist(c) < curr_dist(cwt.at)) return false;
return is_descendant(ts::right_parent(c, curr_dist));
}
const int scrollspeed = 100;
bool not_only_descendants = false;
#if CAP_GMP
string produce_coef_formula(vector<mpq_class> coef) {
#else
string produce_coef_formula(vector<int> coef) {
#endif
string fmt = "a(d+" + its(isize(coef)) + ") = ";
bool first = true;
for(int i=0; i<isize(coef); i++) if(coef[i]) {
if(first && coef[i] == 1) ;
else if(first) fmt += its(coef[i]);
else if(coef[i] == 1) fmt += " + ";
else if(coef[i] == -1) fmt += " - ";
else if(coef[i] > 1) fmt += " + " + its(coef[i]);
else if(coef[i] < -1) fmt += " - " + its(-coef[i]);
fmt += "a(d";
if(i != isize(coef) - 1)
fmt += "+" + its(isize(coef) - 1 - i);
fmt += ")";
first = false;
}
return fmt;
}
void expansion_analyzer::view_distances_dialog() {
static int lastticks;
if(scrolling_distances && !closed_manifold) {
scrolltime += SDL_GetTicks() - lastticks;
first_distance += scrolltime / scrollspeed;
scrolltime %= scrollspeed;
}
lastticks = SDL_GetTicks();
if(first_distance < 0) first_distance = 0;
dynamicval<color_t> dv(distcolors[0], forecolor);
dialog::init("");
cmode |= sm::DIALOG_STRICT_X | sm::EXPANSION;
int maxlen = closed_manifold ? 128 : 16 + first_distance;
vector<bignum> qty(maxlen);
auto& expansion = get_expansion();
bool really_use_analyzer = use_analyzer && sizes_known();
if(really_use_analyzer) {
int t;
if(reg3::in_rule() || currentmap->strict_tree_rules()) {
if(!N) preliminary_grouping();
t = rootid;
}
else
t = type_in_reduced(expansion, cwt.at, curr_dist);
for(int r=0; r<maxlen; r++)
qty[r] = expansion.get_descendants(r, t);
}
else {
if(distance_from == dfPlayer) {
celllister cl(cwt.at, closed_manifold ? maxlen-1 : gamerange(), 100000, NULL);
for(int d: cl.dists)
if(d >= 0 && d < maxlen) qty[d]++;
}
else {
celllister cl(cwt.at, closed_manifold ? maxlen-1 : gamerange(), 100000, NULL);
for(cell *c: cl.lst) if((not_only_descendants || is_descendant(c)) && curr_dist(c) < maxlen) qty[curr_dist(c)]++;
}
#if !CAP_GMP
if(sizes_known() && !not_only_descendants) {
find_coefficients();
if(gamerange()+1 >= valid_from && coefficients_known == 2) {
for(int i=gamerange()+1; i<maxlen; i++)
for(int j=0; j<isize(coef); j++) {
qty[i].addmul(qty[i-1-j], coef[j]);
}
}
}
#endif
}
dialog::addBreak(100 - 100 * scrolltime / scrollspeed);
for(int i=first_distance; i<maxlen; i++) if(!qty[i].digits.empty())
dialog::addInfo(its(i) + ": " + qty[i].get_str(100), distcolors[i]);
dialog::addBreak(100 * scrolltime / scrollspeed);
if(sizes_known() || bt::in()) {
if(euclid && !arb::in()) {
dialog::addBreak(200);
dialog::addInfo("a(d) = " + its(get_descendants(10).approx_int() - get_descendants(9).approx_int()) + "d", forecolor);
}
else {
dialog::addBreak(100);
find_coefficients();
if(coefficients_known == 2) {
string fmt = produce_coef_formula(coef);
fmt += " (d>" + its(valid_from-1) + ")";
dialog::addHelp(fmt);
}
else dialog::addBreak(100);
dialog::addInfo("Θ(" + fts(get_growth(), 8) + "...ᵈ)", forecolor);
}
}
dialog::addItem(XLAT("scroll"), 'S');
dialog::addItem(XLAT("configure"), 'C');
dialog::display();
}
EX void enable_viewdists() {
first_distance = 0;
scrolltime = 0;
viewdists = true;
if(!mod_allowed()) {
number_coding = ncDistance;
distance_from = dfPlayer;
}
show_distance_lists = true;
}
bool expansion_handleKey(int sym, int uni) {
if((cmode & sm::NORMAL) && viewdists) {
if(uni == 'S' && (cmode & sm::EXPANSION)) scrolling_distances = !scrolling_distances;
else if(uni == 'C') pushScreen(viewdist_configure_dialog);
else if(uni == 'A' && (cmode & sm::EXPANSION)) use_analyzer = !use_analyzer;
else if(sym == SDLK_ESCAPE) first_distance = 0, viewdists = false;
else return false;
return true;
}
return false;
}
int expansion_hook = addHook(hooks_handleKey, 0, expansion_handleKey);
#if !ISMINI
void compute_coefficients() {
println(hlog, gp::operation_name(), " ", ginf[geometry].tiling_name);
start_game();
auto& expansion = get_expansion();
printf(" sizes:");
for(int i=0; i<expansion.valid_from+10; i++) printf(" %d", expansion.get_descendants(i).approx_int());
printf(" N = %d\n", expansion.N);
expansion.find_coefficients();
if(expansion.coefficients_known == 2) {
println(hlog, " coefficients:");
for(auto& x: expansion.coef) println(hlog, " ", x);
println(hlog, " (tested on %d to %d)\n", expansion.valid_from, expansion.tested_to);
}
}
#if CAP_COMMANDLINE
int expansion_readArgs() {
using namespace arg;
if(0) ;
else if(argis("-vap")) {
PHASEFROM(2);
start_game();
auto& expansion = get_expansion();
shift(); int radius = argi();
while(true) {
string s = expansion.approximate_descendants(radius, 100);
printf("s = %s\n", s.c_str());
if(isize(expansion.descendants) >= radius) break;
}
}
else if(argis("-csizes")) {
PHASEFROM(2);
start_game();
auto& expansion = get_expansion();
expansion.get_growth();
shift(); for(int i=0; i<argi(); i++)
printf("%s / %s\n", expansion.get_descendants(i).get_str(1000).c_str(), expansion.get_descendants(i, expansion.diskid).get_str(1000).c_str());
}
else if(argis("-csolve")) {
PHASEFROM(2);
start_game();
auto& expansion = get_expansion();
printf("preliminary_grouping...\n");
expansion.preliminary_grouping();
printf("N = %d\n", expansion.N);
for(int i=0; i<expansion.N; i++) {
printf("%d:", i);
for(int c: expansion.children[i]) printf(" %d", c);
printf("\n");
}
printf("reduce_grouping...\n");
expansion.reduce_grouping();
printf("N = %d\n", expansion.N);
for(int i=0; i<expansion.N; i++) {
printf("%d:", i);
for(int c: expansion.children[i]) printf(" %d", c);
printf("\n");
}
println(hlog, "growth = ", expansion.get_growth());
expansion.find_coefficients();
if(expansion.coefficients_known == 2) {
println(hlog, " sizes:");
for(int i=0; i<expansion.valid_from+10; i++)
println(hlog, "[", i, "] = ", expansion.get_descendants(i).get_str(10000));
println(hlog, " disks:");
for(int i=0; i<expansion.valid_from+10; i++)
println(hlog, "[", i, "] = ", expansion.get_descendants(i, expansion.diskid).get_str(10000));
vector<string> disks;
for(int i=0; i<expansion.valid_from+10; i++)
disks.push_back(expansion.get_descendants(i, expansion.diskid).get_str(10000));
println(hlog, "disks = ", disks);
println(hlog, "coefficients: ", expansion.coef);
println(hlog, "i.e. ", produce_coef_formula(expansion.coef));
println(hlog, "coefficients tested from ", expansion.valid_from, " to ", expansion.tested_to);
}
}
#if CAP_GP
else if(argis("-csolve_tab")) {
for(eGeometry geo: {gNormal, gOctagon, g45, g46, g47}) {
set_geometry(geo);
set_variation(eVariation::pure);
compute_coefficients();
set_variation(eVariation::bitruncated);
compute_coefficients();
for(int x=1; x<9; x++)
for(int y=0; y<=x; y++) {
if(x == 1 && y == 0) continue;
if(x == 1 && y == 1 && S3 == 3) continue;
if(x+y > 10) continue;
stop_game();
gp::param = gp::loc(x, y);
set_variation(eVariation::goldberg);
compute_coefficients();
}
}
}
#endif
else if(argis("-expansion")) {
cheat(); viewdists = true;
shift(); distance_from = (eDistanceFrom) argi();
shift(); number_coding = (eNumberCoding) argi();
shift(); use_color_codes = argi() & 1; use_analyzer = argi() & 2; show_distance_lists = argi() & 4;
not_only_descendants = argi() & 8;
}
else if(argis("-expansion-labelcolor")) {
dist_label_colored = false;
shift(); dist_label_color = argcolor(24);
}
else if(argis("-expansion-off")) {
viewdists = false;
}
else return 1;
return 0;
}
auto ea_hook = addHook(hooks_args, 100, expansion_readArgs);
#endif
#endif
EX expansion_analyzer& get_expansion() {
if(!cgi.expansion) cgi.expansion = make_shared<expansion_analyzer> ();
return *cgi.expansion;
}
EX void set_sibling_limit() {
auto& sibling_limit = get_expansion().sibling_limit;
if(0) ;
#if CAP_IRR
else if(IRREGULAR) sibling_limit = 3;
#endif
#if CAP_BT
else if(bt::in()) sibling_limit = 3;
#endif
#if CAP_GP
else {
auto p = gp::univ_param();
sibling_limit = 2 * p.first + p.second;
}
#else
else sibling_limit = PURE ? 2 : 3;
#endif
}
int celldist0(cell *c) {
if(bt::in()) return celldistAlt(c);
else return celldist(c);
}
bool in_segment(cell *left, cell *mid, cell *right) {
while(true) {
if(mid == left) return true;
if(left == right) return false;
left = ts::right_of(left, celldist0);
}
}
int sibling_distance(cell *a, cell *b, int limit) {
int counting = 0;
while(true) {
if(a == b) return counting;
if(limit == 0) return INF;
counting++; limit--;
a = ts::right_of(a, celldist0);
}
}
/** An algorithm for computing distance between two cells.
This algorithm runs correctly in O(d) assuming that:
- distances from the origin are known
- the set of cells in distance d from the origin forms a cycle
- the map is Gromov hyperbolic (with sibling_limit computed correctly) and planar
- all vertices have valence <= 4
- each vertex has at most two parents
*/
EX int hyperbolic_celldistance(cell *c1, cell *c2) {
int found_distance = INF;
int d = 0, d1 = celldist0(c1), d2 = celldist0(c2), sl_used = 0;
auto& sibling_limit = get_expansion().sibling_limit;
cell *cl1=c1, *cr1=c1, *cl2=c2, *cr2=c2;
while(true) {
if(a45 && BITRUNCATED) {
// some cells in this tiling have three parents,
// making the usual algorithm fail
if(d2 == d1+1) {
swap(d1, d2); swap(cl1, cl2); swap(c1, c2); swap(cr1, cr2);
}
auto short_distances = [cl1, cr1, d, &found_distance] (cell *c) {
celllister cl(c, 4, 1000, cl1);
if(cl.listed(cl1)) found_distance = min(found_distance, d + cl.getdist(cl1));
if(cl.listed(cr1)) found_distance = min(found_distance, d + cl.getdist(cr1));
};
if(d1 <= d2+1) {
short_distances(cl2);
if(cl2 != cr2) short_distances(cr2);
}
}
if(d >= found_distance) {
if(sl_used == sibling_limit && IRREGULAR) {
printf("sibling_limit used: %d\n", sibling_limit); sibling_limit++;
}
return found_distance;
}
if(d1 == d2) {
if(cl1 == c1 && in_segment(cl2, c1, cr2)) return d;
if(cl2 == c2 && in_segment(cl1, c2, cr1)) return d;
if(valence() == 3) {
int dx = min(sibling_distance(cr1, cl2, sibling_limit), sibling_distance(cr2, cl1, sibling_limit));
if(d + dx <= found_distance) {
found_distance = d + dx;
sl_used = dx;
}
}
else {
if(cl1 == cr2 || cr1 == cl2) found_distance = d;
}
}
if(d >= found_distance) {
if(sl_used == sibling_limit && IRREGULAR) {
printf("sibling_limit used: %d\n", sibling_limit); sibling_limit++;
}
return found_distance;
}
if(d1 >= d2) {
cl1 = ts::left_parent(cl1, celldist0);
cr1 = ts::right_parent(cr1, celldist0);
d++; d1--;
}
if(d1 < d2) {
cl2 = ts::left_parent(cl2, celldist0);
cr2 = ts::right_parent(cr2, celldist0);
d++; d2--;
}
}
}
}
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