hyperrogue/expansion.cpp

// HyperRogue -- expansion_analyzer
// Copyright (C) 2011-2018 Zeno Rogue, see 'hyper.cpp' for details

namespace hr {

int subtype(cell *c) {
  return patterns::getpatterninfo(c, patterns::PAT_NONE, 0).id;
  }

bignum& bignum::operator +=(const bignum& b) {
  int K = isize(b.digits);
  if(K > isize(digits)) digits.resize(K);
  int carry = 0;
  for(int i=0; i<K || carry; i++) {
    if(i >= isize(digits)) digits.push_back(0);
    digits[i] += carry;
    if(i < K) digits[i] += b.digits[i];
    if(digits[i] >= BASE) {
      digits[i] -= BASE;
      carry = 1;
      }
    else carry = 0;
    }
  return *this;
  }

bool bignum::operator < (const bignum& b) const {
  if(isize(digits) != isize(b.digits))
    return isize(digits) < isize(b.digits);
  for(int i = isize(digits)-1; i>=0; i--)
    if(digits[i] != b.digits[i])
      return digits[i] < b.digits[i];
  return false;
  }

void bignum::addmul(const bignum& b, int factor) {
  int K = isize(b.digits);
  if(K > isize(digits)) digits.resize(K);
  int carry = 0;
  for(int i=0; i<K || (carry > 0 && carry < -1) || (carry == -1 && i < isize(digits)); i++) {
    if(i >= isize(digits)) digits.push_back(0);
    long long l = digits[i];
    l += carry;
    if(i < K) l += b.digits[i] * factor;
    carry = 0;
    if(l >= BASE) carry = l / BASE;
    if(l < 0) carry = -(BASE-1-l) / BASE;
    l -= carry * BASE;
    digits[i] = l;
    }
  if(carry < 0) digits.back() -= BASE;
  while(isize(digits) && digits.back() == 0) digits.pop_back();
  }

bignum hrand(bignum b) {
  bignum res;
  int d = isize(b.digits);
  while(true) {
    res.digits.resize(d);
    for(int i=0; i<d-1; i++) res.digits[i] = hrand(bignum::BASE);
    res.digits.back() = hrand(b.digits.back() + 1);
    if(res < b) return res;
    }  
  }

void operator ++(bignum &b, int) {
  int i = 0;
  while(true) {
    if(isize(b.digits) == i) { b.digits.push_back(1); break; }
    else if(b.digits[i] == bignum::BASE-1) {
      b.digits[i] = 0;
      i++;
      }
    else {
      b.digits[i]++;
      break;
      }      
    }
  }

void operator --(bignum &b, int) {
  int i = 0;
  while(true) {
    if(isize(b.digits) == i) { b.digits.push_back(bignum::BASE-1); break; }
    else if(b.digits[i] == 0) {
      b.digits[i] = bignum::BASE-1;
      i++;
      }
    else {
      b.digits[i]--;
      break;
      }      
    }
  }

string bignum::get_str(int max_length) {
  if(digits.empty()) return "0";
  string ret = its(digits.back());
  for(int i=isize(digits)-2; i>=0; i--) {
    if(isize(ret) > max_length && i) {
      ret += XLAT(" (%1 more digits)", its(9 * (i+1)));
      return ret;
      }

    ret += " ";
    string val = its(digits[i]);
    while(isize(val) < 9) val = "0" + val;
    ret += val;
    }
  return ret;
  }

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());
  }

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(binarytiling) 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();
  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() {
  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) {
  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;
  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();
  }

int expansion_analyzer::valid(int v, int step) {
  if(step < 0) return 0;
  if(get_descendants(step+v+v+5).approx_int() >= bignum::BASE) return 0;
  ld matrix[100][128];
  for(int i=0; i<v; i++)
  for(int j=0; j<v+1; j++)
    matrix[i][j] = get_descendants(step+i+j).approx();
  
  for(int k=0; k<v; k++) {
    int nextrow = k;
    while(nextrow < v && std::abs(matrix[nextrow][k]) < 1e-6)
      nextrow++;
    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();
      }
    ld divv = 1. / 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) {
      ld 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);
  for(int i=0; i<v; i++) coef[i] = int(floor(matrix[v-1-i][v] + .5));
    
  for(int t=step+v; t<step+v+v+5; t++) if(!verify(t)) return 2;
  tested_to = step+v+v+5;
  while(tested_to < step+v+v+100 && get_descendants(tested_to).approx_ll() < bignum::BASE2) {
    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<1000; 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;
    // for(int i=0; i<N; i++) printf("%lf ", eigen[i]); printf("total = %lf\n", 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();
  }

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(binarytiling) 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;
  }

bool sizes_known() {
  if(bounded) return false;
  // Castle Anthrax is infinite
  if(binarytiling) return false;
  // not implemented
  if(archimedean) return false;
  return true;  
  }

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 };
string dfnames[3] = { "player", "start", "land" };

eDistanceFrom distance_from = dfPlayer;

enum eNumberCoding { ncNone, ncDistance, ncType, ncDebug };
string ncnames[4] = { "NO", "distance", "type", "debug" };
eNumberCoding number_coding = ncDistance;

bool mod_allowed() {
  return cheater || autocheat || archimedean || tour::on;
  }

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(eubinary || c->master->alt) return celldistAlt(c);
      return inmirror(c) ? (c->landparam & 255) : c->landparam;
    }
  return 0;    
  }

int position;

int type_in_reduced(expansion_analyzer& ea, cell *c, const cellfunction& f) {
  int a = ea.N;
  int t = type_in(ea, c, f);
  if(expansion.N != a) {
    expansion.reduce_grouping();
    t = type_in(ea, c, f);
    }
  return t;
  }

// which=1 => right, which=-1 => left

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

void generate_around(cell *c) {
  forCellCM(c2, c) if(c2->mpdist > BARLEV) setdist(c2, BARLEV, c);
  }
  
namespace ts {
  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);
    }

  cell *verified_add_gen(cell *c, int which, int bonus, const cellfunction& cf) {
    return verified_add(c, which, bonus, cf);
    }
  
  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);
    }
  
  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();
    }

  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();
    }

  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);
    }
  }

bool viewdists = false, use_color_codes = true, use_analyzer = true, show_distance_lists = true;

int first_distance = 0, scrolltime = 0;
bool scrolling_distances = false;

color_t distribute_color(int id) {
  color_t v = 0xFFFFFF;
  for(int z=0; z<24; z++) if(id & (1<<z)) part(v, (z%3)) &=~ (1<<(7-(z/3)));
  return v; 
  }

void do_viewdist(cell *c, const transmatrix& V, color_t& wcol, color_t& fcol) {
  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 = its(cd);
      dc = distcolors[cd];
      break;
      }
    case ncType: {
      int t = type_in_reduced(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 ncNone: ;
    }

  // 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);
  }

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(XLAT("color codes"), use_color_codes, 'u');
  dialog::add_action([] () { use_color_codes = !use_color_codes; });

  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"), "");
    });

  int id = 0;
  for(auto& lp: linepatterns::patterns) {
    using namespace linepatterns;
    if(among(lp.id, 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(XLAT(distance_from ? "show number of descendants by distance" : "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;

void expansion_analyzer::view_distances_dialog() {
  static int lastticks;
  if(scrolling_distances && !bounded) {
    scrolltime += SDL_GetTicks() - lastticks;
    first_distance += scrolltime / scrollspeed;
    scrolltime %= scrollspeed;
    }
  lastticks = SDL_GetTicks();
  
  dynamicval<color_t> dv(distcolors[0], forecolor);
  dialog::init("");
  cmode |= sm::DIALOG_STRICT_X | sm::EXPANSION;
  
  int maxlen = bounded ? 128 : 16 + first_distance;
  vector<bignum> qty(maxlen);
  
  bool really_use_analyzer = use_analyzer && sizes_known();
  
  if(really_use_analyzer) {
    int 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, bounded ? maxlen-1 : gamerange(), 100000, NULL);
      for(int d: cl.dists)
        if(d >= 0 && d < maxlen) qty[d]++;
      }
    else {
      celllister cl(cwt.at, bounded ? 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(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]);
            }
        }
      }
    }
  
  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() || binarytiling) {
    if(euclid) {
      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 = "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;
          }
        fmt += " (d>" + its(valid_from-1) + ")";
        dialog::addHelp(fmt);
        }
      else dialog::addBreak(100);
      
      char buf[20];
      snprintf(buf, 20, "%.8lf", (double) get_growth());
      dialog::addInfo("Θ(" + string(buf) + "...ᵈ)", forecolor);
      }
    }
  
  dialog::addItem(XLAT("scroll"), 'S');
  dialog::addItem(XLAT("configure"), 'C');
  dialog::display();
  }

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 !CAP_MINI
void compute_coefficients() {
  printf("%s %s\n", gp::operation_name().c_str(), ginf[geometry].tiling_name);
  start_game();
  
    printf("  sizes:");
    for(int i=0; i<10; i++) printf(" %d", expansion.get_descendants(i).approx_int());
    
    printf("  N = %d\n", expansion.N);

  expansion.find_coefficients();      
  if(expansion.coefficients_known == 2) {
    printf("  coefficients:"); for(int x: expansion.coef) printf(" %d", x);
    printf(" (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();
    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();
    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();
    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");
      }
    printf("growth = %lf\n", (double) expansion.get_growth());
    expansion.find_coefficients();      
    if(expansion.coefficients_known == 2) {
      printf("coefficients:"); for(int x: expansion.coef) printf(" %d", x);
      printf(", valid from %d to %d\n", expansion.valid_from, 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);
        need_reset_geometry = true;
        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-off")) {
    viewdists = false;
    }

  else return 1;
  return 0;
  }

auto ea_hook = addHook(hooks_args, 100, expansion_readArgs);
#endif
#endif

expansion_analyzer expansion;

int sibling_limit = 0;

void set_sibling_limit() {
  if(0) ;
  #if CAP_IRR
  else if(IRREGULAR) sibling_limit = 3;
  #endif
  #if CAP_BT
  else if(binarytiling) 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(binarytiling) 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);
    }
  }

int hyperbolic_celldistance(cell *c1, cell *c2) {  
  int found_distance = INF;
  
  int d = 0, d1 = celldist0(c1), d2 = celldist0(c2), sl_used = 0;

  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--;
      }
    }
  }

}