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hyperrogue/expansion.cpp
2018-09-12 06:10:56 +02:00

415 lines
12 KiB
C++

// 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;
}
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;
}
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);
res.push_back(subtype(c1) * 4 + celldist(c1) - d);
}
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;
}
void expansion_analyzer::preliminary_grouping() {
samples.clear();
codeid.clear();
children.clear();
sample_id(currentmap->gamestart());
for(int i=0; i<isize(samples); i++) {
children.emplace_back();
auto c = samples[i];
int d = celldist(c);
for(int k=0; k<c->type; k++) {
cell *c1 = c->cmove(k);
if(celldist(c1) != d+1) continue;
cell *c2 = c->cmove((k+1) % c->type);
if(celldist(c2) != d+1) continue;
children.back().push_back(sample_id(c1));
}
}
N = isize(samples);
rootid = 0;
}
void expansion_analyzer::reduce_grouping() {
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);
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 = N;
children.push_back(children[rootid]);
children[diskid].push_back(diskid);
N++;
}
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();
}
bool sizes_known() {
if(bounded) return false;
// Castle Anthrax is infinite
if(binarytiling) return false;
// not implemented
if(archimedean) return false;
return true;
}
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);
}
void expansion_analyzer::view_distances_dialog() {
distcolors[0] = forecolor;
dialog::init("");
long long qty[64];
vector<cell*>& ac = currentmap->allcells();
for(int i=0; i<64; i++) qty[i] = 0;
for(int i=0; i<isize(ac); i++) {
int d = celldistance(ac[i], cwt.at);
if(d >= 0 && d < 64) qty[d]++;
}
if(sizes_known()) {
find_coefficients();
if(gamerange() >= valid_from && coefficients_known == 2) {
for(int i=gamerange()+1; i<64; i++) {
qty[i] = 0;
for(int j=0; j<isize(coef); j++)
qty[i] += qty[i-1-j] * coef[j];
}
}
}
for(int i=0; i<(bounded ? 64 : 16); i++) if(qty[i])
dialog::addInfo(its(qty[i]), distcolors[i&7]);
if(binarytiling) {
dialog::addBreak(300);
dialog::addInfo("a(d) ~ 2ᵈ");
}
else if(sizes_known()) {
if(euclid) {
dialog::addBreak(300);
dialog::addInfo("a(d) = " + its(get_descendants(10).approx_int() - get_descendants(9).approx_int()) + "d", forecolor);
}
else {
dialog::addBreak(200);
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;
}
dialog::addHelp(fmt);
}
else dialog::addBreak(100);
char buf[20];
snprintf(buf, 20, "%.8lf", (double) get_growth());
dialog::addInfo("a(d) ~ " + string(buf) + "", forecolor);
}
}
dialog::display();
}
#if !CAP_MINI
void compute_coefficients() {
printf("%s %s\n", gp::operation_name().c_str(), ginf[geometry].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);
}
}
int readArgs() {
using namespace arg;
if(0) ;
else if(argis("-vap")) {
PHASEFROM(2);
start_game();
while(true) {
string s = expansion.approximate_descendants(10000, 100);
printf("s = %s\n", s.c_str());
if(isize(expansion.descendants) >= 10000) break;
}
}
else if(argis("-csizes")) {
PHASEFROM(2);
start_game();
expansion.get_growth();
for(int i=0; i<30; 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);
printf("reduce_grouping...\n");
expansion.reduce_grouping();
printf("N = %d\n", expansion.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);
}
}
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();
}
}
}
else return 1;
return 0;
}
auto ea_hook = addHook(hooks_args, 100, readArgs);
#endif
expansion_analyzer expansion;
}