mirror of
https://github.com/zenorogue/hyperrogue.git
synced 2024-11-20 03:54:47 +00:00
415 lines
12 KiB
C++
415 lines
12 KiB
C++
// HyperRogue -- expansion_analyzer
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// Copyright (C) 2011-2018 Zeno Rogue, see 'hyper.cpp' for details
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namespace hr {
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int subtype(cell *c) {
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return patterns::getpatterninfo(c, patterns::PAT_NONE, 0).id;
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}
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bignum& bignum::operator +=(const bignum& b) {
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int K = isize(b.digits);
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if(K > isize(digits)) digits.resize(K);
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int carry = 0;
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for(int i=0; i<K || carry; i++) {
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if(i >= isize(digits)) digits.push_back(0);
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digits[i] += carry;
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if(i < K) digits[i] += b.digits[i];
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if(digits[i] >= BASE) {
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digits[i] -= BASE;
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carry = 1;
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}
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else carry = 0;
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}
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return *this;
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}
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string bignum::get_str(int max_length) {
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if(digits.empty()) return "0";
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string ret = its(digits.back());
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for(int i=isize(digits)-2; i>=0; i--) {
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if(isize(ret) > max_length && i) {
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ret += XLAT(" (%1 more digits)", its(9 * (i+1)));
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return ret;
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}
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ret += " ";
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string val = its(digits[i]);
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while(isize(val) < 9) val = "0" + val;
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ret += val;
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}
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return ret;
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}
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vector<int> expansion_analyzer::gettype(cell *c) {
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vector<int> res;
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res.push_back(subtype(c) * 4 + 2);
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int d = celldist(c);
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for(int i=0; i<c->type; i++) {
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cell *c1 = c->cmove(i);
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res.push_back(subtype(c1) * 4 + celldist(c1) - d);
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}
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return res;
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}
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int expansion_analyzer::sample_id(cell *c) {
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auto t = gettype(c);
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if(codeid.count(t)) return codeid[t];
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auto &cit = codeid[t];
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cit = isize(samples);
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samples.push_back(c);
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return cit;
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}
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void expansion_analyzer::preliminary_grouping() {
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samples.clear();
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codeid.clear();
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children.clear();
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sample_id(currentmap->gamestart());
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for(int i=0; i<isize(samples); i++) {
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children.emplace_back();
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auto c = samples[i];
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int d = celldist(c);
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for(int k=0; k<c->type; k++) {
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cell *c1 = c->cmove(k);
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if(celldist(c1) != d+1) continue;
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cell *c2 = c->cmove((k+1) % c->type);
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if(celldist(c2) != d+1) continue;
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children.back().push_back(sample_id(c1));
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}
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}
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N = isize(samples);
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rootid = 0;
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}
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void expansion_analyzer::reduce_grouping() {
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vector<int> grouping;
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grouping.resize(N);
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int nogroups = 1;
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for(int i=0; i<N; i++) grouping[i] = 0;
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while(true) {
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vector< pair<vector<int>, int > > childgroups(N);
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for(int i=0; i<N; i++) {
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childgroups[i].second = i;
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for(int j: children[i])
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childgroups[i].first.push_back(grouping[j]);
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sort(childgroups[i].first.begin(), childgroups[i].first.end());
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}
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sort(childgroups.begin(), childgroups.end());
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int newgroups = 0;
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for(int i=0; i<N; i++) {
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if(i == 0 || childgroups[i].first != childgroups[i-1].first) newgroups++;
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grouping[childgroups[i].second] = newgroups - 1;
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}
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if(nogroups == newgroups) break;
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nogroups = newgroups;
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}
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vector<int> groupsample(nogroups);
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for(int i=0; i<N; i++) groupsample[grouping[i]] = i;
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vector<vector<int>> newchildren(nogroups);
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for(int i=0; i<nogroups; i++)
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for(int j: children[groupsample[i]])
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newchildren[i].push_back(grouping[j]);
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children = move(newchildren);
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for(auto& p: codeid) p.second = grouping[p.second];
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N = nogroups;
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rootid = grouping[rootid];
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diskid = N;
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children.push_back(children[rootid]);
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children[diskid].push_back(diskid);
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N++;
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}
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template<class T> int size_upto(vector<T>& v, int s) {
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int res = isize(v);
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if(res < s) v.resize(s);
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return res;
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}
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bignum& expansion_analyzer::get_descendants(int level) {
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if(!N) preliminary_grouping(), reduce_grouping();
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return get_descendants(level, rootid);
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}
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bignum& expansion_analyzer::get_descendants(int level, int type) {
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auto& pd = descendants;
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size_upto(pd, level+1);
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for(int d=0; d<=level; d++)
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for(int i=size_upto(pd[d], N); i<N; i++)
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if(d == 0) pd[d][i].be(1);
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else for(int j: children[i])
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pd[d][i] += pd[d-1][j];
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return pd[level][type];
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}
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bool expansion_analyzer::verify(int id) {
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if(id < isize(coef)) return false;
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long long res = 0;
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for(int t=0; t<isize(coef); t++)
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res += coef[t] * get_descendants(id-t-1).approx_ll();
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return res == get_descendants(id).approx_ll();
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}
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int expansion_analyzer::valid(int v, int step) {
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if(step < 0) return 0;
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if(get_descendants(step+v+v+5).approx_int() >= bignum::BASE) return 0;
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ld matrix[100][128];
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for(int i=0; i<v; i++)
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for(int j=0; j<v+1; j++)
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matrix[i][j] = get_descendants(step+i+j).approx();
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for(int k=0; k<v; k++) {
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int nextrow = k;
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while(nextrow < v && std::abs(matrix[nextrow][k]) < 1e-6)
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nextrow++;
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if(nextrow == v) return 1;
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if(nextrow != k) {
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// printf("swap %d %d\n", k, nextrow);
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for(int l=0; l<=v; l++) swap(matrix[k][l], matrix[nextrow][l]);
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// display();
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}
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ld divv = 1. / matrix[k][k];
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for(int k1=k; k1<=v; k1++) matrix[k][k1] *= divv;
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// printf("divide %d\n", k);
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// display();
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for(int k1=k+1; k1<v; k1++) if(matrix[k1][k] != 0) {
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ld coef = -matrix[k1][k];
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for(int k2=k; k2<=v; k2++) matrix[k1][k2] += matrix[k][k2] * coef;
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}
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// printf("zeros below %d\n", k);
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// display();
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}
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for(int k=v-1; k>=0; k--)
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for(int l=k-1; l>=0; l--)
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if(matrix[l][k]) matrix[l][v] -= matrix[l][k] * matrix[k][v];
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coef.resize(v);
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for(int i=0; i<v; i++) coef[i] = int(floor(matrix[v-1-i][v] + .5));
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for(int t=step+v; t<step+v+v+5; t++) if(!verify(t)) return 2;
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tested_to = step+v+v+5;
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while(tested_to < step+v+v+100 && get_descendants(tested_to).approx_ll() < bignum::BASE2) {
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if(!verify(tested_to)) return 2;
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tested_to++;
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}
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valid_from = step+v;
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return 3;
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}
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void expansion_analyzer::find_coefficients() {
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if(coefficients_known) return;
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if(!N) preliminary_grouping(), reduce_grouping();
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for(int v=1; v<25; v++)
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for(int step=0; step<1000; step++) {
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int val = valid(v, step);
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if(val == 0) break;
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if(val == 3) { coefficients_known = 2; return; }
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}
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coefficients_known = 1;
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}
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ld growth;
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ld expansion_analyzer::get_growth() {
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if(growth >= 1) return growth;
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if(!N) preliminary_grouping(), reduce_grouping();
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vector<ld> eigen(N, 1);
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ld total;
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for(int iter=0; iter<100000; iter++) {
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total = 0;
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vector<ld> neweigen(N, 0);
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for(int i=0; i<N; i++) {
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for(int j: children[i]) neweigen[i] += eigen[j];
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total += neweigen[i];
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}
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for(int i=0; i<N; i++) eigen[i] = .1 * eigen[i] + .9 * neweigen[i] / total;
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// for(int i=0; i<N; i++) printf("%lf ", eigen[i]); printf("total = %lf\n", total);
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}
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return growth = total;
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}
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void expansion_analyzer::reset() {
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N = 0;
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growth = 0;
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coefficients_known = 0;
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samples.clear();
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codeid.clear();
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children.clear();
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coef.clear();
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descendants.clear();
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}
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bool sizes_known() {
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if(bounded) return false;
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// Castle Anthrax is infinite
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if(binarytiling) return false;
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// not implemented
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if(archimedean) return false;
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return true;
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}
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string expansion_analyzer::approximate_descendants(int d, int max_length) {
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auto t = SDL_GetTicks();
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while(isize(descendants) <= d && SDL_GetTicks() < t + 100)
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get_descendants(isize(descendants));
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if(isize(descendants) > d)
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return get_descendants(d).get_str(max_length);
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int v = isize(descendants) - 1;
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bignum& b = get_descendants(v);
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if(b.digits.empty()) return "0";
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ld log_10 = log(b.digits.back()) / log(10) + 9 * (isize(b.digits) - 1) + (d - v) * log(get_growth()) / log(10);
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int more_digits = int(log_10);
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return XLAT("about ") + fts(pow(10, log_10 - more_digits)) + "E" + its(more_digits);
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}
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void expansion_analyzer::view_distances_dialog() {
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distcolors[0] = forecolor;
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dialog::init("");
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long long qty[64];
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vector<cell*>& ac = currentmap->allcells();
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for(int i=0; i<64; i++) qty[i] = 0;
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for(int i=0; i<isize(ac); i++) {
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int d = celldistance(ac[i], cwt.at);
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if(d >= 0 && d < 64) qty[d]++;
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}
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if(sizes_known()) {
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find_coefficients();
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if(gamerange() >= valid_from && coefficients_known == 2) {
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for(int i=gamerange()+1; i<64; i++) {
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qty[i] = 0;
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for(int j=0; j<isize(coef); j++)
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qty[i] += qty[i-1-j] * coef[j];
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}
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}
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}
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for(int i=0; i<(bounded ? 64 : 16); i++) if(qty[i])
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dialog::addInfo(its(qty[i]), distcolors[i&7]);
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if(binarytiling) {
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dialog::addBreak(300);
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dialog::addInfo("a(d) ~ 2ᵈ");
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}
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else if(sizes_known()) {
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if(euclid) {
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dialog::addBreak(300);
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dialog::addInfo("a(d) = " + its(get_descendants(10).approx_int() - get_descendants(9).approx_int()) + "d", forecolor);
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}
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else {
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dialog::addBreak(200);
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if(coefficients_known == 2) {
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string fmt = "a(d+" + its(isize(coef)) + ") = ";
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bool first = true;
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for(int i=0; i<isize(coef); i++) if(coef[i]) {
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if(first && coef[i] == 1) ;
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else if(first) fmt += its(coef[i]);
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else if(coef[i] == 1) fmt += " + ";
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else if(coef[i] == -1) fmt += " - ";
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else if(coef[i] > 1) fmt += " + " + its(coef[i]);
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else if(coef[i] < -1) fmt += " - " + its(-coef[i]);
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fmt += "a(d";
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if(i != isize(coef) - 1)
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fmt += "+" + its(isize(coef) - 1 - i);
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fmt += ")";
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first = false;
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}
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dialog::addHelp(fmt);
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}
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else dialog::addBreak(100);
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char buf[20];
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snprintf(buf, 20, "%.8lf", (double) get_growth());
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dialog::addInfo("a(d) ~ " + string(buf) + "ᵈ", forecolor);
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}
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}
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dialog::display();
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}
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#if !CAP_MINI
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void compute_coefficients() {
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printf("%s %s\n", gp::operation_name().c_str(), ginf[geometry].name);
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start_game();
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printf(" sizes:");
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for(int i=0; i<10; i++) printf(" %d", expansion.get_descendants(i).approx_int());
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printf(" N = %d\n", expansion.N);
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expansion.find_coefficients();
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if(expansion.coefficients_known == 2) {
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printf(" coefficients:"); for(int x: expansion.coef) printf(" %d", x);
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printf(" (tested on %d to %d)\n", expansion.valid_from, expansion.tested_to);
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}
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}
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int readArgs() {
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using namespace arg;
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if(0) ;
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else if(argis("-vap")) {
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PHASEFROM(2);
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start_game();
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while(true) {
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string s = expansion.approximate_descendants(10000, 100);
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printf("s = %s\n", s.c_str());
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if(isize(expansion.descendants) >= 10000) break;
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}
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}
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else if(argis("-csizes")) {
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PHASEFROM(2);
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start_game();
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expansion.get_growth();
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for(int i=0; i<30; i++)
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printf("%s / %s\n", expansion.get_descendants(i).get_str(1000).c_str(), expansion.get_descendants(i, expansion.diskid).get_str(1000).c_str());
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}
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else if(argis("-csolve")) {
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PHASEFROM(2);
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start_game();
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printf("preliminary_grouping...\n");
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expansion.preliminary_grouping();
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printf("N = %d\n", expansion.N);
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printf("reduce_grouping...\n");
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expansion.reduce_grouping();
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printf("N = %d\n", expansion.N);
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printf("growth = %lf\n", (double) expansion.get_growth());
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expansion.find_coefficients();
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if(expansion.coefficients_known == 2) {
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printf("coefficients:"); for(int x: expansion.coef) printf(" %d", x);
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printf(", valid from %d to %d\n", expansion.valid_from, expansion.tested_to);
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}
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}
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else if(argis("-csolve_tab")) {
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for(eGeometry geo: {gNormal, gOctagon, g45, g46, g47}) {
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set_geometry(geo);
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set_variation(eVariation::pure);
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compute_coefficients();
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set_variation(eVariation::bitruncated);
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compute_coefficients();
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for(int x=1; x<9; x++)
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for(int y=0; y<=x; y++) {
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if(x == 1 && y == 0) continue;
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if(x == 1 && y == 1 && S3 == 3) continue;
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if(x+y > 10) continue;
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stop_game();
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gp::param = gp::loc(x, y);
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need_reset_geometry = true;
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set_variation(eVariation::goldberg);
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compute_coefficients();
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}
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}
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}
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else return 1;
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return 0;
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}
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auto ea_hook = addHook(hooks_args, 100, readArgs);
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#endif
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expansion_analyzer expansion;
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} |