167 lines
4.0 KiB
C++
167 lines
4.0 KiB
C++
#include <iostream>
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#include <vector>
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#include <iomanip>
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#include <chrono>
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using Gens=std::vector<int>;
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using Table=std::vector<Gens>;
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void pp(const Gens &g, int w) {
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for (const auto &e : g) {
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std::cout << std::setw(w) << e << " ";
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}
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std::cout << std::endl;
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}
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void pp(const Table &t) {
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std::cout << "| table:" << std::endl;
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int w = 3;
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for (size_t i = 0; i < t.size(); ++i) {
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std::cout << std::setw(w) << i << " | ";
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pp(t[i], w);
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}
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}
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void add_row(const int ngens, const std::vector<Gens> &rels,
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Table &cosets, std::vector<Table> &reltables,
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Table &starts, Table &ends) {
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int C = cosets.size();
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cosets.emplace_back(ngens, -1);
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for (unsigned int i = 0; i < rels.size(); ++i) {
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auto &table = reltables[i];
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unsigned int R = rels[i].size();
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table.emplace_back(R + 1, -1);
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table[C][0] = C;
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table[C][R] = C;
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starts[i].push_back(0);
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ends[i].push_back(R);
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}
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}
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int add_coset(const int ngens, const std::vector<Gens> &rels,
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Table &cosets, std::vector<Table> &reltables,
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Table &starts, Table &ends,
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int coset_scan_hint) {
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int C = cosets.size();
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for (int c = coset_scan_hint; c < C; ++c) {
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std::vector<int> &row = cosets[c];
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for (int g = 0; g < ngens; ++g) {
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if (row[g] == -1) {
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row[g] = C;
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add_row(ngens, rels, cosets, reltables, starts, ends);
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cosets[C][g] = c;
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return c;
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}
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}
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}
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return -1;
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}
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/**
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* learn until it can't
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*/
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void learn(Table &coset, const std::vector<Gens> &rels,
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std::vector<Table> &reltables, Table &starts, Table &ends) {
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unsigned int nrels = rels.size();
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while (true) {
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bool complete = true;
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for (unsigned int r = 0; r < nrels; ++r) {
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auto &table = reltables[r];
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const auto &rel = rels[r];
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for (unsigned int c = 0; c < table.size(); c++) {
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auto &row = table[c];
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auto s = starts[r][c];
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auto e = ends[r][c];
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if (s == e - 1) continue;
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while (row[s + 1] == -1) {
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const int &lookup = coset[row[s]][rel[s]];
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if (lookup < 0) break;
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s++;
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row[s] = lookup;
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}
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while (row[e - 1] == -1) {
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const int &lookup = coset[row[e]][rel[e - 1]];
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if (lookup < 0) break;
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e--;
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row[e] = lookup;
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}
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if (s == e - 1) {
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complete = false;
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const int &gen = rel[s];
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coset[row[s]][gen] = row[e];
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coset[row[e]][gen] = row[s];
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}
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starts[r][c] = s;
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ends[r][c] = e;
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}
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}
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if (complete) break;
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}
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}
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Table solve_tc(int ngens, const Gens &subgens, const std::vector<Gens> &rels) {
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Table cosets;
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std::vector<Table> reltables(rels.size());
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// storing progress for each relation table row
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Table starts(rels.size()); // [rel_table][coset]
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Table ends(rels.size());
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// set up initial coset
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add_row(ngens, rels, cosets, reltables, starts, ends);
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for (const auto &gen : subgens) {
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cosets[0][gen] = 0;
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}
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int coset_scan_hint = 0;
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while (coset_scan_hint >= 0) {
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learn(cosets, rels, reltables, starts, ends);
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coset_scan_hint = add_coset(ngens, rels, cosets, reltables, starts, ends, coset_scan_hint);
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}
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return cosets;
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}
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int main() {
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auto s = std::chrono::system_clock::now();
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auto cosets = solve_tc(4, {}, {
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{0, 1, 0, 1, 0, 1, 0, 1, 0, 1},
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{1, 2, 1, 2, 1, 2},
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{2, 3, 2, 3, 2, 3},
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{0, 2, 0, 2},
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{0, 3, 0, 3},
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{1, 3, 1, 3},
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});
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auto e = std::chrono::system_clock::now();
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std::chrono::duration<float> diff = e - s;
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std::cout << diff.count() << "s" << std::endl;
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// pp(cosets);
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return 0;
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}
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