Merge pull request #2 from allemangD/todd-coxeter-algorithm

Todd coxeter algorithm

.idea/cosets.iml

@@ -1,2 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<module classpath="CMake" type="CPP_MODULE" version="4" />

.idea/misc.xml

@@ -1,15 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<project version="4">
-  <component name="CMakeWorkspace" PROJECT_DIR="$PROJECT_DIR$" />
-  <component name="CidrRootsConfiguration">
-    <sourceRoots>
-      <file path="$PROJECT_DIR$/cosets/src" />
-    </sourceRoots>
-    <libraryRoots>
-      <file path="$PROJECT_DIR$/vendor" />
-    </libraryRoots>
-  </component>
-  <component name="JavaScriptSettings">
-    <option name="languageLevel" value="ES6" />
-  </component>
-</project>

.idea/modules.xml

@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<project version="4">
-  <component name="ProjectModuleManager">
-    <modules>
-      <module fileurl="file://$PROJECT_DIR$/.idea/cosets.iml" filepath="$PROJECT_DIR$/.idea/cosets.iml" />
-    </modules>
-  </component>
-</project>

.idea/vcs.xml

@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<project version="4">
-  <component name="VcsDirectoryMappings">
-    <mapping directory="$PROJECT_DIR$" vcs="Git" />
-  </component>
-</project>

cosets/CMakeLists.txt

@@ -15,3 +15,5 @@ add_custom_command(
             ${CMAKE_CURRENT_SOURCE_DIR}/src/shaders
             ${CMAKE_CURRENT_BINARY_DIR}/shaders
 )
+
+add_executable(coxeter src/tc.cpp)

cosets/src/main.cpp

@@ -29,16 +29,16 @@ public:
 
       program = build_program("main", vs, fs);
 
-      float verts_data[4 * VERTS_N]{
-         +.5f, +.5f, 0.f, 0.f,
-         +.5f, -.5f, 0.f, 0.f,
-         -.5f, -.5f, 0.f, -.1f,
-         -.5f, +.5f, 0.f, -.1f,
+      glm::vec4 verts_data[VERTS_N]{
+         {+0.5, +0.5, +0.5, +0.0},
+         {+0.5, -0.5, +0.5, +0.0},
+         {-0.5, -0.5, +0.5, +0.0},
+         {-0.5, +0.5, +0.5, +0.0},
 
-         +.5f, +.5f, 0.f, .1f,
-         +.5f, -.5f, 0.f, .1f,
-         -.5f, -.5f, 0.2f, .0f,
-         -.5f, +.5f, 0.2f, .0f,
+         {+0.5, +0.5, +0.5, -0.5},
+         {+0.5, -0.5, +0.5, -0.5},
+         {-0.5, -0.5, +0.5, +0.5},
+         {-0.5, +0.5, +0.5, +0.5},
       };
 
       glGenBuffers(1, &verts);

cosets/src/tc.cpp

@@ -0,0 +1,222 @@
+#include <iostream>
+#include <vector>
+#include <iomanip>
+#include <algorithm>
+#include <cmath>
+
+
+struct Table {
+   int N;
+   std::vector<std::vector<int>> fwd;
+   std::vector<std::vector<int>> rev;
+
+   explicit Table(int N) {
+      add_row();
+      this->N = N;
+   }
+
+   void add_row() {
+      fwd.emplace_back(N, -1);
+      rev.emplace_back(N, -1);
+   }
+
+   int add_coset() {
+      for (int from = 0; from < (int) size(); ++from) {
+         for (int gen = 0; gen < N; ++gen) {
+            if (get(from, gen) < 0) {
+               int to = (int) size();
+               add_row();
+               set(from, gen, to);
+               return to;
+            }
+         }
+      }
+      return 0;
+   }
+
+   [[nodiscard]] unsigned size() const {
+      return fwd.size();
+   }
+
+   void set(int from, int gen, int to) {
+      fwd[from][gen] = to;
+      rev[to][gen] = from;
+   }
+
+   [[nodiscard]] int get(int from, int gen) const {
+      return fwd[from][gen];
+   }
+
+   [[nodiscard]] int rget(int gen, int to) const {
+      return rev[to][gen];
+   }
+
+   std::vector<std::vector<int>> words() {
+      std::vector<std::vector<int> *> vecs(size());
+      vecs[0] = new std::vector<int>();
+
+      while (std::find(vecs.begin(), vecs.end(), nullptr) != vecs.end()) {
+         for (int from = 0; from < (int) vecs.size(); ++from) {
+            std::vector<int> *word = vecs[from];
+            if (word == nullptr) {
+               continue;
+            }
+
+            for (int gen = 0; gen < (int) N; ++gen) {
+               int to = get(from, gen);
+               if (vecs[to] != nullptr) {
+                  continue;
+               }
+
+               vecs[to] = new std::vector<int>(*word);
+               vecs[to]->push_back(gen);
+            }
+         }
+      }
+
+      std::vector<std::vector<int>> res(size());
+      for (int i = 0; i < (int) size(); ++i) {
+         res[i] = *vecs[i];
+      }
+
+      return res;
+   }
+};
+
+struct Row {
+   std::vector<int>::const_iterator l;
+   std::vector<int>::const_iterator r;
+
+   int from;
+   int to;
+
+   Row(const std::vector<int> &vec, int cos) {
+      this->l = vec.begin();
+      this->r = vec.end() - 1;
+      this->from = cos;
+      this->to = cos;
+   }
+
+   bool learn(Table *table) {
+      if (r - l == 0) {
+         return false;
+      }
+
+      while (r - l > 0) {
+         int next = table->get(from, *l);
+         if (next < 0) break;
+         l++;
+         from = next;
+      }
+
+      while (r - l > 0) {
+         int next = table->rget(*r, to);
+         if (next < 0) break;
+         r--;
+         to = next;
+      }
+
+      if (r - l == 0) {
+         table->set(from, *l, to);
+         return true;
+      }
+
+      return false;
+   }
+};
+
+std::ostream &operator<<(std::ostream &out, const Row &row) {
+   out << "[ " << row.from << " | ";
+   auto it = row.l;
+   while (row.r - it > 0) {
+      out << *it << " ";
+      it++;
+   }
+   out << "| " << row.to << " ]";
+   return out;
+}
+
+Table *solve(int gens, const std::vector<int> &subgens, const std::vector<std::vector<int>> &rels) {
+   auto *table = new Table(gens);
+
+   for (int gen : subgens)
+      table->set(0, gen, 0);
+
+   std::vector<Row> rows;
+   rows.reserve(rels.size());
+   for (const auto &rel : rels)
+      rows.emplace_back(rel, 0);
+
+   while (!rows.empty()) {
+      while (true) {
+         bool learned = false;
+         for (int i = (int) rows.size() - 1; i >= 0; i--) {
+            if (rows[i].learn(table)) {
+               learned = true;
+               rows.erase(rows.begin() + i);
+            }
+         }
+         if (!learned)
+            break;
+      }
+
+      int i = (int) table->size();
+      if (table->add_coset() > 0) {
+         for (const auto &rel : rels)
+            rows.emplace_back(rel, i);
+      } else {
+         break;
+      }
+   }
+
+   return table;
+}
+
+std::ostream &operator<<(std::ostream &out, const Table &table) {
+   int k = ceil(log10(table.size()));
+
+   out << "[";
+   for (unsigned j = 0; j < table.size(); ++j) {
+      auto arr = table.fwd[j];
+      out << " " << std::setw(k) << j << " [";
+      for (int i = 0; i < table.N; ++i) {
+         out << arr[i];
+
+         if (i < table.N - 1)
+            out << " ";
+      }
+
+      out << "]";
+      if (j < table.fwd.size() - 1)
+         out << "\n ";
+   }
+   out << "]\n";
+
+   return out;
+}
+
+int main(int argc, char *argv[]) {
+   std::vector<std::vector<int>> ids{
+      {0, 0},
+      {1, 1},
+      {2, 2},
+      {0, 1, 0, 1, 0, 1, 0, 1},
+      {1, 2, 1, 2, 1, 2},
+      {0, 2, 0, 2}
+   };
+
+   Table *table = solve(3, {0, 1}, ids);
+
+   std::cout << table->size() << std::endl;
+   std::cout << *table << std::endl;
+
+   for (const auto &v : table->words()) {
+      std::cout << "[ ";
+      for (auto e : v) {
+         std::cout << e << " ";
+      }
+      std::cout << "]\n";
+   }
+
+   return 0;
+}