Add spanning tree path to cosets.

example/CMakeLists.txt

@@ -1,2 +1,5 @@
 add_executable(bench bench.cpp)
 target_link_libraries(bench PRIVATE tc)
+
+add_executable(path path.cpp)
+target_link_libraries(path PRIVATE tc)

example/path.cpp

@@ -0,0 +1,17 @@
+#include "solver.h"
+#include "groups.h"
+
+#include <ctime>
+#include <iostream>
+
+int main() {
+    auto cube = tc::group::B(3);
+    auto vars = tc::solve(cube, {});
+
+    for (int target = 1; target < vars.len; target++) {
+        auto &action = vars.path[target];
+        std::cout << action.coset << " " << action.gen << " " << target << std::endl;
+    }
+
+    return 0;
+}

include/cosets.h

@@ -4,9 +4,15 @@
 #include <vector>
 
 namespace tc {
+    struct Action {
+        int coset = -1;
+        int gen = -1;
+    };
+
     struct Cosets {
         int ngens;
         std::vector<int> data;
+        std::vector<Action> path;
         int len;
 
         explicit Cosets(int ngens);
@@ -21,5 +27,4 @@ namespace tc {
 
         [[nodiscard]] int get(int idx) const;
     };
-
 }

src/cosets.cpp

@@ -7,11 +7,16 @@ namespace tc {
     void Cosets::add_row() {
         len++;
         data.resize(data.size() + ngens, -1);
+        path.resize(path.size() + 1);
     }
 
     void Cosets::put(int coset, int gen, int target) {
         data[coset * ngens + gen] = target;
         data[target * ngens + gen] = coset;
+
+        if (path[target].coset == -1) {
+            path[target] = {coset, gen};
+        }
     }
 
     void Cosets::put(int idx, int target) {
@@ -19,6 +24,10 @@ namespace tc {
         int gen = idx % ngens;
         data[idx] = target;
         data[target * ngens + gen] = coset;
+
+        if (path[target].coset == -1) {
+            path[target] = {coset, gen};
+        }
     }
 
     int Cosets::get(int coset, int gen) const {