add walk to path

example/path.cpp

@@ -7,10 +7,20 @@ int main() {
     auto cube = tc::group::B(3);
     auto vars = cube.solve();
 
-    for (size_t target = 1; target < vars.size(); target++) {
-        auto &action = vars.path.get(target);
-        std::cout << action.from_idx << " * " << action.gen << " = " << target << std::endl;
+    auto words = vars.path.walk<std::string>(
+        "",
+        {"a", "b", "c"},
+        [](auto a, auto b) { return a + b; }
+    );
+
+    for (const auto &word : words) {
+        std::cout << word << std::endl;
     }
 
+//    for (size_t target = 1; target < vars.size(); target++) {
+//        auto &action = vars.path.get(target);
+//        std::cout << action.from_idx << " * " << action.gen << " = " << target << std::endl;
+//    }
+
     return 0;
 }

include/tc/core.hpp

@@ -1,8 +1,9 @@
 #pragma once
 
-#include<array>
-#include<vector>
-#include<string>
+#include <array>
+#include <functional>
+#include <vector>
+#include <string>
 
 namespace tc {
     struct Action {
@@ -25,10 +26,30 @@ namespace tc {
 
         void add_row();
 
-        [[nodiscard]] const Action get(int to_idx) const;
+        [[nodiscard]] Action get(int to_idx) const;
 
         void put(int from_idx, int gen, int to_idx);
 
+        template<class T>
+        [[nodiscard]] std::vector<T> walk(
+            T start,
+            std::vector<T> gen_values,
+            std::function<T(const T&, const T&)> op
+        ) const {
+            std::vector<T> res(size());
+            res[0] = start;
+
+            for (int i = 1; i < res.size(); ++i) {
+                auto action = path[i];
+                const auto &from = res[action.from_idx];
+                const auto &val = gen_values[action.gen];
+                res[i] = op(from, val);
+            }
+
+            return res;
+        }
+
+
         [[nodiscard]] size_t size() const;
     };
 

src/core.cpp

@@ -12,7 +12,7 @@ namespace tc {
         path.resize(path.size() + 1);
     }
 
-    const Action Path::get(int to_idx) const {
+    Action Path::get(int to_idx) const {
         return path[to_idx];
     }