feat: add backtrack support

src/core/fast_cal/fast_cal.h

@@ -131,6 +131,11 @@ public:
 
     // ------------------------------------------------------------------------------------- //
 
+    /// Backtrack the shortest path from specified case.
+    std::vector<RawCode> backtrack(RawCode code);
+
+    // ------------------------------------------------------------------------------------- //
+
 private:
     // ------------------------------------------------------------------------------------- //
 

src/core/fast_cal/internal/demo.cc

@@ -96,13 +96,29 @@ std::vector<RawCode> FastCalPro::furthest() {
     }
 }
 
+std::vector<RawCode> FastCalPro::backtrack(RawCode code) {
+    if (const auto match = cases_.find(code.unwrap()); match == cases_.end()) {
+        return {}; // case not found
+    }
+    std::vector<RawCode> path;
+    while (code != 0) {
+        path.emplace_back(code);
+        code = RawCode::unsafe_create(cases_.find(code.unwrap())->second.back);
+    }
+    std::reverse(path.begin(), path.end());
+    return path;
+}
+
 RawCode FastCal_demo(RawCode raw_code) {
     klotski::fast_cal::FastCalPro fc {raw_code};
-    return fc.solve().value();
+//    return fc.solve().value();
 
-//    auto tmp = fc.solve();
+    auto tmp = fc.solve();
 //    std::cout << tmp.value().to_common_code() << std::endl;
 
+    auto path = fc.backtrack(tmp.value());
+    std::cout << path.size() << std::endl;
+
 //    auto tmp = fc.solve_multi();
 //    for (const auto x : tmp) {
 //        std::cout << x.to_common_code() << std::endl;
@@ -118,5 +134,5 @@ RawCode FastCal_demo(RawCode raw_code) {
 //    });
 //    std::cout << tmp.value().to_common_code() << std::endl;
 
-//    return RawCode::unsafe_create(0);
+    return RawCode::unsafe_create(0);
 }