solver: prune insufficient valley capacity

A selected valley cannot admit a square wider than itself until it reaches the lower neighbouring rim. Reject states whose remaining narrow-square area cannot fill that strip, including width-one and width-two gaps.

Keep an unpruned benchmark mode and dedicated counters so the rule remains independently measurable. Record the soundness argument and the measured default-on improvement.

Tests: Debug CTest (12 passed)

Tests: ASan+UBSan CTest (12 passed)

Refs: #10

benchmarks/benchmark.cc

@@ -29,6 +29,7 @@ namespace {
   auto solve(std::uint64_t order, bool instrument,
              SearchPolicy policy, bool direct_search,
              SymmetryBreaking symmetry,
+             Pruning pruning,
              SearchCounters &counters)
       -> TimedSolution {
     auto const predecessor_order =
@@ -37,8 +38,8 @@ namespace {
     auto predecessor =
         instrument
             ? search_solution_instrumented(predecessor_order, counters,
-                                           policy, symmetry)
-            : search_solution(predecessor_order, policy, symmetry);
+                                           policy, symmetry, pruning)
+            : search_solution(predecessor_order, policy, symmetry, pruning);
     auto const search_end = Clock::now();
 
     auto const construction_begin = Clock::now();
@@ -94,10 +95,10 @@ namespace {
 }
 
 int main(int argc, char **argv) {
-  if (argc < 3 || argc > 6) {
+  if (argc < 3 || argc > 7) {
     std::cerr << "usage: partridge_benchmark ORDER counters|plain "
                  "[ascending|descending|best-fit] [public|direct] "
-                 "[d4|none]\n";
+                 "[d4|none] [valley-capacity|none]\n";
     return 2;
   }
   auto const order = static_cast<std::uint64_t>(std::strtoull(argv[1], nullptr, 10));
@@ -134,10 +135,20 @@ int main(int argc, char **argv) {
     std::cerr << "symmetry mode must be d4 or none\n";
     return 2;
   }
+  auto const pruning =
+      argc < 7 || std::string_view(argv[6]) == "valley-capacity"
+          ? Pruning::valley_capacity
+          : Pruning::disabled;
+  if (argc == 7 && std::string_view(argv[6]) != "valley-capacity" &&
+      std::string_view(argv[6]) != "none") {
+    std::cerr << "pruning mode must be valley-capacity or none\n";
+    return 2;
+  }
 
   SearchCounters counters;
   auto timed =
-      solve(order, instrument, policy, direct_search, symmetry, counters);
+      solve(order, instrument, policy, direct_search, symmetry, pruning,
+            counters);
 
   auto const validation_begin = Clock::now();
   auto const validation_ok = valid(order, timed.result);
@@ -165,6 +176,9 @@ int main(int argc, char **argv) {
       << ",\"symmetry_breaking\":\""
       << (symmetry == SymmetryBreaking::d4_unit_square ? "d4" : "none")
       << "\""
+      << ",\"pruning\":\""
+      << (pruning == Pruning::valley_capacity ? "valley-capacity" : "none")
+      << "\""
       << ",\"solved\":" << boolean(!timed.result.squares().empty())
       << ",\"valid\":" << boolean(validation_ok)
       << ",\"timing_seconds\":{\"solve\":" << timed.search_seconds
@@ -177,6 +191,10 @@ int main(int argc, char **argv) {
       << ",\"backtracks\":" << counters.backtracks
       << ",\"prune_checks\":" << counters.prune_checks
       << ",\"prune_hits\":" << counters.prune_hits
+      << ",\"valley_capacity_checks\":"
+      << counters.valley_capacity_checks
+      << ",\"valley_capacity_prunes\":"
+      << counters.valley_capacity_prunes
       << ",\"generated_tasks\":" << counters.generated_tasks
       << ",\"completed_tasks\":" << counters.completed_tasks << "}}\n";
   return validation_ok ? 0 : 1;

benchmarks/run.py

@@ -80,7 +80,7 @@ def environment(binary):
 
 
 def run_once(
-    binary, order, mode, search_policy, search_route, symmetry, timeout
+    binary, order, mode, search_policy, search_route, symmetry, pruning, timeout
 ):
     started = time.monotonic()
     try:
@@ -92,6 +92,7 @@ def run_once(
                 search_policy,
                 search_route,
                 symmetry,
+                pruning,
             ],
             check=False,
             capture_output=True,
@@ -237,6 +238,11 @@ def main():
         action="store_true",
         help="disable unique-unit-square D4 symmetry breaking",
     )
+    parser.add_argument(
+        "--no-pruning",
+        action="store_true",
+        help="disable valley-capacity pruning",
+    )
     parser.add_argument(
         "--measure-overhead",
         action="store_true",
@@ -269,6 +275,7 @@ def main():
                     args.search_policy,
                     "direct" if args.direct_search else "public",
                     "none" if args.no_symmetry else "d4",
+                    "none" if args.no_pruning else "valley-capacity",
                     args.timeout,
                 )
         for trial in range(args.repetitions):
@@ -281,6 +288,7 @@ def main():
                         args.search_policy,
                         "direct" if args.direct_search else "public",
                         "none" if args.no_symmetry else "d4",
+                        "none" if args.no_pruning else "valley-capacity",
                         args.timeout,
                     )
                 )
@@ -310,6 +318,7 @@ def main():
             "candidate_order": args.search_policy,
             "search_route": "direct" if args.direct_search else "public",
             "symmetry_breaking": "none" if args.no_symmetry else "d4",
+            "pruning": "none" if args.no_pruning else "valley-capacity",
             "stdout": "captured; rendered grid suppressed by probe",
         },
         "cases": cases,