FUZZ: Test that BnB finds best solution

diff --git a/src/wallet/test/fuzz/coinselection.cpp b/src/wallet/test/fuzz/coinselection.cpp
index a0b2142e..012bc6cb 100644
--- a/src/wallet/test/fuzz/coinselection.cpp
+++ b/src/wallet/test/fuzz/coinselection.cpp
@@ -217,6 +217,132 @@ FUZZ_TARGET(coin_grinder_is_optimal)
     assert(!result_cg);
 }
 
+FUZZ_TARGET(bnb_finds_min_waste)
+{
+    FuzzedDataProvider fuzzed_data_provider{buffer.data(), buffer.size()};
+
+    FastRandomContext fast_random_context{ConsumeUInt256(fuzzed_data_provider)};
+    CoinSelectionParams coin_params{fast_random_context};
+    coin_params.m_subtract_fee_outputs = false;
+    // Set effective feerate up to 10'000'000 sats per kvB (10'000 sat/vB).
+    coin_params.m_effective_feerate = CFeeRate{ConsumeMoney(fuzzed_data_provider, 10'000'000), 1'000};
+    coin_params.m_long_term_feerate = CFeeRate{ConsumeMoney(fuzzed_data_provider, 10'000'000), 1'000};
+    coin_params.m_discard_feerate = CFeeRate{ConsumeMoney(fuzzed_data_provider, 10'000'000), 1'000};
+    coin_params.m_cost_of_change = ConsumeMoney(fuzzed_data_provider);
+
+    coin_params.change_output_size = fuzzed_data_provider.ConsumeIntegralInRange(1, MAX_SCRIPT_SIZE);
+    coin_params.m_change_fee = coin_params.m_effective_feerate.GetFee(coin_params.change_output_size);
+    coin_params.change_spend_size = fuzzed_data_provider.ConsumeIntegralInRange<int>(41, 1000);
+    const auto change_spend_fee{coin_params.m_discard_feerate.GetFee(coin_params.change_spend_size)};
+    coin_params.m_cost_of_change = coin_params.m_change_fee + change_spend_fee;
+    CScript change_out_script = CScript() << std::vector<unsigned char>(coin_params.change_output_size, OP_TRUE);
+    const auto dust{GetDustThreshold(CTxOut{/*nValueIn=*/0, change_out_script}, coin_params.m_discard_feerate)};
+    coin_params.min_viable_change = std::max(change_spend_fee + 1, dust);
+
+    // Create some coins
+    CAmount max_spendable{0};
+    int next_locktime{0};
+    // Too many output groups (>17?) would make it possible to generate UTXO
+    // pool and target combinations that cannot be completely searched by BnB
+    // before running into the attempt limit (see BnB "Exhaust..." test). The
+    // brute force search also gets exponentially more expensive with bigger
+    // UTXO pools.
+    // Choose 1–16 of 16 provides ample fuzzing space.
+    static constexpr unsigned max_output_groups{16};
+    std::vector<OutputGroup> group_pos;
+    LIMITED_WHILE(fuzzed_data_provider.ConsumeBool(), max_output_groups)
+    {
+        // With maximum m_effective_feerate 10'000 s/vB and n_input_bytes = 20'000 B, input_fee <= MAX_MONEY.
+        const int n_input_bytes{fuzzed_data_provider.ConsumeIntegralInRange<int>(1, 20'000)};
+        const CAmount input_fee = coin_params.m_effective_feerate.GetFee(n_input_bytes);
+        // Ensure that each UTXO has at least an effective value of 1 sat
+        const CAmount eff_value{fuzzed_data_provider.ConsumeIntegralInRange<CAmount>(1, MAX_MONEY + group_pos.size() - max_spendable - max_output_groups)};
+        const CAmount amount{eff_value + input_fee};
+        std::vector<COutput> temp_utxo_pool;
+
+        AddCoin(amount, /*n_input=*/0, n_input_bytes, ++next_locktime, temp_utxo_pool, coin_params.m_effective_feerate);
+        max_spendable += eff_value;
+
+        auto output_group = OutputGroup(coin_params);
+        output_group.Insert(std::make_shared<COutput>(temp_utxo_pool.at(0)), /*ancestors=*/0, /*descendants=*/0);
+        group_pos.push_back(output_group);
+    }
+    size_t num_groups = group_pos.size();
+    assert(num_groups <= max_output_groups);
+
+    // Only choose targets below max_spendable
+    const CAmount target{fuzzed_data_provider.ConsumeIntegralInRange<CAmount>(1, std::max(CAmount{1}, max_spendable - coin_params.m_cost_of_change))};
+
+    // Brute force optimal solution (lowest waste, but cannot be superset of another solution)
+    std::vector<uint32_t> solutions;
+    int best_waste{std::numeric_limits<int>::max()};
+    int best_weight{std::numeric_limits<int>::max()};
+    for (uint32_t pattern = 1; (pattern >> num_groups) == 0; ++pattern) {
+        // BnB does not permit adding more inputs to a solution, i.e. a superset of a solution cannot ever be a solution.
+        // The search pattern guarantees that any superset will only be visited after all its subsets have been traversed.
+        bool is_superset = false;
+        for (uint32_t sol : solutions) {
+            if ((pattern & sol) == sol) {
+                is_superset = true;
+                break;
+            }
+        }
+        if (is_superset) {
+            continue;
+        }
+
+        CAmount subset_amount{0};
+        CAmount subset_waste{0};
+        int subset_weight{0};
+        for (unsigned i = 0; i < num_groups; ++i) {
+            if ((pattern >> i) & 1) {
+                subset_amount += group_pos[i].GetSelectionAmount();
+                subset_waste += group_pos[i].fee - group_pos[i].long_term_fee;
+                subset_weight += group_pos[i].m_weight;
+            }
+        }
+        if (subset_amount >= target && subset_amount <= target + coin_params.m_cost_of_change) {
+            solutions.push_back(pattern);
+            // Add the excess (overselection that gets dropped to fees) to waste score
+            CAmount excess = subset_amount - target;
+            subset_waste += excess;
+            SelectionResult result_bf(target, SelectionAlgorithm::MANUAL);
+
+            for (unsigned i = 0; i < num_groups; ++i) {
+                if ((pattern >> i) & 1) {
+                    result_bf.AddInput(group_pos[i]);
+                }
+            }
+            if (subset_waste < best_waste) {
+                best_waste = subset_waste;
+                result_bf.RecalculateWaste(coin_params.min_viable_change, coin_params.m_cost_of_change, coin_params.m_change_fee);
+                assert(result_bf.GetWaste() == best_waste);
+                best_weight = subset_weight;
+            }
+        }
+    }
+
+    int high_max_selection_weight = fuzzed_data_provider.ConsumeIntegralInRange<int>(best_weight, std::numeric_limits<int>::max());
+    auto result_bnb = SelectCoinsBnB(group_pos, target, coin_params.m_cost_of_change, high_max_selection_weight);
+
+    if (!solutions.size() || !result_bnb) {
+        // Either both BnB and Brute Force find a solution or neither does.
+        assert(!result_bnb == !solutions.size());
+    } else {
+        // If brute forcing found a solution with an acceptable weight, BnB must find at least one solution with at most 16 output groups
+        assert(result_bnb);
+        result_bnb->RecalculateWaste(coin_params.min_viable_change, coin_params.m_cost_of_change, coin_params.m_change_fee);
+        assert(result_bnb->GetWeight() <= high_max_selection_weight);
+        assert(result_bnb->GetSelectedEffectiveValue() >= target);
+        assert(result_bnb->GetSelectedEffectiveValue() <= target + coin_params.m_cost_of_change);
+        assert(best_waste <= result_bnb->GetWaste());
+        if (result_bnb->GetAlgoCompleted()) {
+            // If BnB exhausted the search space, it must return an optimal solution (tied on waste score)
+            assert(best_waste == result_bnb->GetWaste());
+        }
+    }
+}
+
 enum class CoinSelectionAlgorithm {
     BNB,
     SRD,