feat: Gosper's hack

config.yml

@@ -105,6 +105,9 @@ notebook:
     - enumerate: enumerate
       code_ext: hpp
       test_ext: cpp
+    - gosper: 枚举 n 位二进制数中恰有 k 个 1 的数
+      code_ext: hpp
+      test_ext: cpp
     io:
     - ios128: 128 位整数的 IO
       code_ext: hpp

src/code/enum/gosper.hpp

@@ -0,0 +1,34 @@
+#ifndef TIFALIBS_ENUM_GOSPER
+#define TIFALIBS_ENUM_GOSPER
+
+#include "../bit/lowbit.hpp"
+
+namespace tifa_libs {
+
+template <u32 ID = 0>
+class Gosper {
+  static inline u32 n_, k_;
+  u64 now_;
+
+ public:
+  static constexpr void set(u32 n, u32 k) {
+    assert(k <= n && n < 64);
+    n_ = n;
+    k_ = k;
+  }
+  static Gosper begin() { return (1_u64 << k_) - 1; }
+  static Gosper end() { return 1_u64 << n_; }
+
+  constexpr Gosper(u64 now = *begin()) : now_(now) { assert(now == *end() || std::popcount(now) == k_); }
+
+  constexpr u64 operator*() const { return now_; }
+  constexpr bool operator!=(Gosper const &x) const { return now_ != x.now_; }
+  constexpr void operator++() {
+    u64 c = bit::lowbit(now_), r = now_ + c;
+    now_ = ((r ^ now_) / 4 / c) | r;
+  }
+};
+
+}  // namespace tifa_libs
+
+#endif

src/doc_md/enum/gosper.md

@@ -0,0 +1,4 @@
+---
+title: gosper
+documentation_of: //src/code/enum/gosper.hpp
+---

src/test_cpverifier/unit-test/enum/gosper.cpp

@@ -0,0 +1,49 @@
+#define UNITTEST
+#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
+
+#include "../../../code/enum/gosper.hpp"
+
+#include "../../../code/comb/binom.hpp"
+#include "../../../code/math/mint.hpp"
+#include "../../../code/math/mintdata_s30.hpp"
+#include "../base.hpp"
+
+using mint = tifa_libs::math::mint<tifa_libs::math::mintdata_s30<998244353>>;
+
+template <u32 ID>
+void test(u32 n, u32 kmax) {
+  using Gosper = tifa_libs::Gosper<ID>;
+  auto binom = tifa_libs::math::Binom<mint>(n);
+  for (u32 k = 0; k <= kmax; ++k) {
+    Gosper::set(n, k);
+    Gosper gs;
+    u32 cnt = 0, cnt_correct = binom.mCn(n, k).val();
+    for (auto i : gs) {
+      ++cnt;
+      check((u32)std::popcount(i), k, check_param(n), check_param(k), check_param(std::bitset<64>(i).to_string()));
+    }
+    check(cnt, cnt_correct, check_param(n), check_param(k));
+  }
+}
+
+int main() {
+  auto tcase = tifa_libs::unittest::pre_test();
+
+  switch (tcase) {
+    case tifa_libs::unittest::ts_example_00: test<1>(1, 1); break;
+    case tifa_libs::unittest::ts_example_01: test<1>(2, 2); break;
+    case tifa_libs::unittest::ts_random_00: test<1>(3, 3); break;
+    case tifa_libs::unittest::ts_random_01: test<1>(4, 4); break;
+    case tifa_libs::unittest::ts_random_02: test<1>(5, 5); break;
+    case tifa_libs::unittest::ts_random_03: test<1>(6, 6); break;
+    case tifa_libs::unittest::ts_random_04: test<2>(10, 10); break;
+    case tifa_libs::unittest::ts_random_05: test<2>(20, 20); break;
+    case tifa_libs::unittest::ts_random_06: test<2>(30, 10); break;
+    case tifa_libs::unittest::ts_random_07: test<2>(40, 8); break;
+    case tifa_libs::unittest::ts_random_08: test<2>(50, 7); break;
+    case tifa_libs::unittest::ts_random_09: test<2>(60, 6); break;
+    default: break;
+  }
+
+  tifa_libs::unittest::post_test();
+}