CF869C The Intriguing Obsession

https://www.luogu.com.cn/record/81299371

Luogu/CF869C/CF869C.cpp

@@ -0,0 +1,89 @@
+#include <iostream>
+#include <array>
+#include <type_traits>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 5005;
+const int mod = 998244353;
+
+template <int x>
+using number = std::integral_constant<int, x>;
+
+template <int n>
+struct factorial : number<static_cast<long long>(n) * factorial<n - 1>::value % mod> {};
+
+template <>
+struct factorial<0> : number<1> {};
+
+template <int... S>
+constexpr std::array<int, sizeof...(S)> get_factorial_table_impl(std::integer_sequence<int, S...>) {
+    return {factorial<S>::value...};
+}
+
+template <int S>
+constexpr auto get_factorial_table() {
+    return get_factorial_table_impl(std::make_integer_sequence<int, S>{});
+}
+
+template <int n>
+struct inverse : number<static_cast<long long>(mod - (mod / n)) * inverse<mod % n>::value % mod> {};
+
+template <>
+struct inverse<1> : number<1> {};
+
+template <>
+struct inverse<0> : number<1> {};
+
+template <int n>
+struct factorial_inverse : number<static_cast<long long>(factorial_inverse<n - 1>::value) * inverse<n>::value % mod> {};
+
+template <>
+struct factorial_inverse<1> : number<1> {};
+
+template <>
+struct factorial_inverse<0> : number<1> {};
+
+template <int... S>
+constexpr std::array<int, sizeof...(S)> get_factorial_inverse_table_impl(std::integer_sequence<int, S...>) {
+    return {factorial_inverse<S>::value...};
+}
+
+template <int S>
+constexpr auto get_factorial_inverse_table() {
+    return get_factorial_inverse_table_impl(std::make_integer_sequence<int, S>{});
+}
+
+int a, b, c, ab, ac, bc, ans;
+
+constexpr auto fac = get_factorial_table<N>(),
+               fac_inv = get_factorial_inverse_table<N>();
+
+inline int C(int n, int m) {
+    return static_cast<long long>(fac[n]) * fac_inv[m] % mod * fac_inv[n - m] % mod;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> a >> b >> c;
+
+    for (int i = 0; i <= std::min(a, b); i++) {
+        ab = (ab + static_cast<long long>(C(a, i)) * C(b, i) % mod * fac[i] % mod) % mod;
+    }
+
+    for (int i = 0; i <= std::min(a, c); i++) {
+        ac = (ac + static_cast<long long>(C(a, i)) * C(c, i) % mod * fac[i] % mod) % mod;
+    }
+
+    for (int i = 0; i <= std::min(b, c); i++) {
+        bc = (bc + static_cast<long long>(C(b, i)) * C(c, i) % mod * fac[i] % mod) % mod;
+    }
+
+    cout << (((static_cast<long long>(ab) * ac) % mod * bc) % mod) % mod << endl;
+
+    return 0;
+}