結果
問題 | No.2327 Inversion Sum |
ユーザー |
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提出日時 | 2023-05-28 14:55:27 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 26 ms / 2,000 ms |
コード長 | 13,561 bytes |
コンパイル時間 | 1,497 ms |
コンパイル使用メモリ | 131,400 KB |
最終ジャッジ日時 | 2025-02-13 12:15:02 |
ジャッジサーバーID (参考情報) |
judge3 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 30 |
ソースコード
#ifndef LOCAL#define FAST_IO#endif// ============#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <cmath>#include <iomanip>#include <iostream>#include <list>#include <map>#include <numeric>#include <queue>#include <random>#include <set>#include <stack>#include <string>#include <tuple>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>#define OVERRIDE(a, b, c, d, ...) d#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)#define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i)#define ALL(x) begin(x), end(x)using namespace std;using u32 = unsigned int;using u64 = unsigned long long;using i32 = signed int;using i64 = signed long long;using f64 = double;using f80 = long double;template <typename T>using Vec = vector<T>;template <typename T>bool chmin(T &x, const T &y) {if (x > y) {x = y;return true;}return false;}template <typename T>bool chmax(T &x, const T &y) {if (x < y) {x = y;return true;}return false;}template <typename T>Vec<tuple<i32, i32, T>> runlength(const Vec<T> &a) {if (a.empty()) {return Vec<tuple<i32, i32, T>>();}Vec<tuple<i32, i32, T>> ret;i32 prv = 0;REP(i, 1, a.size()) {if (a[i - 1] != a[i]) {ret.emplace_back(prv, i, a[i - 1]);prv = i;}}ret.emplace_back(prv, (i32)a.size(), a.back());return ret;}#ifdef INT128using u128 = __uint128_t;using i128 = __int128_t;istream &operator>>(istream &is, i128 &x) {i64 v;is >> v;x = v;return is;}ostream &operator<<(ostream &os, i128 x) {os << (i64)x;return os;}istream &operator>>(istream &is, u128 &x) {u64 v;is >> v;x = v;return is;}ostream &operator<<(ostream &os, u128 x) {os << (u64)x;return os;}#endif[[maybe_unused]] constexpr i32 INF = 1000000100;[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;struct SetUpIO {SetUpIO() {#ifdef FAST_IOios::sync_with_stdio(false);cin.tie(nullptr);#endifcout << fixed << setprecision(15);}} set_up_io;// ============#ifdef DEBUGF#else#define DBG(x) (void)0#endif// ============#include <cassert>#include <iostream>#include <type_traits>// ============constexpr bool is_prime(unsigned n) {if (n == 0 || n == 1) {return false;}for (unsigned i = 2; i * i <= n; ++i) {if (n % i == 0) {return false;}}return true;}constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {unsigned ret = 1, self = x;while (y != 0) {if (y & 1) {ret = (unsigned) ((unsigned long long) ret * self % mod);}self = (unsigned) ((unsigned long long) self * self % mod);y /= 2;}return ret;}template <unsigned mod>constexpr unsigned primitive_root() {static_assert(is_prime(mod), "`mod` must be a prime number.");if (mod == 2) {return 1;}unsigned primes[32] = {};int it = 0;{unsigned m = mod - 1;for (unsigned i = 2; i * i <= m; ++i) {if (m % i == 0) {primes[it++] = i;while (m % i == 0) {m /= i;}}}if (m != 1) {primes[it++] = m;}}for (unsigned i = 2; i < mod; ++i) {bool ok = true;for (int j = 0; j < it; ++j) {if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {ok = false;break;}}if (ok)return i;}return 0;}// y >= 1template <typename T>constexpr T safe_mod(T x, T y) {x %= y;if (x < 0) {x += y;}return x;}// y != 0template <typename T>constexpr T floor_div(T x, T y) {if (y < 0) {x *= -1;y *= -1;}if (x >= 0) {return x / y;} else {return -((-x + y - 1) / y);}}// y != 0template <typename T>constexpr T ceil_div(T x, T y) {if (y < 0) {x *= -1;y *= -1;}if (x >= 0) {return (x + y - 1) / y;} else {return -(-x / y);}}// ============template <unsigned mod>class ModInt {static_assert(mod != 0, "`mod` must not be equal to 0.");static_assert(mod < (1u << 31),"`mod` must be less than (1u << 31) = 2147483648.");unsigned val;public:static constexpr unsigned get_mod() {return mod;}constexpr ModInt() : val(0) {}template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>constexpr ModInt(T x) : val((unsigned) (x % mod)) {}static constexpr ModInt raw(unsigned x) {ModInt<mod> ret;ret.val = x;return ret;}constexpr unsigned get_val() const {return val;}constexpr ModInt operator+() const {return *this;}constexpr ModInt operator-() const {return ModInt<mod>(0u) - *this;}constexpr ModInt &operator+=(const ModInt &rhs) {val += rhs.val;if (val >= mod)val -= mod;return *this;}constexpr ModInt &operator-=(const ModInt &rhs) {if (val < rhs.val)val += mod;val -= rhs.val;return *this;}constexpr ModInt &operator*=(const ModInt &rhs) {val = (unsigned long long)val * rhs.val % mod;return *this;}constexpr ModInt &operator/=(const ModInt &rhs) {val = (unsigned long long)val * rhs.inv().val % mod;return *this;}friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {return ModInt<mod>(lhs) += rhs;}friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {return ModInt<mod>(lhs) -= rhs;}friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {return ModInt<mod>(lhs) *= rhs;}friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {return ModInt<mod>(lhs) /= rhs;}constexpr ModInt pow(unsigned long long x) const {ModInt<mod> ret = ModInt<mod>::raw(1);ModInt<mod> self = *this;while (x != 0) {if (x & 1)ret *= self;self *= self;x >>= 1;}return ret;}constexpr ModInt inv() const {static_assert(is_prime(mod), "`mod` must be a prime number.");assert(val != 0);return this->pow(mod - 2);}friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {long long val;is >> val;x.val = val % mod + (val < 0 ? mod : 0);return is;}friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {os << x.val;return os;}friend bool operator==(const ModInt &lhs, const ModInt &rhs) {return lhs.val == rhs.val;}friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {return lhs.val != rhs.val;}};[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;// ============// ============#include <vector>#include <cassert>template <typename T>class FactorialTable {std::vector<T> fac;std::vector<T> ifac;public:FactorialTable() : fac(1, T(1)), ifac(1, T(1)) {}FactorialTable(int n) : fac(n + 1), ifac(n + 1) {assert(n >= 0);fac[0] = T(1);for (int i = 1; i <= n; ++i) {fac[i] = fac[i - 1] * T(i);}ifac[n] = T(1) / T(fac[n]);for (int i = n; i > 0; --i) {ifac[i - 1] = ifac[i] * T(i);}}void resize(int n) {int old = n_max();if (n <= old) {return;}fac.resize(n + 1);for (int i = old + 1; i <= n; ++i) {fac[i] = fac[i - 1] * T(i);}ifac.resize(n + 1);ifac[n] = T(1) / T(fac[n]);for (int i = n; i > old; --i) {ifac[i - 1] = ifac[i] * T(i);}}inline int n_max() const {return (int) fac.size() - 1;}inline T fact(int n) const {assert(n >= 0 && n <= n_max());return fac[n];}inline T inv_fact(int n) const {assert(n >= 0 && n <= n_max());return ifac[n];}inline T choose(int n, int k) const {assert(k <= n_max() && n <= n_max());if (k > n || k < 0) {return T(0);}return fac[n] * ifac[k] * ifac[n - k];}inline T multi_choose(int n, int k) const {assert(n >= 1 && k >= 0 && k + n - 1 <= n_max());return choose(k + n - 1, k);}inline T n_terms_sum_k(int n, int k) const {assert(n >= 0);if (k < 0) {return T(0);}if (n == 0) {return k == 0 ? T(1) : T(0);}return choose(n + k - 1, n - 1);}};// ============// ============#include <cassert>#include <vector>// ============#include <limits>#include <utility>template <typename T>struct Add {using Value = T;static Value id() {return T(0);}static Value op(const Value &lhs, const Value &rhs) {return lhs + rhs;}static Value inv(const Value &x) {return -x;}};template <typename T>struct Mul {using Value = T;static Value id() {return Value(1);}static Value op(const Value &lhs, const Value &rhs) {return lhs * rhs;}static Value inv(const Value &x) {return Value(1) / x;}};template <typename T>struct Min {using Value = T;static Value id() {return std::numeric_limits<T>::max();}static Value op(const Value &lhs, const Value &rhs) {return std::min(lhs, rhs);}};template <typename T>struct Max {using Value = T;static Value id() {return std::numeric_limits<Value>::min();}static Value op(const Value &lhs, const Value &rhs) {return std::max(lhs, rhs);}};template <typename T>struct Xor {using Value = T;static Value id() {return T(0);}static Value op(const Value &lhs, const Value &rhs) {return lhs ^ rhs;}static Value inv(const Value &x) {return x;}};template <typename Monoid>struct Reversible {using Value = std::pair<typename Monoid::Value, typename Monoid::Value>;static Value id() {return Value(Monoid::id(), Monoid::id());}static Value op(const Value &v1, const Value &v2) {return Value(Monoid::op(v1.first, v2.first),Monoid::op(v2.second, v1.second));}};// ============template <typename CommutativeGroup>class FenwickTree {public:using Value = typename CommutativeGroup::Value;private:std::vector<Value> data;public:FenwickTree(int n) : data(n, CommutativeGroup::id()) {}void add(int idx, const Value &x) {assert(idx >= 0 && idx < (int) data.size());for (; idx < (int) data.size(); idx |= idx + 1) {data[idx] = CommutativeGroup::op(data[idx], x);}}Value sum(int r) const {assert(r >= 0 && r <= (int) data.size());Value ret = CommutativeGroup::id();for (; r > 0; r &= r - 1) {ret = CommutativeGroup::op(ret, data[r - 1]);}return ret;}Value sum(int l, int r) const {assert(l >= 0 && l <= r && r <= (int) data.size());return CommutativeGroup::op(sum(r), CommutativeGroup::inv(sum(l)));}};template <typename T>using FenwickTreeAdd = FenwickTree<Add<T>>;// ============using Mint = ModInt<mod998244353>;int main() {i32 n, m;cin >> n >> m;Vec<i32> p(n, -1);REP(i, m) {i32 a, b;cin >> a >> b;--a;--b;p[b] = a;}FactorialTable<Mint> table(n);Mint ans;ans += Mint(n - m) * Mint(n - m - 1) / Mint(4);{FenwickTreeAdd<i32> fw(n);i64 s = 0;REP(i, n) {if (p[i] != -1) {fw.add(p[i], 1);s += fw.sum(p[i] + 1, n);}}ans += Mint(s);}Vec<i32> vac(n + 1, 0);REP(i, n) {vac[i + 1] = vac[i] + (i32)(p[i] == -1);}Vec<i32> dec(n + 1, 0);REP(i, n) {if (p[i] != -1) {dec[p[i] + 1] = 1;}}REP(i, n) {dec[i + 1] += dec[i];}if (n != m) {REP(i, n) {if (p[i] != -1) {Mint l = Mint(vac[i]) / Mint(n - m);ans += l * Mint(n - m - p[i] + dec[p[i]]);Mint r = Mint(1) - l;ans += r * Mint(p[i] - dec[p[i]]);}}}ans *= table.fact(n - m);cout << ans << '\n';}