結果

問題 No.2327 Inversion Sum
ユーザー ForestedForested
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
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30
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ソースコード

diff #
プレゼンテーションモードにする

#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 INT128
using 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_IO
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
cout << 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 >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
x %= y;
if (x < 0) {
x += y;
}
return x;
}
// y != 0
template <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 != 0
template <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';
}
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