結果

問題 No.2327 Inversion Sum
ユーザー 👑 emthrm
提出日時 2023-05-28 14:16:38
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 34 ms / 2,000 ms
コード長 7,778 bytes
コンパイル時間 4,480 ms
コンパイル使用メモリ 258,332 KB
実行使用メモリ 5,504 KB
最終ジャッジ日時 2024-12-27 00:18:41
合計ジャッジ時間 6,509 ms
ジャッジサーバーID
(参考情報)
judge2 / judge5
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
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
IOSetup() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
std::cout << fixed << setprecision(20);
}
} iosetup;
template <unsigned int M>
struct MInt {
unsigned int v;
constexpr MInt() : v(0) {}
constexpr MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
static constexpr MInt raw(const int x) {
MInt x_;
x_.v = x;
return x_;
}
static constexpr int get_mod() { return M; }
static constexpr void set_mod(const int divisor) {
assert(std::cmp_equal(divisor, M));
}
static void init(const int x) {
inv<true>(x);
fact(x);
fact_inv(x);
}
template <bool MEMOIZES = false>
static MInt inv(const int n) {
// assert(0 <= n && n < M && std::gcd(n, M) == 1);
static std::vector<MInt> inverse{0, 1};
const int prev = inverse.size();
if (n < prev) return inverse[n];
if constexpr (MEMOIZES) {
// "n!" and "M" must be disjoint.
inverse.resize(n + 1);
for (int i = prev; i <= n; ++i) {
inverse[i] = -inverse[M % i] * raw(M / i);
}
return inverse[n];
}
int u = 1, v = 0;
for (unsigned int a = n, b = M; b;) {
const unsigned int q = a / b;
std::swap(a -= q * b, b);
std::swap(u -= q * v, v);
}
return u;
}
static MInt fact(const int n) {
static std::vector<MInt> factorial{1};
if (const int prev = factorial.size(); n >= prev) {
factorial.resize(n + 1);
for (int i = prev; i <= n; ++i) {
factorial[i] = factorial[i - 1] * i;
}
}
return factorial[n];
}
static MInt fact_inv(const int n) {
static std::vector<MInt> f_inv{1};
if (const int prev = f_inv.size(); n >= prev) {
f_inv.resize(n + 1);
f_inv[n] = inv(fact(n).v);
for (int i = n; i > prev; --i) {
f_inv[i - 1] = f_inv[i] * i;
}
}
return f_inv[n];
}
static MInt nCk(const int n, const int k) {
if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
fact_inv(n - k) * fact_inv(k));
}
static MInt nPk(const int n, const int k) {
return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);
}
static MInt nHk(const int n, const int k) {
return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));
}
static MInt large_nCk(long long n, const int k) {
if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
inv<true>(k);
MInt res = 1;
for (int i = 1; i <= k; ++i) {
res *= inv(i) * n--;
}
return res;
}
constexpr MInt pow(long long exponent) const {
MInt res = 1, tmp = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
}
return res;
}
constexpr MInt& operator+=(const MInt& x) {
if ((v += x.v) >= M) v -= M;
return *this;
}
constexpr MInt& operator-=(const MInt& x) {
if ((v += M - x.v) >= M) v -= M;
return *this;
}
constexpr MInt& operator*=(const MInt& x) {
v = (unsigned long long){v} * x.v % M;
return *this;
}
MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }
constexpr auto operator<=>(const MInt& x) const = default;
constexpr MInt& operator++() {
if (++v == M) [[unlikely]] v = 0;
return *this;
}
constexpr MInt operator++(int) {
const MInt res = *this;
++*this;
return res;
}
constexpr MInt& operator--() {
v = (v == 0 ? M - 1 : v - 1);
return *this;
}
constexpr MInt operator--(int) {
const MInt res = *this;
--*this;
return res;
}
constexpr MInt operator+() const { return *this; }
constexpr MInt operator-() const { return raw(v ? M - v : 0); }
constexpr MInt operator+(const MInt& x) const { return MInt(*this) += x; }
constexpr MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
constexpr MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
MInt operator/(const MInt& x) const { return MInt(*this) /= x; }
friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
return os << x.v;
}
friend std::istream& operator>>(std::istream& is, MInt& x) {
long long v;
is >> v;
x = MInt(v);
return is;
}
};
using ModInt = MInt<MOD>;
template <typename Abelian>
struct FenwickTree {
explicit FenwickTree(const int n, const Abelian ID = 0)
: n(n), ID(ID), data(n, ID) {}
void add(int idx, const Abelian val) {
for (; idx < n; idx |= idx + 1) {
data[idx] += val;
}
}
Abelian sum(int idx) const {
Abelian res = ID;
for (--idx; idx >= 0; idx = (idx & (idx + 1)) - 1) {
res += data[idx];
}
return res;
}
Abelian sum(const int left, const int right) const {
return left < right ? sum(right) - sum(left) : ID;
}
Abelian operator[](const int idx) const { return sum(idx, idx + 1); }
int lower_bound(Abelian val) const {
if (val <= ID) [[unlikely]] return 0;
int res = 0;
for (int mask = std::bit_ceil(static_cast<unsigned int>(n + 1)) >> 1;
mask > 0; mask >>= 1) {
const int idx = res + mask - 1;
if (idx < n && data[idx] < val) {
val -= data[idx];
res += mask;
}
}
return res;
}
private:
const int n;
const Abelian ID;
std::vector<Abelian> data;
};
template <typename T>
long long inversion_number(const std::vector<T>& a) {
const int n = a.size();
std::vector<T> b = a;
std::sort(b.begin(), b.end());
b.erase(std::unique(b.begin(), b.end()), b.end());
FenwickTree<int> bit(b.size());
long long res = 0;
for (int i = 0; i < n; ++i) {
const int idx = std::distance(
b.begin(), std::lower_bound(b.begin(), b.end(), a[i]));
res += i - bit.sum(idx + 1);
bit.add(idx, 1);
}
return res;
}
int main() {
int n, m; cin >> n >> m;
vector<int> v(n, -1), is_fixed(n, false);
while (m--) {
int p, k; cin >> p >> k; --p; --k;
v[k] = p;
is_fixed[p] = true;
}
vector<int> hole_num(n, 0);
REP(i, n) {
if (v[i] == -1) hole_num[i] = 1;
}
for (int i = n - 2; i >= 0; --i) {
hole_num[i] += hole_num[i + 1];
}
// REP(i, n) cout << hole_num[i] << " \n"[i + 1 == n];
vector<int> not_fixed_num(n, 0);
REP(i, n) {
if (!is_fixed[i]) not_fixed_num[i] = 1;
}
FOR(i, 1, n) not_fixed_num[i] += not_fixed_num[i - 1];
// REP(i, n) cout << not_fixed_num[i] << " \n"[i + 1 == n];
ModInt ans = 0;
const int x = not_fixed_num[n - 1];
//
vector<int> fixed;
REP(i, n) {
if (v[i] != -1) fixed.emplace_back(v[i]);
}
ans += ModInt::fact(x) * inversion_number(fixed);
// not
if (x > 0) {
REP(i, n) {
if (v[i] != -1) {
ans += ModInt::fact(x - 1) * hole_num[i] * not_fixed_num[v[i]]; //
ans += ModInt::fact(x - 1) * (x - hole_num[i]) * (x - not_fixed_num[v[i]]); //
}
}
}
// not not
ans += ModInt::fact(x) * x * (x - 1) / 2 / 2;
cout << ans << '\n';
return 0;
}
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