結果

問題 No.2327 Inversion Sum
ユーザー tokusakurai
提出日時 2023-05-28 13:42:44
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 77 ms / 2,000 ms
コード長 12,023 bytes
コンパイル時間 2,363 ms
コンパイル使用メモリ 208,712 KB
最終ジャッジ日時 2025-02-13 10:10:12
ジャッジサーバーID
(参考情報)
judge4 / judge1
このコードへのチャレンジ
(要ログイン)
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 rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T>;
template <typename T>
bool chmax(T &x, const T &y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
bool chmin(T &x, const T &y) {
return (x > y) ? (x = y, true) : false;
}
template <typename T>
int flg(T x, int i) {
return (x >> i) & 1;
}
int popcount(int x) { return __builtin_popcount(x); }
int popcount(ll x) { return __builtin_popcountll(x); }
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
void print(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
if (v.empty()) cout << '\n';
}
template <typename T>
void printn(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}
template <typename T>
int lb(const vector<T> &v, T x) {
return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, T x) {
return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
void rearrange(vector<T> &v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
int n = v.size();
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
return ret;
}
template <typename T>
void reorder(vector<T> &a, const vector<int> &ord) {
int n = a.size();
vector<T> b(n);
for (int i = 0; i < n; i++) b[i] = a[ord[i]];
swap(a, b);
}
template <typename T>
T floor(T x, T y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return (x >= 0 ? x / y : (x - y + 1) / y);
}
template <typename T>
T ceil(T x, T y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return (x >= 0 ? (x + y - 1) / y : x / y);
}
template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first + q.first, p.second + q.second);
}
template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first - q.first, p.second - q.second);
}
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
S a;
T b;
is >> a >> b;
p = make_pair(a, b);
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
return os << p.first << ' ' << p.second;
}
struct io_setup {
io_setup() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout << fixed << setprecision(15);
}
} io_setup;
constexpr int inf = (1 << 30) - 1;
constexpr ll INF = (1LL << 60) - 1;
// constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;
template <int mod>
struct Mod_Int {
int x;
Mod_Int() : x(0) {}
Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
static int get_mod() { return mod; }
Mod_Int &operator+=(const Mod_Int &p) {
if ((x += p.x) >= mod) x -= mod;
return *this;
}
Mod_Int &operator-=(const Mod_Int &p) {
if ((x += mod - p.x) >= mod) x -= mod;
return *this;
}
Mod_Int &operator*=(const Mod_Int &p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
Mod_Int &operator/=(const Mod_Int &p) {
*this *= p.inverse();
return *this;
}
Mod_Int &operator++() { return *this += Mod_Int(1); }
Mod_Int operator++(int) {
Mod_Int tmp = *this;
++*this;
return tmp;
}
Mod_Int &operator--() { return *this -= Mod_Int(1); }
Mod_Int operator--(int) {
Mod_Int tmp = *this;
--*this;
return tmp;
}
Mod_Int operator-() const { return Mod_Int(-x); }
Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }
Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }
Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }
Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }
bool operator==(const Mod_Int &p) const { return x == p.x; }
bool operator!=(const Mod_Int &p) const { return x != p.x; }
Mod_Int inverse() const {
assert(*this != Mod_Int(0));
return pow(mod - 2);
}
Mod_Int pow(long long k) const {
Mod_Int now = *this, ret = 1;
for (; k > 0; k >>= 1, now *= now) {
if (k & 1) ret *= now;
}
return ret;
}
friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }
friend istream &operator>>(istream &is, Mod_Int &p) {
long long a;
is >> a;
p = Mod_Int<mod>(a);
return is;
}
};
using mint = Mod_Int<MOD>;
template <typename T>
struct Combination {
static vector<T> _fac, _ifac;
Combination() {}
static void init(int n) {
_fac.resize(n + 1), _ifac.resize(n + 1);
_fac[0] = 1;
for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i;
_ifac[n] = _fac[n].inverse();
for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i;
}
static T fac(int k) { return _fac[k]; }
static T ifac(int k) { return _ifac[k]; }
static T inv(int k) { return fac(k - 1) * ifac(k); }
static T P(int n, int k) {
if (k < 0 || n < k) return 0;
return fac(n) * ifac(n - k);
}
static T C(int n, int k) {
if (k < 0 || n < k) return 0;
return fac(n) * ifac(n - k) * ifac(k);
}
// n k
static T H(int n, int k) {
if (n < 0 || k < 0) return 0;
return k == 0 ? 1 : C(n + k - 1, k);
}
// n k 1
static T second_stirling_number(int n, int k) {
T ret = 0;
for (int i = 0; i <= k; i++) {
T tmp = C(k, i) * T(i).pow(n);
ret += ((k - i) & 1) ? -tmp : tmp;
}
return ret * ifac(k);
}
// n k
static T bell_number(int n, int k) {
if (n == 0) return 1;
k = min(k, n);
vector<T> pref(k + 1);
pref[0] = 1;
for (int i = 1; i <= k; i++) {
if (i & 1) {
pref[i] = pref[i - 1] - ifac(i);
} else {
pref[i] = pref[i - 1] + ifac(i);
}
}
T ret = 0;
for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i];
return ret;
}
};
template <typename T>
vector<T> Combination<T>::_fac = vector<T>();
template <typename T>
vector<T> Combination<T>::_ifac = vector<T>();
using comb = Combination<mint>;
template <typename T>
struct Binary_Indexed_Tree {
vector<T> bit;
const int n;
Binary_Indexed_Tree(const vector<T> &v) : n((int)v.size()) {
bit.resize(n + 1);
copy(begin(v), end(v), begin(bit) + 1);
build();
}
Binary_Indexed_Tree(int n, T x = 0) : Binary_Indexed_Tree(vector<T>(n, x)) {}
void set(int i, const T &x) { bit[i + 1] = x; }
void build() {
for (int a = 2; a <= n; a <<= 1) {
for (int b = a; b <= n; b += a) bit[b] += bit[b - a / 2];
}
}
void add(int i, const T &x) {
for (i++; i <= n; i += (i & -i)) bit[i] += x;
}
void change(int i, const T &x) { add(i, x - query(i, i + 1)); }
T sum(int i) const {
i = min(i, n);
if (i <= 0) return 0;
T ret = 0;
for (; i > 0; i -= (i & -i)) ret += bit[i];
return ret;
}
T query(int l, int r) const {
l = max(l, 0), r = min(r, n);
if (l >= r) return 0;
return sum(r) - sum(l);
}
T operator[](int i) const { return query(i, i + 1); }
// v[0]+...+v[r] >= x r ( n)
int lower_bound(T x) const {
int ret = 0;
for (int k = 31 - __builtin_clz(n); k >= 0; k--) {
if (ret + (1 << k) <= n && bit[ret + (1 << k)] < x) x -= bit[ret += (1 << k)];
}
return ret;
}
// v[0]+...+v[r] > x r ( n)
int upper_bound(T x) const {
int ret = 0;
for (int k = 31 - __builtin_clz(n); k >= 0; k--) {
if (ret + (1 << k) <= n && bit[ret + (1 << k)] <= x) x -= bit[ret += (1 << k)];
}
return ret;
}
};
template <typename T>
long long inversion_number(const vector<T> &a) {
int n = a.size();
vector<int> v(n);
iota(begin(v), end(v), 0);
sort(begin(v), end(v), [&](int i, int j) {
if (a[i] != a[j]) return a[i] < a[j];
return i < j;
});
Binary_Indexed_Tree<int> bit(n, 0);
long long ret = 0;
for (int i = 0; i < n; i++) {
ret += bit.query(v[i] + 1, n);
bit.add(v[i], 1);
}
return ret;
}
// a b
template <typename T>
long long inversion_number(const vector<T> &a, const vector<T> &b) {
int n = a.size();
assert(b.size() == n);
vector<int> u(n), v(n);
iota(begin(u), end(u), 0);
sort(begin(u), end(u), [&](int i, int j) {
if (a[i] != a[j]) return a[i] < a[j];
return i < j;
});
iota(begin(v), end(v), 0);
sort(begin(v), end(v), [&](int i, int j) {
if (b[i] != b[j]) return b[i] < b[j];
return i < j;
});
vector<int> w(n);
for (int i = 0; i < n; i++) {
if (a[u[i]] != b[v[i]]) return -1;
w[v[i]] = u[i];
}
Binary_Indexed_Tree<int> bit(n, 0);
long long ret = 0;
for (int i = 0; i < n; i++) {
ret += bit.query(w[i] + 1, n);
bit.add(w[i], 1);
}
return ret;
}
void solve() {
int N, M;
cin >> N >> M;
comb::init(N);
mint ans = 0;
vector<int> p(N, -1); // i
vector<int> q(N, -1); // i
rep(i, M) {
int x, t;
cin >> x >> t;
x--, t--;
p[x] = t;
q[t] = x;
}
vector<int> v;
int cnt = 0;
rep(i, N) {
if (q[i] != -1) v.eb(q[i]);
if (q[i] == -1) cnt++;
}
vector<int> ids;
rep(i, N) {
if (p[i] == -1) ids.eb(i);
}
ans += inversion_number(v);
if (cnt == 0) {
cout << ans << '\n';
return;
}
int c1 = 0;
rep(i, N) {
if (q[i] != -1) {
int j = q[i];
int d1 = lb(ids, j);
int d2 = cnt - d1;
int c2 = cnt - c1;
ans += mint(d1) * mint(c2) / mint(cnt);
ans += mint(d2) * mint(c1) / mint(cnt);
} else {
c1++;
}
}
ans += mint(cnt) * mint(cnt - 1) / 4;
ans *= comb::fac(cnt);
cout << ans << '\n';
}
int main() {
int T = 1;
// cin >> T;
while (T--) solve();
}
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