結果
問題 | No.2327 Inversion Sum |
ユーザー |
|
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 |
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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
#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 個の区別できる箱に、k 個の区別できない玉を入れる場合の数static T H(int n, int k) {if (n < 0 || k < 0) return 0;return k == 0 ? 1 : C(n + k - 1, k);}// n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数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 個の区別できる玉を、k 個の区別しない箱に入れる場合の数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 を満たす最小の r (なければ 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 を満たす最小の r (なければ 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 を b に変換するのに必要な最小バブルソート回数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 の位置vector<int> q(N, -1); // i 番目が何か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();}