結果
| 問題 | No.1758 Lazy Segment Tree...? |
| ユーザー |
 tokusakurai
|
| 提出日時 | 2021-10-16 10:39:35 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,388 ms / 8,000 ms |
| コード長 | 9,783 bytes |
| コンパイル時間 | 2,191 ms |
| コンパイル使用メモリ | 207,740 KB |
| 最終ジャッジ日時 | 2025-01-25 01:32:28 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 36 |
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 rep2(i, x, n) for (int i = x; i <= n; i++)#define rep3(i, x, n) for (int i = x; i >= n; i--)#define each(e, v) for (auto &e : v)#define pb push_back#define eb emplace_back#define all(x) x.begin(), x.end()#define rall(x) x.rbegin(), x.rend()#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>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;}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' : ' ');}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;}struct io_setup {io_setup() {ios_base::sync_with_stdio(false);cin.tie(NULL);cout << fixed << setprecision(15);}} io_setup;const int inf = (1 << 30) - 1;const ll INF = (1LL << 60) - 1;// const int MOD = 1000000007;const 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 Matrix {vector<vector<T>> A;Matrix(int m, int n) : A(m, vector<T>(n, 0)) {}int height() const { return A.size(); }int width() const { return A.front().size(); }inline const vector<T> &operator[](int k) const { return A[k]; }inline vector<T> &operator[](int k) { return A[k]; }static Matrix I(int l) {Matrix ret(l, l);for (int i = 0; i < l; i++) ret[i][i] = 1;return ret;}Matrix &operator*=(const Matrix &B) {int m = height(), n = width(), p = B.width();assert(n == B.height());Matrix ret(m, p);for (int i = 0; i < m; i++) {for (int k = 0; k < n; k++) {for (int j = 0; j < p; j++) ret[i][j] += A[i][k] * B[k][j];}}swap(A, ret.A);return *this;}Matrix operator*(const Matrix &B) const { return Matrix(*this) *= B; }Matrix pow(long long k) const {int m = height(), n = width();assert(m == n);Matrix now = *this, ret = I(n);for (; k > 0; k >>= 1, now *= now) {if (k & 1) ret *= now;}return ret;}bool eq(const T &a, const T &b) const {return a == b;// return abs(a-b) <= EPS;}pair<int, T> row_reduction(vector<T> &b) { //行基本変形を用いて簡約化を行い、(階数、行列式)の組を返すint m = height(), n = width(), check = 0, rank = 0;T det = 1;assert(b.size() == m);for (int j = 0; j < n; j++) {int pivot = check;for (int i = check; i < m; i++) {if (A[i][j] != 0) pivot = i;// if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; //Tが小数の場合はこちら}if (check != pivot) det *= T(-1);swap(A[check], A[pivot]), swap(b[check], b[pivot]);if (eq(A[check][j], T(0))) {det = T(0);continue;}rank++;det *= A[check][j];T r = T(1) / A[check][j];for (int k = j + 1; k < n; k++) A[check][k] *= r;b[check] *= r;A[check][j] = T(1);for (int i = 0; i < m; i++) {if (i == check) continue;if (!eq(A[i][j], 0)) {for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[check][k];b[i] -= A[i][j] * b[check];}A[i][j] = T(0);}if (++check == m) break;}return make_pair(rank, det);}pair<int, T> row_reduction() {vector<T> b(height(), T(0));return row_reduction(b);}Matrix inverse() { //行基本変形によって正方行列の逆行列を求めるif (height() != width()) return Matrix(0, 0);int n = height();Matrix ret = I(n);for (int j = 0; j < n; j++) {int pivot = j;for (int i = j; i < n; i++) {if (A[i][j] != 0) pivot = i;// if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; //Tが小数の場合はこちら}swap(A[j], A[pivot]), swap(ret[j], ret[pivot]);if (eq(A[j][j], T(0))) return Matrix(0, 0);T r = T(1) / A[j][j];for (int k = j + 1; k < n; k++) A[j][k] *= r;for (int k = 0; k < n; k++) ret[j][k] *= r;A[j][j] = T(1);for (int i = 0; i < n; i++) {if (i == j) continue;if (!eq(A[i][j], T(0))) {for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[j][k];for (int k = 0; k < n; k++) ret[i][k] -= A[i][j] * ret[j][k];}A[i][j] = T(0);}}return ret;}vector<vector<T>> Gausiann_elimination(vector<T> b) { // Ax=bの解の1つと解空間の基底の組を返すint m = height(), n = width();row_reduction(b);vector<vector<T>> ret;vector<int> p(m, n);vector<bool> is_zero(n, true);for (int i = 0; i < m; i++) {for (int j = 0; j < n; j++) {if (!eq(A[i][j], T(0))) {p[i] = j;break;}}if (p[i] < n)is_zero[p[i]] = false;else if (!eq(b[i], T(0)))return {};}vector<T> x(n, T(0));for (int i = 0; i < m; i++) {if (p[i] < n) x[p[i]] = b[i];}ret.push_back(x);for (int j = 0; j < n; j++) {if (!is_zero[j]) continue;x[j] = T(1);for (int i = 0; i < m; i++) {if (p[i] < n) x[p[i]] = -A[i][j];}ret.push_back(x), x[j] = T(0);}return ret;}};int main() {ll N, K;cin >> N >> K;mint tw = mint(2).inverse(), sx = mint(6).inverse();vector<mint> c(N, 0);rep2(i, 1, N - 1) {mint x = N - i;c[i] += (x + 1) * x * (x + 1) * tw;c[i] -= x * (x + 1) * (x * 2 + 1) * sx;}mint ans = 0;mint S = N * (N + 1);using mat = Matrix<mint>;mint ALL = S.pow(K - 1);rep2(i, 1, N - 1) {mat A(3, 3);mint P = mint(i) * mint(N + 1 - i), Q = S - P;P /= S, Q /= S;A[0][0] = Q, A[0][1] = P, A[1][0] = P, A[1][1] = Q;A[2][1] = 1, A[2][2] = 1;mat x(3, 1);x[0][0] = 1;A = A.pow(K) * x;ans += A[2][0] * ALL * c[i];}cout << ans * tw << '\n';}