結果

問題 No.2857 Div Array
ユーザー SnowBeenDidingSnowBeenDiding
提出日時 2024-08-25 15:44:36
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 49 ms / 2,000 ms
コード長 4,539 bytes
コンパイル時間 5,603 ms
コンパイル使用メモリ 314,760 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-08-25 15:44:44
合計ジャッジ時間 6,571 ms
ジャッジサーバーID
(参考情報)
judge5 / judge3
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ファイルパターン 結果
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

#include <atcoder/all>
#include <bits/stdc++.h>
#define rep(i, a, b) for (ll i = (ll)(a); i < (ll)(b); i++)
using namespace atcoder;
using namespace std;
typedef long long ll;
using mint = modint998244353;
template <class T> struct Matrix {
vector<vector<T>> A;
Matrix() {}
Matrix(size_t n, size_t m) : A(n, std::vector<T>(m, zero())) {}
Matrix(size_t n) : A(n, std::vector<T>(n, zero())) {};
T zero() { return (T(0)); }
size_t height() const { return (A.size()); }
size_t width() const { return (A[0].size()); }
inline const vector<T> &operator[](int k) const { return (A.at(k)); }
inline vector<T> &operator[](int k) { return (A.at(k)); }
static Matrix I(size_t n) {
Matrix mat(n);
for (int i = 0; i < n; i++)
mat[i][i] = 1;
return (mat);
}
Matrix &operator+=(const Matrix &B) {
size_t n = height(), m = width();
assert(n == B.height() && m == B.width());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
(*this)[i][j] += B[i][j];
return (*this);
}
Matrix &operator-=(const Matrix &B) {
size_t n = height(), m = width();
assert(n == B.height() && m == B.width());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
(*this)[i][j] -= B[i][j];
return (*this);
}
Matrix &operator*=(const Matrix &B) {
size_t n = height(), m = B.width(), p = width();
assert(p == B.height());
vector<vector<T>> C(n, vector<T>(m, zero()));
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
for (int k = 0; k < p; k++)
C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
A.swap(C);
return (*this);
}
Matrix &operator^=(long long k) {
Matrix B = Matrix::I(height());
while (k > 0) {
if (k & 1)
B *= *this;
*this *= *this;
k >>= 1LL;
}
A.swap(B.A);
return (*this);
}
Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }
bool operator==(const Matrix &B) const {
size_t n = height(), m = width();
if (n != B.height() || m != B.width())
return false;
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
if ((*this)[i][j] != B[i][j])
return false;
return true;
}
friend ostream &operator<<(ostream &os, Matrix &p) {
size_t n = p.height(), m = p.width();
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
os << p[i][j] << (j + 1 == m ? "\n" : " ");
}
}
return (os);
}
T determinant() { // O(n^3)
Matrix B(*this);
assert(width() == height());
T ret = 1;
for (int i = 0; i < width(); i++) {
int idx = -1;
for (int j = i; j < width(); j++) {
if (B[j][i] != 0)
idx = j;
}
if (idx == -1)
return (0);
if (i != idx) {
ret *= -1;
swap(B[i], B[idx]);
}
ret *= B[i][i];
T vv = B[i][i];
for (int j = 0; j < width(); j++) {
B[i][j] /= vv;
}
for (int j = i + 1; j < width(); j++) {
T a = B[j][i];
for (int k = 0; k < width(); k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return (ret);
}
};
int main() {
const int mod = 998244353;
int n, m, k;
cin >> n >> m >> k;
vector<int> ct(m + 1);
rep(i, 1, m + 1) { ct[m / i]++; }
int len = 0;
vector<int> id, idct;
rep(i, 0, m + 1) {
if (ct[i]) {
id.push_back(i);
idct.push_back(ct[i]);
len++;
}
}
Matrix<mint> v(len, len);
rep(i, 0, len) rep(j, 0, len) {
if (abs(id[i] - id[j]) > k)
continue;
v[i][j] = idct[i];
}
v ^= n - 1;
mint ans = 0;
rep(i, 0, len) rep(j, 0, len) { ans += v[i][j] * idct[j]; }
cout << ans.val() << endl;
}
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