結果

問題 No.2857 Div Array
ユーザー ochiaigawa
提出日時 2024-08-25 14:31:42
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 25 ms / 2,000 ms
コード長 4,947 bytes
コンパイル時間 2,148 ms
コンパイル使用メモリ 212,972 KB
最終ジャッジ日時 2025-02-24 01:10:34
ジャッジサーバーID
(参考情報)
judge4 / judge3
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
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>
#include <atcoder/modint>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
using namespace std;
using mint = atcoder::modint998244353;
template <typename T>
class Matrix {
public:
Matrix() {}
explicit Matrix(int N) : Matrix(N, N) {}
explicit Matrix(int H, int W) : mat(H, vector<T>(W)) {}
int height() const {
return (int) mat.size();
}
int width() const {
return (int) mat[0].size();
}
const std::vector<T> &operator[](int k) const {
return mat[k];
}
std::vector<T> &operator[](int k) {
return mat[k];
}
static inline Matrix I(int N) {
Matrix ret(N);
for(int i = 0; i < N; i++) ret[i][i] = T(1);
return ret;
}
Matrix &operator+=(const Matrix &other) {
int H = height();
int W = width();
assert(H == other.height() && W == other.width());
for(int i = 0; i < H; i++) {
for(int j = 0; j < W; j++) {
(*this)[i][j] += other[i][j];
}
}
return (*this);
}
Matrix &operator+=(T X) {
int H = height();
int W = width();
for(int i = 0; i < H; i++) {
for(int j = 0; j < W; j++) {
mat[i][j] += X;
}
}
return (*this);
}
Matrix &operator-=(const Matrix &other) {
int H = height();
int W = width();
assert(H == other.height() && W == other.width());
for(size_t i = 0; i < H; i++) {
for(size_t j = 0; j < W; j++) {
(*this)[i][j] -= other[i][j];
}
}
return (*this);
}
Matrix &operator-=(T X) {
int H = height();
int W = width();
for(int i = 0; i < H; i++) {
for(int j = 0; j < W; j++) {
mat[i][j] -= X;
}
}
return (*this);
}
Matrix &operator*=(T X) {
int H = height();
int W = width();
for(int i = 0; i < H; i++) {
for(int j = 0; j < W; j++) {
mat[i][j] *= X;
}
}
return (*this);
}
Matrix &operator/=(T X) {
int H = height();
int W = width();
for(int i = 0; i < H; i++) {
for(int j = 0; j < W; j++) {
mat[i][j] /= X;
}
}
return (*this);
}
Matrix operator+(const Matrix &other) const {
return (Matrix(*this) += other);
}
Matrix operator+(T X) const {
return (Matrix(*this) += X);
}
Matrix operator-(const Matrix &other) const {
return (Matrix(*this) -= other);
}
Matrix operator-(T X) const {
return (Matrix(*this) -= X);
}
Matrix operator*(T X) const {
return (Matrix(*this) *= X);
}
Matrix operator/(T X) const {
return (Matrix(*this) /= X);
}
Matrix mat_mul(Matrix &other) {
int h0 = height();
int w0 = width();
int h1 = other.height();
int w1 = other.width();
assert(w0 == h1);
vector<vector<T>> ret(h0, vector<T>(w1, T(0)));
for(int i = 0; i < h0; i++) {
for(int j = 0; j < w1; j++) {
for(int k = 0; k < w0; k++) {
ret[i][j] += (*this)[i][k] * other[k][j];
}
}
}
this->mat.swap(ret);
return (*this);
}
Matrix pow(long long k) const {
Matrix A = (*this);
assert(height() == width());
Matrix ret = Matrix::I(height());
while(k) {
if(k & 1) {
ret.mat_mul(A);
}
A.mat_mul(A);
k >>= 1LL;
}
return ret;
}
T sum() {
Matrix A = (*this);
T ret = 0;
int h = height();
int w = width();
for(int i = 0; i < h; i++) {
for(int j = 0; j < w; j++) {
ret += A[i][j];
}
}
return T(ret);
}
vector<T> rsum() {
Matrix A = (*this);
int h = height();
int w = width();
vector<T> ret(h, T(0));
for(int i = 0; i < h; i++) {
for(int j = 0; j < w; j++) {
ret[i] += A[i][j];
}
}
return ret;
}
private:
std::vector<std::vector<T>> mat;
};
int main() {
cin.tie(0); cout.tie(0);
ios::sync_with_stdio(false);
int N, M, K;
cin >> N >> M >> K;
vector<int> C(M + 1);
for(int i = 1; i <= M; i++) {
C[M / i]++;
}
vector<int> I(M + 1), V;
int sz = 0;
for(int i = 0; i <= M; i++) {
if(C[i] > 0) {
I[i] = sz++;
V.emplace_back(C[i]);
}
}
assert(accumulate(V.begin(), V.end(), 0) == M);
assert(accumulate(C.begin(), C.end(), 0) == M);
Matrix<mint> m(sz);
for(int i = 0; i <= M; i++) {
if(C[i] == 0) {
continue;
}
for(int j = 0; j <= M; j++) {
if(C[j] == 0) {
continue;
}
if(abs(i - j) <= K) {
m[I[j]][I[i]] += C[j];
}
}
}
m = m.pow(N - 1);
mint ans = 0;
for(int i = 0; i < sz; i++) {
for(int j = 0; j < sz; j++) {
ans += m[i][j] * V[j];
}
}
cout << ans.val() << '\n';
return 0;
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0