結果

問題 No.2857 Div Array
ユーザー t98slidert98slider
提出日時 2024-08-25 20:35:42
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 27 ms / 2,000 ms
コード長 5,493 bytes
コンパイル時間 2,176 ms
コンパイル使用メモリ 210,448 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-08-25 20:35:46
合計ジャッジ時間 3,786 ms
ジャッジサーバーID
(参考情報)
judge4 / judge2
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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>
using namespace std;
using ll = long long;
template<class T> ostream& operator << (ostream& os, const vector<T>& vec) {
if(vec.empty()) return os;
os << vec[0];
for(auto it = vec.begin(); ++it != vec.end(); ) os << ' ' << *it;
return os;
}
template<const unsigned int MOD> struct prime_modint {
using mint = prime_modint;
unsigned int v;
prime_modint() : v(0) {}
prime_modint(unsigned int a) { a %= MOD; v = a; }
prime_modint(unsigned long long a) { a %= MOD; v = a; }
prime_modint(int a) { a %= (int)(MOD); if(a < 0)a += MOD; v = a; }
prime_modint(long long a) { a %= (int)(MOD); if(a < 0)a += MOD; v = a; }
static constexpr int mod() { return MOD; }
mint& operator++() {v++; if(v == MOD)v = 0; return *this;}
mint& operator--() {if(v == 0)v = MOD; v--; return *this;}
mint operator++(int) { mint result = *this; ++*this; return result; }
mint operator--(int) { mint result = *this; --*this; return result; }
mint& operator+=(const mint& rhs) { v += rhs.v; if(v >= MOD) v -= MOD; return *this; }
mint& operator-=(const mint& rhs) { if(v < rhs.v) v += MOD; v -= rhs.v; return *this; }
mint& operator*=(const mint& rhs) {
v = (unsigned int)((unsigned long long)(v) * rhs.v % MOD);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint r = 1, x = *this;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const { assert(v); return pow(MOD - 2); }
friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; }
friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; }
friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; }
friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; }
friend bool operator==(const mint& lhs, const mint& rhs) { return (lhs.v == rhs.v); }
friend bool operator!=(const mint& lhs, const mint& rhs) { return (lhs.v != rhs.v); }
friend std::ostream& operator << (std::ostream &os, const mint& rhs) noexcept { return os << rhs.v; }
};
//using mint = prime_modint<1000000007>;
using mint = prime_modint<998244353>;
template <class T, size_t N> struct Matrix {
std::array<std::array<T, N>, N> A{};
Matrix() {}
Matrix(const std::array<std::array<T, N>, N> &M) : A(M){}
Matrix(const std::vector<std::vector<T>> &M) {
for(size_t i = 0; i < N; i++){
for(size_t j = 0; j < N; j++){
A[i][j] = M[i][j];
}
}
}
const std::array<T, N>& operator[](int i) const { return A[i]; }
std::array<T, N>& operator[](int i) { return A[i]; }
Matrix& operator+=(const Matrix& rhs) {
for(size_t i = 0; i < N; i++){
for(size_t j = 0; j < N; j++){
A[i][j] += rhs[i][j];
}
}
return *this;
}
Matrix& operator-=(const Matrix& rhs) {
for(size_t i = 0; i < N; i++){
for(size_t j = 0; j < N; j++){
A[i][j] -= rhs[i][j];
}
}
return *this;
}
Matrix& operator*=(const Matrix& rhs) {
std::array<std::array<T, N>, N> res{};
for(size_t i = 0; i < N; i++){
for(size_t k = 0; k < N; k++){
for(size_t j = 0; j < N; j++){
res[i][j] += A[i][k] * rhs[k][j];
}
}
}
swap(A, res);
return *this;
}
Matrix& operator+() const { return *this; }
Matrix& operator-() const { return Matrix() - *this; }
friend Matrix operator+(const Matrix& lhs, const Matrix& rhs) {
return Matrix(lhs) += rhs;
}
friend Matrix operator-(const Matrix& lhs, const Matrix& rhs) {
return Matrix(lhs) -= rhs;
}
friend Matrix operator*(const Matrix& lhs, const Matrix& rhs) {
return Matrix(lhs) *= rhs;
}
friend bool operator==(const Matrix& lhs, const Matrix& rhs) {
return (lhs.A == rhs.A);
}
friend bool operator!=(const Matrix& lhs, const Matrix& rhs) {
return (lhs.A != rhs.A);
}
Matrix pow(long long v){
Matrix res, temp = A;
for(size_t i = 0; i < N; i++)res[i][i] = 1;
while(v){
if(v & 1)res *= temp;
temp *= temp;
v >>= 1;
}
return res;
}
friend std::ostream& operator << (std::ostream &os, const Matrix& rhs) noexcept {
for(size_t i = 0; i < N; i++){
if(i) os << '\n';
for(size_t j = 0; j < N; j++){
os << (j ? " " : "") << rhs[i][j];
}
}
return os;
}
};
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int n, m, k;
cin >> n >> m >> k;
if(n == 1){
cout << m << '\n';
return 0;
}
vector<int> c(m), d;
for(int i = 1; i <= m; i++){
c[m - i] = m / i;
}
d = c;
d.erase(unique(d.begin(), d.end()), d.end());
int M = d.size();
vector<int> cnt(M);
for(int i = 1, di = M - 1; i <= m; i++){
while(d[di] > c[m - i]) di--;
cnt[di]++;
}
Matrix<mint, 64> Mt;
for(int y = 0; y < M; y++){
for(int x = 0; x < M; x++){
if(abs(d[y] - d[x]) <= k) Mt[y][x] = cnt[x];
}
}
auto B = Mt.pow(n - 1);
mint ans;
for(int y = 0; y < M; y++){
for(int x = 0; x < M; x++){
ans += cnt[y] * B[y][x];
}
}
cout << ans << '\n';
}
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