結果

問題 No.1321 塗るめた
ユーザー shobonvipshobonvip
提出日時 2024-11-12 02:18:35
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 305 ms / 2,000 ms
コード長 4,490 bytes
コンパイル時間 5,465 ms
コンパイル使用メモリ 276,504 KB
実行使用メモリ 17,656 KB
最終ジャッジ日時 2024-11-12 02:18:51
合計ジャッジ時間 13,840 ms
ジャッジサーバーID
(参考情報)
judge1 / judge5
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
sample AC * 2
other AC * 45
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

/**
author: shobonvip
created: 2024.11.12 01:47:20
**/
#include<bits/stdc++.h>
using namespace std;
//* ATCODER
#include<atcoder/all>
using namespace atcoder;
typedef modint998244353 mint;
//*/
/* BOOST MULTIPRECISION
#include<boost/multiprecision/cpp_int.hpp>
using namespace boost::multiprecision;
//*/
typedef long long ll;
#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)
#define all(v) v.begin(), v.end()
template <typename T> bool chmin(T &a, const T &b) {
if (a <= b) return false;
a = b;
return true;
}
template <typename T> bool chmax(T &a, const T &b) {
if (a >= b) return false;
a = b;
return true;
}
template <typename T> T max(vector<T> &a){
assert(!a.empty());
T ret = a[0];
for (int i=0; i<(int)a.size(); i++) chmax(ret, a[i]);
return ret;
}
template <typename T> T min(vector<T> &a){
assert(!a.empty());
T ret = a[0];
for (int i=0; i<(int)a.size(); i++) chmin(ret, a[i]);
return ret;
}
template <typename T> T sum(vector<T> &a){
T ret = 0;
for (int i=0; i<(int)a.size(); i++) ret += a[i];
return ret;
}
//defmodfact
const int COMinitMAX = 998244;
mint fact[COMinitMAX+1], factinv[COMinitMAX+1];
void modfact(){
fact[0] = 1;
for (int i=1; i<=COMinitMAX; i++){
fact[i] = fact[i-1] * i;
}
factinv[COMinitMAX] = fact[COMinitMAX].inv();
for (int i=COMinitMAX-1; i>=0; i--){
factinv[i] = factinv[i+1] * (i+1);
}
}
mint binom(int a, int b){
if (a<b || b<0) return mint(0);
return fact[a]*factinv[b]*factinv[a-b];
}
//--------
// Inv of Polynomial
// O(N log N)
// T should be modint
template<typename T>
std::vector<T> poly_inv(std::vector<T> &a, int M = -314159265){
if (M == -314159265) M = (int)a.size();
else if (M <= 0) return {};
int n = a.size();
T r = a[0].pow(T::mod()-2);
int m = 1;
std::vector<T> res = {r};
while (m < M){
std::vector<T> f = a;
f.resize(std::min(n, 2*m));
std::vector<T> h = atcoder::convolution(f, res);
for (int i=0; i<std::min(2*m, (int)h.size()); i++){
h[i] = -h[i];
}
h[0] += 2;
h.resize(2*m);
h = atcoder::convolution(h, res);
h.resize(2*m);
swap(res, h);
m <<= 1;
}
res.resize(M);
return res;
}
vector<mint> poly_log(vector<mint> &a, int M = -314159265){
if (M == -314159265) M = (int)a.size();
else if (M <= 0) return {};
int n = a.size();
if (n == 1) return vector<mint>(M, 0);
vector<mint> b(n-1);
for (int i=0; i<n-1; i++){
b[i] = a[i+1] * (i+1);
}
vector<mint> t = convolution<mint>(b, poly_inv(a, M));
vector<mint> ret(M);
for (int i=0; i<M-1; i++){
ret[i+1] = t[i] * factinv[i+1] * fact[i];
}
return ret;
}
vector<mint> poly_exp(vector<mint> &a, int M = -314159265){
if (M == -314159265) M = (int)a.size();
else if (M <= 0) return {};
int n = a.size();
int m = 1;
vector<mint> res = {1};
while (m < M){
vector<mint> f(2*m);
for (int i=0; i<min(n, 2*m); i++) f[i] = a[i];
vector<mint> v = poly_log(res, 2*m);
vector<mint> w(2*m);
for (int i=0; i<2*m; i++) w[i] = f[i] - v[i];
w[0] += 1;
vector<mint> g = convolution<mint>(res, w);
res.insert(res.end(), g.begin()+m, g.begin()+2*m);
m <<= 1;
}
res.resize(M);
return res;
}
vector<mint> poly_pow_nonzero(vector<mint> &a, ll m, ll l){
int n = a.size();
mint bais = a[0].pow(m);
mint invs;
if (a[0].val() == 0) invs = 0;
else invs = a[0].inv();
vector<mint> r(n);
for (int i=0; i<n; i++) r[i] = a[i] * invs;
r = poly_log(r, l);
for (int i=0; i<l; i++) r[i] = r[i] * m;
r = poly_exp(r, l);
for (int i=0; i<l; i++) r[i] = r[i] * bais;
return r;
}
vector<mint> poly_pow(vector<mint> &a, ll m, ll l){
int n = a.size();
int ind = 0;
for (int i=0; i<n; i++){
if (a[i].val() != 0){
ind = i;
break;
}
}
ll g = min(m, (ll)3141592653);
if (g*ind >= l){
return vector<mint>(l, 0);
}
vector<mint> ret(g*ind);
vector<mint> b(n-ind);
for (int i=0; i<n-ind; i++) b[i] = a[i+ind];
vector<mint> tmp;
if (l-g*ind > 0) tmp = poly_pow_nonzero(b, m, l-g*ind);
else tmp = {};
ret.insert(ret.end(), tmp.begin(), tmp.end());
return ret;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
modfact();
int n, m, k; cin >> n >> m >> k;
vector<mint> f(n+1);
rep(i,1,n+1){
f[i] = (mint(2).pow(i) - 1) * factinv[i];
}
vector<mint> g = poly_pow(f, k, n+1);
mint ans = 0;
for (int l=k; l<=n; l++) {
mint x = g[l];
x *= binom(n, l);
x *= fact[l];
x *= mint(m-k).pow(n-l);
ans += x;
}
ans *= binom(m, k);
cout << ans.val() << '\n';
}
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