結果
| 問題 | No.1574 Swap and Repaint |
| ユーザー |
👑  hos.lyric
|
| 提出日時 | 2021-08-07 04:28:41 |
| 言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 282 ms / 10,000 ms |
| コード長 | 13,329 bytes |
| コンパイル時間 | 1,574 ms |
| コンパイル使用メモリ | 115,612 KB |
| 実行使用メモリ | 18,652 KB |
| 最終ジャッジ日時 | 2024-10-03 12:37:50 |
| 合計ジャッジ時間 | 6,151 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 7 ms
9,412 KB |
| testcase_01 | AC | 7 ms
9,412 KB |
| testcase_02 | AC | 8 ms
9,556 KB |
| testcase_03 | AC | 7 ms
9,448 KB |
| testcase_04 | AC | 8 ms
9,600 KB |
| testcase_05 | AC | 7 ms
9,432 KB |
| testcase_06 | AC | 8 ms
9,416 KB |
| testcase_07 | AC | 8 ms
9,416 KB |
| testcase_08 | AC | 7 ms
9,472 KB |
| testcase_09 | AC | 9 ms
9,600 KB |
| testcase_10 | AC | 8 ms
9,600 KB |
| testcase_11 | AC | 7 ms
9,596 KB |
| testcase_12 | AC | 8 ms
9,580 KB |
| testcase_13 | AC | 9 ms
9,564 KB |
| testcase_14 | AC | 8 ms
9,600 KB |
| testcase_15 | AC | 9 ms
9,600 KB |
| testcase_16 | AC | 8 ms
9,548 KB |
| testcase_17 | AC | 8 ms
9,592 KB |
| testcase_18 | AC | 73 ms
11,772 KB |
| testcase_19 | AC | 274 ms
18,400 KB |
| testcase_20 | AC | 68 ms
11,952 KB |
| testcase_21 | AC | 65 ms
11,800 KB |
| testcase_22 | AC | 63 ms
11,456 KB |
| testcase_23 | AC | 21 ms
10,104 KB |
| testcase_24 | AC | 235 ms
16,228 KB |
| testcase_25 | AC | 129 ms
13,888 KB |
| testcase_26 | AC | 14 ms
9,728 KB |
| testcase_27 | AC | 55 ms
10,944 KB |
| testcase_28 | AC | 276 ms
18,652 KB |
| testcase_29 | AC | 272 ms
18,520 KB |
| testcase_30 | AC | 270 ms
18,648 KB |
| testcase_31 | AC | 270 ms
18,644 KB |
| testcase_32 | AC | 268 ms
18,648 KB |
| testcase_33 | AC | 271 ms
18,652 KB |
| testcase_34 | AC | 282 ms
18,524 KB |
| testcase_35 | AC | 271 ms
18,520 KB |
ソースコード
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353U;
constexpr unsigned MO2 = 2U * MO;
constexpr int FFT_MAX = 23;
using Mint = ModInt<MO>;
constexpr Mint FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 911660635U, 372528824U, 929031873U, 452798380U, 922799308U, 781712469U, 476477967U, 166035806U, 258648936U, 584193783U, 63912897U, 350007156U, 666702199U, 968855178U, 629671588U, 24514907U, 996173970U, 363395222U, 565042129U, 733596141U, 267099868U, 15311432U};
constexpr Mint INV_FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 86583718U, 509520358U, 337190230U, 87557064U, 609441965U, 135236158U, 304459705U, 685443576U, 381598368U, 335559352U, 129292727U, 358024708U, 814576206U, 708402881U, 283043518U, 3707709U, 121392023U, 704923114U, 950391366U, 428961804U, 382752275U, 469870224U};
constexpr Mint FFT_RATIOS[FFT_MAX] = {911660635U, 509520358U, 369330050U, 332049552U, 983190778U, 123842337U, 238493703U, 975955924U, 603855026U, 856644456U, 131300601U, 842657263U, 730768835U, 942482514U, 806263778U, 151565301U, 510815449U, 503497456U, 743006876U, 741047443U, 56250497U, 867605899U};
constexpr Mint INV_FFT_RATIOS[FFT_MAX] = {86583718U, 372528824U, 373294451U, 645684063U, 112220581U, 692852209U, 155456985U, 797128860U, 90816748U, 860285882U, 927414960U, 354738543U, 109331171U, 293255632U, 535113200U, 308540755U, 121186627U, 608385704U, 438932459U, 359477183U, 824071951U, 103369235U};
// as[rev(i)] <- \sum_j \zeta^(ij) as[j]
void fft(Mint *as, int n) {
assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
int m = n;
if (m >>= 1) {
for (int i = 0; i < m; ++i) {
const unsigned x = as[i + m].x; // < MO
as[i + m].x = as[i].x + MO - x; // < 2 MO
as[i].x += x; // < 2 MO
}
}
if (m >>= 1) {
Mint prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + m; ++i) {
const unsigned x = (prod * as[i + m]).x; // < MO
as[i + m].x = as[i].x + MO - x; // < 3 MO
as[i].x += x; // < 3 MO
}
prod *= FFT_RATIOS[__builtin_ctz(++h)];
}
}
for (; m; ) {
if (m >>= 1) {
Mint prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + m; ++i) {
const unsigned x = (prod * as[i + m]).x; // < MO
as[i + m].x = as[i].x + MO - x; // < 4 MO
as[i].x += x; // < 4 MO
}
prod *= FFT_RATIOS[__builtin_ctz(++h)];
}
}
if (m >>= 1) {
Mint prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + m; ++i) {
const unsigned x = (prod * as[i + m]).x; // < MO
as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x; // < 2 MO
as[i + m].x = as[i].x + MO - x; // < 3 MO
as[i].x += x; // < 3 MO
}
prod *= FFT_RATIOS[__builtin_ctz(++h)];
}
}
}
for (int i = 0; i < n; ++i) {
as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x; // < 2 MO
as[i].x = (as[i].x >= MO) ? (as[i].x - MO) : as[i].x; // < MO
}
}
// as[i] <- (1/n) \sum_j \zeta^(-ij) as[rev(j)]
void invFft(Mint *as, int n) {
assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
int m = 1;
if (m < n >> 1) {
Mint prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + m; ++i) {
const unsigned long long y = as[i].x + MO - as[i + m].x; // < 2 MO
as[i].x += as[i + m].x; // < 2 MO
as[i + m].x = (prod.x * y) % MO; // < MO
}
prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
}
m <<= 1;
}
for (; m < n >> 1; m <<= 1) {
Mint prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + (m >> 1); ++i) {
const unsigned long long y = as[i].x + MO2 - as[i + m].x; // < 4 MO
as[i].x += as[i + m].x; // < 4 MO
as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x; // < 2 MO
as[i + m].x = (prod.x * y) % MO; // < MO
}
for (int i = i0 + (m >> 1); i < i0 + m; ++i) {
const unsigned long long y = as[i].x + MO - as[i + m].x; // < 2 MO
as[i].x += as[i + m].x; // < 2 MO
as[i + m].x = (prod.x * y) % MO; // < MO
}
prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
}
}
if (m < n) {
for (int i = 0; i < m; ++i) {
const unsigned y = as[i].x + MO2 - as[i + m].x; // < 4 MO
as[i].x += as[i + m].x; // < 4 MO
as[i + m].x = y; // < 4 MO
}
}
const Mint invN = Mint(n).inv();
for (int i = 0; i < n; ++i) {
as[i] *= invN;
}
}
void fft(vector<Mint> &as) {
fft(as.data(), as.size());
}
void invFft(vector<Mint> &as) {
invFft(as.data(), as.size());
}
vector<Mint> convolve(vector<Mint> as, vector<Mint> bs) {
if (as.empty() || bs.empty()) return {};
const int len = as.size() + bs.size() - 1;
int n = 1;
for (; n < len; n <<= 1) {}
as.resize(n); fft(as);
bs.resize(n); fft(bs);
for (int i = 0; i < n; ++i) as[i] *= bs[i];
invFft(as);
as.resize(len);
return as;
}
vector<Mint> square(vector<Mint> as) {
if (as.empty()) return {};
const int len = as.size() + as.size() - 1;
int n = 1;
for (; n < len; n <<= 1) {}
as.resize(n); fft(as);
for (int i = 0; i < n; ++i) as[i] *= as[i];
invFft(as);
as.resize(len);
return as;
}
////////////////////////////////////////////////////////////////////////////////
constexpr int LIM = 300'010;
Mint inv[LIM], fac[LIM], invFac[LIM];
void prepare() {
inv[1] = 1;
for (int i = 2; i < LIM; ++i) {
inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
}
fac[0] = invFac[0] = 1;
for (int i = 1; i < LIM; ++i) {
fac[i] = fac[i - 1] * i;
invFac[i] = invFac[i - 1] * inv[i];
}
}
Mint binom(Int n, Int k) {
if (n < 0) {
if (k >= 0) {
return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
} else if (n - k >= 0) {
return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
} else {
return 0;
}
} else {
if (0 <= k && k <= n) {
assert(n < LIM);
return fac[n] * invFac[k] * invFac[n - k];
} else {
return 0;
}
}
}
/*
A(x) := \sum_{j=0}^{N-1} A[j] x^j
B(x) := x^-1 + (N - 3) x^0 + x^1
C[i][j] := [x^j] (A(x) B(x)^i) (0 <= i <= N, -N <= j <= 2 N - 1)
ans[i] := \sum_{j=-N}^{2N-1} C[i][j] D[j]
D[j] := (contribution of balls at j)
D[-1 - j] = D[j] = D[2 N - 1 - j] (0 <= j <= N - 1)
transpose
for e[i] (0 <= i <= N)
\sum_{i=0}^N C[i][j] e[i] = [x^j] (A(x) \sum_{i=0}^N e[i] B(x)^i)
DC
*/
/*
[0, n] * [0, n - m + 1]
[ a[0] ]
[ ... a[0] ]
[ a[m-1] ... ]
[ a[m-1] ]
[ ... ]
[ a[0] ]
[ ... ]
[ a[m-1] ]
[x^j] (rev(a) b) m - 1 <= j <= n - 1
*/
vector<Mint> middle(vector<Mint> as, vector<Mint> bs) {
const int m = as.size();
const int n = bs.size();
assert(m <= n);
int nn = 1;
for (; nn < n; nn <<= 1) {}
reverse(as.begin(), as.end());
as.resize(nn, 0);
fft(as);
bs.resize(nn, 0);
fft(bs);
for (int i = 0; i < nn; ++i) {
bs[i] *= as[i];
}
invFft(bs);
bs.resize(n);
bs.erase(bs.begin(), bs.begin() + (m - 1));
return bs;
}
Mint two[LIM], invTwo[LIM];
int N;
vector<int> A;
vector<Mint> ans;
/*
\sum_{i=l}^{r-1} e[i] B(x)^(i-l)
*/
void solve(int l, int r, const vector<Mint> &zs) {
assert((int)zs.size() == 2 * (r - l - 1) + 1);
if (r - l == 1) {
ans[l] = zs[0];
} else {
const int mid = (l + r) / 2;
const int nL = mid - l;
const int nR = r - mid;
/*
[-(nL + nR - 1), nL + nR - 1] * ([-(nL - 1), (nL - 1)], [-(nL + nR - 1), nL + nR - 1])
[ | 1 ]
[ 1 | 1 ]
[ 1 | 1 ]
[ 1 | 1 ]
[ | 1 ]
*/
vector<Mint> zsL(2 * (nL - 1) + 1);
for (int i = 0; i <= 2 * (nL - 1); ++i) {
zsL[i] = zs[nR + i];
}
/*
B(x)^nL
*/
vector<Mint> bs(2 * nL + 1);
bs[0] = 1;
bs[1] = nL * Mint(N - 3);
for (int j = 2; j <= 2 * nL; ++j) {
bs[j] = inv[j] * ((nL - (j - 1)) * Mint(N - 3) * bs[j - 1] + (nL * 2 - (j - 2)) * bs[j - 2]);
}
// cerr<<"bs = ";pv(bs.begin(),bs.end());
/*
[-(nL + nR - 1), nL + nR - 1] * [-(nR - 1), nR - 1]
*/
const auto zsR = middle(bs, zs);
solve(l, mid, zsL);
solve(mid, r, zsR);
}
}
int main() {
prepare();
two[0] = invTwo[0] = 1;
for (int i = 1; i < LIM; ++i) {
two[i] = two[i - 1] * 2;
invTwo[i] = invTwo[i - 1] * inv[2];
}
for (; ~scanf("%d", &N); ) {
A.resize(N);
for (int j = 0; j < N; ++j) {
scanf("%d", &A[j]);
}
/*
overwritten: (1/2^(j-k+1)) * (j - k) (1/(j-k+1))! (k < j < N - 1)
not overwritten: (1/2^(j-k+[j<N-1])) * (1/(j-k)!) (k <= j)
*/
vector<Mint> D(N, 0);
{
Mint sum = 0;
for (int j = 0; j < N - 1; ++j) {
sum += invTwo[j + 1] * j * invFac[j + 1];
sum += invTwo[j + 1] * invFac[j];
D[j] = sum;
}
}
for (int k = 0; k <= N - 1; ++k) {
D[N - 1] += invTwo[N - 1 - k] * invFac[N - 1 - k];
}
{
const Mint all = two[2 * (N - 1)] * fac[N - 1];
for (int j = 0; j < N; ++j) {
D[j] *= all;
}
}
// cerr<<"D = ";pv(D.begin(),D.end());
// {Mint ans0=0;for(int j=0;j<N;++j){ans0+=A[j]*D[j];}cerr<<"ans0 = "<<ans0<<endl;}
/*
[-N, 2 N - 1] * [-N, N]
*/
vector<Mint> as(N), ds(3 * N);
for (int j = 0; j < N; ++j) {
as[j] = A[j];
ds[N - 1 - j] = ds[N + j] = ds[3 * N - 1 - j] = D[j];
}
const auto zs = middle(as, ds);
ans.assign(N + 1, 0);
solve(0, N + 1, zs);
for (int i = 0; i <= N; ++i) {
printf("%u\n", ans[i].x);
}
}
return 0;
}