結果
| 問題 |
No.1307 Rotate and Accumulate
|
| コンテスト | |
| ユーザー |
 emthrm
|
| 提出日時 | 2020-12-04 00:38:02 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 69 ms / 5,000 ms |
| コード長 | 13,850 bytes |
| コンパイル時間 | 2,781 ms |
| コンパイル使用メモリ | 214,660 KB |
| 最終ジャッジ日時 | 2025-01-16 15:02:30 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 19 |
ソースコード
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 1000000007;
// constexpr int MOD = 998244353;
constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
IOSetup() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
std::cout << fixed << setprecision(20);
}
} iosetup;
template <typename T>
struct FPS {
using MUL = std::function<std::vector<T>(const std::vector<T>&, const std::vector<T>&)>;
using SQR = std::function<bool(const T&, T&)>;
std::vector<T> co;
FPS(int deg = 0) : co(deg + 1, 0) {}
FPS(const std::vector<T> &co) : co(co) {}
FPS(std::initializer_list<T> init) : co(init.begin(), init.end()) {}
template <typename InputIter> FPS(InputIter first, InputIter last) : co(first, last) {}
inline const T &operator[](int term) const { return co[term]; }
inline T &operator[](int term) { return co[term]; }
static void set_mul(MUL mul) { get_mul() = mul; }
static void set_sqr(SQR sqr) { get_sqr() = sqr; }
void resize(int deg) { co.resize(deg + 1, 0); }
void shrink() { while (co.size() > 1 && co.back() == 0) co.pop_back(); }
int degree() const { return static_cast<int>(co.size()) - 1; }
FPS &operator=(const std::vector<T> &new_co) {
co.resize(new_co.size());
std::copy(new_co.begin(), new_co.end(), co.begin());
return *this;
}
FPS &operator=(const FPS &x) {
co.resize(x.co.size());
std::copy(x.co.begin(), x.co.end(), co.begin());
return *this;
}
FPS &operator+=(const FPS &x) {
int n = x.co.size();
if (n > co.size()) resize(n - 1);
for (int i = 0; i < n; ++i) co[i] += x.co[i];
return *this;
}
FPS &operator-=(const FPS &x) {
int n = x.co.size();
if (n > co.size()) resize(n - 1);
for (int i = 0; i < n; ++i) co[i] -= x.co[i];
return *this;
}
FPS &operator*=(T x) {
for (T &e : co) e *= x;
return *this;
}
FPS &operator*=(const FPS &x) { return *this = get_mul()(co, x.co); }
FPS &operator/=(T x) {
assert(x != 0);
T inv_x = static_cast<T>(1) / x;
for (T &e : co) e *= inv_x;
return *this;
}
FPS &operator/=(const FPS &x) {
int sz = x.co.size();
if (sz > co.size()) return *this = FPS();
int n = co.size() - sz + 1;
FPS a(co.rbegin(), co.rbegin() + n), b(x.co.rbegin(), x.co.rbegin() + std::min(sz, n));
b = b.inv(n - 1);
a *= b;
return *this = FPS(a.co.rend() - n, a.co.rend());
}
FPS &operator%=(const FPS &x) {
*this -= *this / x * x;
co.resize(static_cast<int>(x.co.size()) - 1);
if (co.empty()) co = {0};
return *this;
}
FPS &operator<<=(int n) {
co.insert(co.begin(), n, 0);
return *this;
}
FPS &operator>>=(int n) {
if (co.size() < n) return *this = FPS();
co.erase(co.begin(), co.begin() + n);
return *this;
}
bool operator==(const FPS &x) const {
FPS a(*this), b(x);
a.shrink(); b.shrink();
int n = a.co.size();
if (n != b.co.size()) return false;
for (int i = 0; i < n; ++i) if (a.co[i] != b.co[i]) return false;
return true;
}
bool operator!=(const FPS &x) const { return !(*this == x); }
FPS operator+() const { return *this; }
FPS operator-() const {
FPS res(*this);
for (T &e : res.co) e = -e;
return res;
}
FPS operator+(const FPS &x) const { return FPS(*this) += x; }
FPS operator-(const FPS &x) const { return FPS(*this) -= x; }
FPS operator*(T x) const { return FPS(*this) *= x; }
FPS operator*(const FPS &x) const { return FPS(*this) *= x; }
FPS operator/(T x) const { return FPS(*this) /= x; }
FPS operator/(const FPS &x) const { return FPS(*this) /= x; }
FPS operator%(const FPS &x) const { return FPS(*this) %= x; }
FPS operator<<(int n) const { return FPS(*this) <<= n; }
FPS operator>>(int n) const { return FPS(*this) >>= n; }
T horner(T val) const {
T res = 0;
for (int i = static_cast<int>(co.size()) - 1; i >= 0; --i) (res *= val) += co[i];
return res;
}
FPS differential() const {
int n = co.size();
assert(n >= 1);
FPS res(n - 1);
for (int i = 1; i < n; ++i) res.co[i - 1] = co[i] * i;
return res;
}
FPS integral() const {
int n = co.size();
FPS res(n + 1);
for (int i = 0; i < n; ++i) res[i + 1] = co[i] / (i + 1);
return res;
}
FPS exp(int deg = -1) const {
assert(co[0] == 0);
int n = co.size();
if (deg == -1) deg = n - 1;
FPS one{1}, res = one;
for (int i = 1; i <= deg; i <<= 1) {
res *= FPS(co.begin(), co.begin() + std::min(n, i << 1)) - res.log((i << 1) - 1) + one;
res.co.resize(i << 1);
}
res.co.resize(deg + 1);
return res;
}
FPS inv(int deg = -1) const {
assert(co[0] != 0);
int n = co.size();
if (deg == -1) deg = n - 1;
FPS res{static_cast<T>(1) / co[0]};
for (int i = 1; i <= deg; i <<= 1) {
res = res + res - res * res * FPS(co.begin(), co.begin() + std::min(n, i << 1));
res.co.resize(i << 1);
}
res.co.resize(deg + 1);
return res;
}
FPS log(int deg = -1) const {
assert(co[0] == 1);
if (deg == -1) deg = static_cast<int>(co.size()) - 1;
FPS integrand = differential() * inv(deg - 1);
integrand.co.resize(deg);
return integrand.integral();
}
FPS pow(long long exponent, int deg = -1) const {
int n = co.size();
if (deg == -1) deg = n - 1;
for (int i = 0; i < n; ++i) {
if (co[i] != 0) {
long long shift = exponent * i;
if (shift > deg) break;
T tmp = 1, base = co[i];
long long e = exponent;
while (e > 0) {
if (e & 1) tmp *= base;
base *= base;
e >>= 1;
}
return ((((*this >> i) * (static_cast<T>(1) / co[i])).log(deg - shift) * static_cast<T>(exponent)).exp(deg - shift) * tmp) << shift;
}
}
return FPS(deg);
}
FPS mod_pow(long long exponent, const FPS &md) const {
FPS inv_rev_md = FPS(md.co.rbegin(), md.co.rend()).inv();
int deg_of_md = md.co.size();
auto mod_mul = [&](FPS &multiplicand, const FPS &multiplier) -> void {
multiplicand *= multiplier;
if (deg_of_md <= multiplicand.co.size()) {
int n = multiplicand.co.size() - deg_of_md + 1;
FPS quotient = FPS(multiplicand.co.rbegin(), multiplicand.co.rbegin() + n) * FPS(inv_rev_md.co.begin(), inv_rev_md.co.begin() + std::min(static_cast<int>(inv_rev_md.co.size()), n));
multiplicand -= FPS(quotient.co.rend() - n, quotient.co.rend()) * md;
}
multiplicand.co.resize(deg_of_md - 1);
if (multiplicand.co.empty()) multiplicand.co = {0};
};
FPS res{1}, base = *this;
mod_mul(base, res);
while (exponent > 0) {
if (exponent & 1) mod_mul(res, base);
mod_mul(base, base);
exponent >>= 1;
}
return res;
}
FPS sqrt(int deg = -1) const {
int n = co.size();
if (deg == -1) deg = n - 1;
if (co[0] == 0) {
for (int i = 1; i < n; ++i) {
if (co[i] == 0) continue;
if (i & 1) return FPS(-1);
int shift = i >> 1;
if (deg < shift) break;
FPS res = (*this >> i).sqrt(deg - shift);
if (res.co.empty()) return FPS(-1);
res <<= shift;
res.resize(deg);
return res;
}
return FPS(deg);
}
T s;
if (!get_sqr()(co[0], s)) return FPS(-1);
FPS res{s};
T half = static_cast<T>(1) / 2;
for (int i = 1; i <= deg; i <<= 1) {
(res += FPS(co.begin(), co.begin() + std::min(n, i << 1)) * res.inv((i << 1) - 1)) *= half;
}
res.resize(deg);
return res;
}
FPS translate(T c) const {
int n = co.size();
std::vector<T> fact(n, 1), inv_fact(n, 1);
for (int i = 1; i < n; ++i) fact[i] = fact[i - 1] * i;
inv_fact[n - 1] = static_cast<T>(1) / fact[n - 1];
for (int i = n - 1; i > 0; --i) inv_fact[i - 1] = inv_fact[i] * i;
std::vector<T> g(n), ex(n);
for (int i = 0; i < n; ++i) g[n - 1 - i] = co[i] * fact[i];
T pow_c = 1;
for (int i = 0; i < n; ++i) {
ex[i] = pow_c * inv_fact[i];
pow_c *= c;
}
std::vector<T> conv = get_mul()(g, ex);
FPS res(n - 1);
for (int i = 0; i < n; ++i) res[i] = conv[n - 1 - i] * inv_fact[i];
return res;
}
private:
static MUL &get_mul() {
static MUL mul = [](const std::vector<T> &a, const std::vector<T> &b) -> std::vector<T> {
int n = a.size(), m = b.size();
std::vector<T> res(n + m - 1, 0);
for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) res[i + j] += a[i] * b[j];
return res;
};
return mul;
}
static SQR &get_sqr() {
static SQR sqr = [](const T &a, T &res) -> bool { return false; };
return sqr;
}
};
namespace fft {
using Real = double;
struct Complex {
Real re, im;
Complex(Real re = 0, Real im = 0) : re(re), im(im) {}
inline Complex operator+(const Complex &x) const { return Complex(re + x.re, im + x.im); }
inline Complex operator-(const Complex &x) const { return Complex(re - x.re, im - x.im); }
inline Complex operator*(const Complex &x) const { return Complex(re * x.re - im * x.im, re * x.im + im * x.re); }
inline Complex mul_real(Real r) const { return Complex(re * r, im * r); }
inline Complex mul_pin(Real r) const { return Complex(-im * r, re * r); }
inline Complex conj() const { return Complex(re, -im); }
};
std::vector<int> butterfly{0};
std::vector<std::vector<Complex>> zeta{{{1, 0}}};
void calc(int n) {
int prev_n = butterfly.size();
if (n <= prev_n) return;
butterfly.resize(n);
int prev_lg = zeta.size(), lg = __builtin_ctz(n);
for (int i = 1; i < prev_n; ++i) butterfly[i] <<= lg - prev_lg;
for (int i = prev_n; i < n; ++i) butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1));
zeta.resize(lg);
for (int i = prev_lg; i < lg; ++i) {
zeta[i].resize(1 << i);
Real angle = -3.14159265358979323846 * 2 / (1 << (i + 1));
for (int j = 0; j < (1 << (i - 1)); ++j) {
zeta[i][j << 1] = zeta[i - 1][j];
Real theta = angle * ((j << 1) + 1);
zeta[i][(j << 1) + 1] = {std::cos(theta), std::sin(theta)};
}
}
}
void sub_dft(std::vector<Complex> &a) {
int n = a.size();
assert(__builtin_popcount(n) == 1);
calc(n);
int shift = __builtin_ctz(butterfly.size()) - __builtin_ctz(n);
for (int i = 0; i < n; ++i) {
int j = butterfly[i] >> shift;
if (i < j) std::swap(a[i], a[j]);
}
for (int block = 1; block < n; block <<= 1) {
int den = __builtin_ctz(block);
for (int i = 0; i < n; i += (block << 1)) for (int j = 0; j < block; ++j) {
Complex tmp = a[i + j + block] * zeta[den][j];
a[i + j + block] = a[i + j] - tmp;
a[i + j] = a[i + j] + tmp;
}
}
}
template <typename T>
std::vector<Complex> dft(const std::vector<T> &a) {
int sz = a.size(), lg = 1;
while ((1 << lg) < sz) ++lg;
std::vector<Complex> c(1 << lg);
for (int i = 0; i < sz; ++i) c[i].re = a[i];
sub_dft(c);
return c;
}
std::vector<Real> real_idft(std::vector<Complex> &a) {
int n = a.size(), half = n >> 1, quarter = half >> 1;
assert(__builtin_popcount(n) == 1);
calc(n);
a[0] = (a[0] + a[half] + (a[0] - a[half]).mul_pin(1)).mul_real(0.5);
int den = __builtin_ctz(half);
for (int i = 1; i < quarter; ++i) {
int j = half - i;
Complex tmp1 = a[i] + a[j].conj(), tmp2 = ((a[i] - a[j].conj()) * zeta[den][j]).mul_pin(1);
a[i] = (tmp1 - tmp2).mul_real(0.5);
a[j] = (tmp1 + tmp2).mul_real(0.5).conj();
}
if (quarter > 0) a[quarter] = a[quarter].conj();
a.resize(half);
sub_dft(a);
std::reverse(a.begin() + 1, a.end());
Real r = 1.0 / half;
std::vector<Real> res(n);
for (int i = 0; i < n; ++i) res[i] = (i & 1 ? a[i >> 1].im : a[i >> 1].re) * r;
return res;
}
void idft(std::vector<Complex> &a) {
int n = a.size();
sub_dft(a);
std::reverse(a.begin() + 1, a.end());
Real r = 1.0 / n;
for (int i = 0; i < n; ++i) a[i] = a[i].mul_real(r);
}
template <typename T>
std::vector<Real> convolution(const std::vector<T> &a, const std::vector<T> &b) {
int a_sz = a.size(), b_sz = b.size(), sz = a_sz + b_sz - 1, lg = 1;
while ((1 << lg) < sz) ++lg;
int n = 1 << lg;
std::vector<Complex> c(n);
for (int i = 0; i < a_sz; ++i) c[i].re = a[i];
for (int i = 0; i < b_sz; ++i) c[i].im = b[i];
sub_dft(c);
c[0] = Complex(c[0].re * c[0].im, 0);
int half = n >> 1;
for (int i = 1; i < half; ++i) {
Complex i_square = c[i] * c[i], j_square = c[n - i] * c[n - i];
c[i] = (j_square.conj() - i_square).mul_pin(0.25);
c[n - i] = (i_square.conj() - j_square).mul_pin(0.25);
}
c[half] = Complex(c[half].re * c[half].im, 0);
std::vector<Real> res = real_idft(c);
res.resize(sz);
return res;
}
} // fft
int main() {
FPS<ll>::set_mul([](const vector<ll> &a, const vector<ll> &b) {
vector<fft::Real> f = fft::convolution(a, b);
int n = f.size();
vector<ll> c(n);
REP(i, n) c[i] = static_cast<ll>(round(f[i]));
return c;
});
int n, q; cin >> n >> q;
FPS<ll> a(n - 1), r(n - 1); REP(i, n) cin >> a[n - 1 - i];
// REP(i, n) cout << a[i] << " \n"[i + 1 == n];
while (q--) {
int ri; cin >> ri;
++r[ri];
}
// REP(i, n) cout << r[i] << " \n"[i + 1 == n];
a *= r;
vector<ll> ans(n, 0);
REP(i, a.degree() + 1) ans[i % n] += a[i];
reverse(ALL(ans));
REP(i, n) cout << ans[i] << " \n"[i + 1 == n];
return 0;
}