結果

問題 No.1410 A lot of Bit Operations
ユーザー ecotteaecottea
提出日時 2023-07-26 16:48:38
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 173 ms / 2,000 ms
コード長 20,607 bytes
コンパイル時間 4,197 ms
コンパイル使用メモリ 279,144 KB
最終ジャッジ日時 2025-02-15 19:15:38
ジャッジサーバーID
(参考情報)
judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 44
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ソースコード

diff #
プレゼンテーションモードにする

#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; // -2^63 2^63 = 9 * 10^18int -2^31 2^31 = 2 * 10^9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vvvvl = vector<vvvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
const vi DX = { 1, 0, -1, 0 }; // 4
const vi DY = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003104004004LL; // (int)INFL = 1010931620;
double EPS = 1e-15;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // mod
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) //
//
template <class T> inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
template <class T> inline T get(T set, int i) { return (set >> i) & T(1); }
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif //
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
using mint = modint1000000007;
//using mint = modint998244353;
//using mint = modint; // mint::set_mod(m);
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>;
#endif
#ifdef _MSC_VER // Visual Studio
#include "local.hpp"
#else // gcc
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define gcd __gcd
#define dump(...)
#define dumpel(v)
#define dump_list(v)
#define dump_mat(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) while (1) cout << "OLE"; }
#endif
void zikken() {
int N = 10;
vi res(N);
rep(n, N) {
repb(p, n) repb(q, n) {
int l = p | q;
int r = (1 << n) - 1 - l;
if (l > r) swap(l, r);
res[n] += r - l + 1;
}
}
dump_list(res);
exit(0);
}
//
/*
* MFPS() : O(1)
* f = 0
*
* MFPS(mint c0) : O(1)
* f = c0
*
* MFPS(mint c0, int n) : O(n)
* n f = c0
*
* MFPS(vm c) : O(n)
* f(z) = c[0] + c[1] z + ... + c[n - 1] z^(n-1)
*
* set_conv(vm(*CONV)(const vm&, const vm&)) : O(1)
* CONV
*
* c + f, f + c : O(1) f + g : O(n)
* f - c : O(1) c - f, f - g, -f : O(n)
* c * f, f * c : O(n) f * g : O(n log n) f * g_sp : O(n k)k : g
* f / c : O(n) f / g : O(n log n) f / g_sp : O(n k)k : g
*
* g_sp {, } vector
* : g(0) != 0
*
* MFPS f.inv(int d) : O(n log n)
* 1 / f mod z^d
* : f(0) != 0
*
* MFPS f.quotient(MFPS g) : O(n log n)
* MFPS f.reminder(MFPS g) : O(n log n)
* pair<MFPS, MFPS> f.quotient_remainder(MFPS g) : O(n log n)
* f g
* : g 0
*
* int f.deg(), int f.size() : O(1)
* f []
*
* MFPS::monomial(int d) : O(d)
* z^d
*
* mint f.assign(mint c) : O(n)
* f z c
*
* f.resize(int d) : O(1)
* mod z^d
*
* f.resize() : O(n)
*
*
* f >> d, f << d : O(n)
* d []
* z^d z^d
*/
struct MFPS {
using SMFPS = vector<pair<int, mint>>;
int n; // + 1
vm c; //
inline static vm(*CONV)(const vm&, const vm&) = convolution; //
// 0
MFPS() : n(0) {}
MFPS(const mint& c0) : n(1), c({ c0 }) {}
MFPS(const int& c0) : n(1), c({ mint(c0) }) {}
MFPS(const mint& c0, int d) : n(d), c(n) { c[0] = c0; }
MFPS(const int& c0, int d) : n(d), c(n) { c[0] = c0; }
MFPS(const vm& c_) : n(sz(c_)), c(c_) {}
MFPS(const vi& c_) : n(sz(c_)), c(n) { rep(i, n) c[i] = c_[i]; }
//
MFPS(const MFPS& f) = default;
MFPS& operator=(const MFPS& f) = default;
MFPS& operator=(const mint& c0) { n = 1; c = { c0 }; return *this; }
//
bool operator==(const MFPS& g) const { return c == g.c; }
bool operator!=(const MFPS& g) const { return c != g.c; }
//
inline mint const& operator[](int i) const { return c[i]; }
inline mint& operator[](int i) { return c[i]; }
//
int deg() const { return n - 1; }
int size() const { return n; }
static void set_conv(vm(*CONV_)(const vm&, const vm&)) {
// verify : https://atcoder.jp/contests/tdpc/tasks/tdpc_fibonacci
CONV = CONV_;
}
//
MFPS& operator+=(const MFPS& g) {
if (n >= g.n) rep(i, g.n) c[i] += g.c[i];
else {
rep(i, n) c[i] += g.c[i];
repi(i, n, g.n - 1) c.push_back(g.c[i]);
n = g.n;
}
return *this;
}
MFPS operator+(const MFPS& g) const { return MFPS(*this) += g; }
//
MFPS& operator+=(const mint& sc) {
if (n == 0) { n = 1; c = { sc }; }
else { c[0] += sc; }
return *this;
}
MFPS operator+(const mint& sc) const { return MFPS(*this) += sc; }
friend MFPS operator+(const mint& sc, const MFPS& f) { return f + sc; }
MFPS& operator+=(const int& sc) { *this += mint(sc); return *this; }
MFPS operator+(const int& sc) const { return MFPS(*this) += sc; }
friend MFPS operator+(const int& sc, const MFPS& f) { return f + sc; }
//
MFPS& operator-=(const MFPS& g) {
if (n >= g.n) rep(i, g.n) c[i] -= g.c[i];
else {
rep(i, n) c[i] -= g.c[i];
repi(i, n, g.n - 1) c.push_back(-g.c[i]);
n = g.n;
}
return *this;
}
MFPS operator-(const MFPS& g) const { return MFPS(*this) -= g; }
//
MFPS& operator-=(const mint& sc) { *this += -sc; return *this; }
MFPS operator-(const mint& sc) const { return MFPS(*this) -= sc; }
friend MFPS operator-(const mint& sc, const MFPS& f) { return -(f - sc); }
MFPS& operator-=(const int& sc) { *this += -sc; return *this; }
MFPS operator-(const int& sc) const { return MFPS(*this) -= sc; }
friend MFPS operator-(const int& sc, const MFPS& f) { return -(f - sc); }
//
MFPS operator-() const { return MFPS(*this) *= -1; }
//
MFPS& operator*=(const mint& sc) { rep(i, n) c[i] *= sc; return *this; }
MFPS operator*(const mint& sc) const { return MFPS(*this) *= sc; }
friend MFPS operator*(const mint& sc, const MFPS& f) { return f * sc; }
MFPS& operator*=(const int& sc) { *this *= mint(sc); return *this; }
MFPS operator*(const int& sc) const { return MFPS(*this) *= sc; }
friend MFPS operator*(const int& sc, const MFPS& f) { return f * sc; }
//
MFPS& operator/=(const mint& sc) { *this *= sc.inv(); return *this; }
MFPS operator/(const mint& sc) const { return MFPS(*this) /= sc; }
MFPS& operator/=(const int& sc) { *this /= mint(sc); return *this; }
MFPS operator/(const int& sc) const { return MFPS(*this) /= sc; }
//
MFPS& operator*=(const MFPS& g) { c = CONV(c, g.c); n = sz(c); return *this; }
MFPS operator*(const MFPS& g) const { return MFPS(*this) *= g; }
//
MFPS inv(int d) const {
// https://nyaannyaan.github.io/library/fps/formal-power-series.hpp
// verify : https://judge.yosupo.jp/problem/inv_of_formal_power_series
//
// 1 / f mod x^d
// f g = 1 (mod x^d)
// g
// d 1, 2, 4, ..., 2^i
//
// d = 1
// g = 1 / f[0] (mod x^1)
//
//
//
// g = h (mod x^k)
//
// g mod x^(2 k)
//
// g - h = 0 (mod x^k)
// ⇒ (g - h)^2 = 0 (mod x^(2 k))
// ⇔ g^2 - 2 g h + h^2 = 0 (mod x^(2 k))
// ⇒ f g^2 - 2 f g h + f h^2 = 0 (mod x^(2 k))
// ⇔ g - 2 h + f h^2 = 0 (mod x^(2 k))  (f g = 1 (mod x^d) )
// ⇔ g = (2 - f h) h (mod x^(2 k))
//
//
// d <= 2^i i d
Assert(!c.empty());
Assert(c[0] != 0);
MFPS g(c[0].inv());
for (int k = 1; k < d; k *= 2) {
g = (2 - *this * g) * g;
g.resize(2 * k);
}
return g.resize(d);
}
MFPS& operator/=(const MFPS& g) { return *this *= g.inv(max(n, g.n)); }
MFPS operator/(const MFPS& g) const { return MFPS(*this) /= g; }
//
MFPS quotient(const MFPS& g) const {
// : https://nyaannyaan.github.io/library/fps/formal-power-series.hpp
// verify : https://judge.yosupo.jp/problem/division_of_polynomials
//
// f(x) = g(x) q(x) + r(x) q(x)
// f n - 1, g m - 1 (n >= m)
// q n - mr m - 2
//
// f^R f
// f^R(x) := f(1/x) x^(n-1)
//
//
// x → 1/x
// f(1/x) = g(1/x) q(1/x) + r(1/x)
// ⇔ f(1/x) x^(n-1) = g(1/x) q(1/x) x^(n-1) + r(1/x) x^(n-1)
// ⇔ f(1/x) x^(n-1) = g(1/x) x^(m-1) q(1/x) x^(n-m) + r(1/x) x^(m-2) x^(n-m+1)
// ⇔ f^R(x) = g^R(x) q^R(x) + r^R(x) x^(n-m+1)
// ⇒ f^R(x) = g^R(x) q^R(x) (mod x^(n-m+1))
// ⇒ q^R(x) = f^R(x) / g^R(x) (mod x^(n-m+1))
//
//
// q mod x^(n-m+1)
// q n - m q
if (n < g.n) return MFPS();
return ((this->rev() / g.rev()).resize(n - g.n + 1)).rev();
}
MFPS reminder(const MFPS& g) const {
// verify : https://judge.yosupo.jp/problem/division_of_polynomials
return (*this - this->quotient(g) * g).resize(g.n - 1);
}
pair<MFPS, MFPS> quotient_remainder(const MFPS& g) const {
// verify : https://judge.yosupo.jp/problem/division_of_polynomials
pair<MFPS, MFPS> res;
res.first = this->quotient(g);
res.second = (*this - res.first * g).resize(g.n - 1);
return res;
}
//
MFPS& operator*=(const SMFPS& g) {
// g
auto it0 = g.begin();
mint g0 = 0;
if (it0->first == 0) {
g0 = it0->second;
it0++;
}
// DP
repir(i, n - 1, 0) {
//
for (auto it = it0; it != g.end(); it++) {
int j; mint gj;
tie(j, gj) = *it;
if (i + j >= n) break;
c[i + j] += c[i] * gj;
}
//
c[i] *= g0;
}
return *this;
}
MFPS operator*(const SMFPS& g) const { return MFPS(*this) *= g; }
//
MFPS& operator/=(const SMFPS& g) {
// g
auto it0 = g.begin();
Assert(it0->first == 0 && it0->second != 0);
mint g0_inv = it0->second.inv();
it0++;
// DP
rep(i, n) {
//
c[i] *= g0_inv;
//
for (auto it = it0; it != g.end(); it++) {
int j; mint gj;
tie(j, gj) = *it;
if (i + j >= n) break;
c[i + j] -= c[i] * gj;
}
}
return *this;
}
MFPS operator/(const SMFPS& g) const { return MFPS(*this) /= g; }
//
MFPS rev() const { MFPS h = *this; reverse(all(h.c)); return h; }
//
static MFPS monomial(int d) {
MFPS mono(0, d + 1);
mono[d] = 1;
return mono;
}
//
MFPS& resize() {
// 0
while (n > 0 && c[n - 1] == 0) {
c.pop_back();
n--;
}
return *this;
}
// x^d
MFPS& resize(int d) {
n = d;
c.resize(d);
return *this;
}
//
mint assign(const mint& x) const {
mint val = 0;
repir(i, n - 1, 0) val = val * x + c[i];
return val;
}
//
MFPS& operator>>=(int d) {
n += d;
c.insert(c.begin(), d, 0);
return *this;
}
MFPS& operator<<=(int d) {
n -= d;
if (n <= 0) { c.clear(); n = 0; }
else c.erase(c.begin(), c.begin() + d);
return *this;
}
MFPS operator>>(int d) const { return MFPS(*this) >>= d; }
MFPS operator<<(int d) const { return MFPS(*this) <<= d; }
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const MFPS& f) {
if (f.n == 0) os << 0;
else {
rep(i, f.n) {
os << f[i].val() << "z^" << i;
if (i < f.n - 1) os << " + ";
}
}
return os;
}
#endif
};
//O(n log n log d)
/*
* f(x)/g(x) x^d
*
* : deg f < deg g, g[0] != 0
*/
mint bostan_mori(const MFPS& f, const MFPS& g, ll d) {
// : http://q.c.titech.ac.jp/docs/progs/polynomial_division.html
// verify : https://atcoder.jp/contests/tdpc/tasks/tdpc_fibonacci
//
// g(-x)
// f(x) / g(x) = f(x) g(-x) / g(x) g(-x)
// g(x) g(-x)
// g(x) g(-x) = e(x^2)
//
//
//
// f(x) g(-x) = E(x^2) + x O(x^2)
// d
// [x^d] f(x) g(-x) / g(x) g(-x)
// = [x^d] E(x^2) / e(x^2)
// = [x^(d/2)] E(x) / e(x)
// d
// [x^d] f(x) g(-x) / g(x) g(-x)
// = [x^d] x O(x^2) / e(x^2)
// = [x^((d-1)/2)] O(x) / e(x)
//
//
// d
Assert(g.n >= 1 && g[0] != 0);
// d = 0
if (d == 0) return f[0] / g[0];
// f2(x) = f(x) g(-x), g2(x) = g(x) g(-x)
MFPS f2, g2 = g;
rep(i, g2.n) if (i % 2 == 1) g2[i] *= -1;
f2 = f * g2;
g2 *= g;
// f3(x) = E(x) or O(x), g3(x) = e(x)
MFPS f3, g3;
if (d % 2 == 0) rep(i, (f2.n + 1) / 2) f3.c.push_back(f2[2 * i]);
else rep(i, f2.n / 2) f3.c.push_back(f2[2 * i + 1]);
f3.n = sz(f3.c);
rep(i, g.n) g3.c.push_back(g2[2 * i]);
g3.n = sz(g3.c);
// d
return bostan_mori(f3, g3, d / 2);
}
//O(d log d log n)
/*
* a[0..d) a[i] = Σj=[0..d) c[j]a[i-1-j]
* a a[n]
*
*
*/
mint linearly_recurrent_sequence(const vm& a, const vm& c, ll n) {
// verify : https://judge.yosupo.jp/problem/kth_term_of_linearly_recurrent_sequence
int d = sz(a);
if (d == 0) return 0;
MFPS A(a), C(c);
MFPS Dnm = 1 - (C >> 1);
MFPS Num = (Dnm * A).resize(d);
return bostan_mori(Num, Dnm, n);
}
//O(n^2)
/*
* a[0..n) c[0..d) d
* a[i] = Σj=[0..d) c[j] a[i-1-j] (∀i∈[d..n))
*/
vm berlekamp_massey(const vm& a) {
// : https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Massey_algorithm
// verify : https://judge.yosupo.jp/problem/find_linear_recurrence
MFPS S(a), C(1), B(1);
int N = sz(a), m = 1; mint b = 1;
rep(n, N) {
mint d = 0;
rep(i, sz(C)) d += C[i] * S[n - i];
if (d == 0) {
m++;
}
else if (2 * C.deg() <= n) {
MFPS T(C);
C -= d * b.inv() * (B >> m);
B = T;
b = d;
m = 1;
}
else {
C -= d * b.inv() * (B >> m);
m++;
}
}
return (-C << 1).c;
}
//O(n m)
/*
* a[0..n) b[0..m) c[0..n+m-1)
* c[k] = Σ_(i+j=k) a[i] b[j]
*/
template <class T>
vector<T> naive_convolution(const vector<T>& a, const vector<T>& b) {
// verify : https://atcoder.jp/contests/abc214/tasks/abc214_g
int n = sz(a), m = sz(b);
if (n == 0 || m == 0) return vector<T>();
// c[k] = Σ_(i+j=k) a[i] b[j]
vector<T> c(n + m - 1);
rep(i, n) rep(j, m) c[i + j] += a[i] * b[j];
return c;
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
// zikken();
ll n; string s;
cin >> n >> s;
MFPS::set_conv(naive_convolution);
mint res = 0;
repb(set, 3) {
if (s[set] == '-') continue;
int N = 10;
vm a(N);
rep(n, N) {
repb(p, n) repb(q, n) {
int l = 0;
rep(i, n) {
if (get(p, i) == 0 && get(q, i) == 0 && get(set, 0) == 1) l += 1 << i;
else if (get(p, i) == 0 && get(q, i) == 1 && get(set, 1) == 1) l += 1 << i;
else if (get(p, i) == 1 && get(q, i) == 0 && get(set, 2) == 1) l += 1 << i;
}
int r = (1 << n) - 1 - l;
if (l > r) swap(l, r);
a[n] += r - l + 1;
}
}
auto c = berlekamp_massey(a);
int m = sz(c);
a.resize(m);
res += linearly_recurrent_sequence(a, c, n);
}
cout << res << endl;
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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0