QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#284774 | #6513. Expression 3 | jrjyy | TL | 4330ms | 413896kb | C++20 | 20.1kb | 2023-12-16 14:59:11 | 2023-12-16 14:59:12 |
Judging History
answer
#include <bits/stdc++.h>
using i64 = long long;
template <typename T>
constexpr T power(T a, i64 b) {
T c{1};
while (b) {
if (b % 2) {
c *= a;
}
a *= a;
b /= 2;
}
return c;
}
template <int P>
struct MInt {
int x;
constexpr MInt() : x{} {}
constexpr MInt(i64 x_) : x{up(x_ % getMod())} {}
static int Mod;
constexpr static int getMod() {
return P > 0 ? P : Mod;
}
constexpr static void setMod(int Mod_) {
Mod = Mod_;
}
constexpr int up(int x) const {
if (x < 0) {
x += getMod();
}
return x;
}
constexpr int down(int x) const {
if (x >= getMod()) {
x -= getMod();
}
return x;
}
constexpr int norm(int x) const {
return up(down(x));
}
constexpr int val() const {
return x;
}
explicit constexpr operator int() const {
return x;
}
constexpr MInt operator-() const {
MInt res;
res.x = norm(getMod() - x);
return res;
}
constexpr MInt inv() const {
assert(x != 0);
return power(*this, getMod() - 2);
}
constexpr MInt &operator+=(MInt rhs) {
x = down(x + rhs.x);
return *this;
}
constexpr MInt &operator-=(MInt rhs) {
x = up(x - rhs.x);
return *this;
}
constexpr MInt &operator*=(MInt rhs) {
x = 1ll * x * rhs.x % getMod();
return *this;
}
constexpr MInt &operator/=(MInt rhs) {
return *this *= rhs.inv();
}
friend constexpr MInt operator+(MInt lhs, MInt rhs) {
return lhs += rhs;
}
friend constexpr MInt operator-(MInt lhs, MInt rhs) {
return lhs -= rhs;
}
friend constexpr MInt operator*(MInt lhs, MInt rhs) {
return lhs *= rhs;
}
friend constexpr MInt operator/(MInt lhs, MInt rhs) {
return lhs /= rhs;
}
friend constexpr bool operator==(MInt lhs, MInt rhs) {
return lhs.val() == rhs.val();
}
friend constexpr bool operator!=(MInt lhs, MInt rhs) {
return lhs.val() != rhs.val();
}
friend constexpr std::istream &operator>>(std::istream &is, MInt &a) {
i64 x = 0;
is >> x;
a = MInt(x);
return is;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const MInt &a) {
return os << a.val();
}
};
template <int P>
int MInt<P>::Mod = P;
template <>
int MInt<0>::Mod = 998244353;
template <int V, int P>
constexpr MInt<P> CInv = MInt<P>(V).inv();
template <int P>
struct IComb {
using Z = MInt<P>;
int n;
std::vector<Z> fac_, ifac_, inv_;
IComb() : n(0), fac_{1}, ifac_{1}, inv_{0} {}
IComb(int n) : IComb{} {
init(n);
}
void init(int m) {
if (m <= n) {
return;
}
assert(m < Z::getMod());
fac_.resize(m + 1);
ifac_.resize(m + 1);
inv_.resize(m + 1);
for (int i = n + 1; i <= m; ++i) {
fac_[i] = fac_[i - 1] * i;
}
ifac_[m] = fac_[m].inv();
for (int i = m; i > n + 1; --i) {
ifac_[i - 1] = ifac_[i] * i;
}
for (int i = m; i > n; --i) {
inv_[i] = ifac_[i] * fac_[i - 1];
}
n = m;
}
Z fac(int m) {
if (n < m) {
init(2 * m);
}
return fac_[m];
}
Z ifac(int m) {
if (n < m) {
init(2 * m);
}
return ifac_[m];
}
Z inv(int m) {
if (n < m) {
init(2 * m);
}
return inv_[m];
}
Z binom(int n, int m) {
if (n < m || m < 0) {
return Z{};
}
return fac(n) * ifac(m) * ifac(n - m);
}
};
template <int P>
IComb<P> icomb;
template <int P>
struct IComplexZ {
using Z = MInt<P>;
static Z i2;
Z a, b;
IComplexZ(Z a_ = 1) : IComplexZ(a_, 0) {}
IComplexZ(Z a_, Z b_) : a(a_), b(b_) {}
IComplexZ &operator*=(const IComplexZ &y) {
*this = IComplexZ(a * y.a + i2 * b * y.b, a * y.b + b * y.a);
return *this;
}
};
template <int P>
typename IComplexZ<P>::Z IComplexZ<P>::i2;
template <int P>
std::vector<MInt<P>> sqrtMod(MInt<P> n) {
static std::mt19937 rnd(std::random_device{}());
if (n == 0) {
return {0};
}
if (P == 2) {
return {1};
}
if (power(n, (P - 1) / 2) != 1) {
return {};
}
MInt<P> a;
do {
a = rnd() % (P - 1) + 1;
} while (power(a * a - n, (P - 1) / 2) == 1);
IComplexZ<P>::i2 = a * a - n;
MInt<P> x = power(IComplexZ<P>(a, 1), (P + 1) / 2).a, y = P - x;
if (x.val() > y.val()) {
std::swap(x, y);
}
if (x == y) {
return {x};
}
return {x, y};
}
namespace Polynomial {
constexpr int bitceil(int x) {
assert(x >= 0);
return x <= 1 ? 1 : 2 << std::__lg(x - 1);
}
template <int P>
std::vector<MInt<P>> roots{1};
template <int P>
constexpr MInt<P> findPrimitiveRoot() {
for (MInt<P> i = 2;; i += 1) {
if (power(i, (P - 1) / 2) != 1) {
return power(i, (P - 1) >> std::__lg(P - 1));
}
}
}
template <int P>
constexpr MInt<P> primitiveRoot = findPrimitiveRoot<P>();
template <int P>
void initRoots(int n) {
assert((n & -n) == n && ((P - 1) & (n - 1)) == 0);
if (int(roots<P>.size()) >= n) {
return;
}
roots<P>.reserve(n);
while (int(roots<P>.size()) < n) {
int l = int(roots<P>.size());
roots<P>.resize(2 * l);
auto w = roots<P>.begin() + l;
w[0] = 1;
MInt<P> x = power(primitiveRoot<P>, (P - 1) / l / 2);
for (int i = 1; i < l; ++i) {
w[i] = w[i - 1] * x;
}
}
}
template <int P>
inline void applyDft(int &x, int &y, int w) {
int t = x - y;
x = x + y;
if (x >= P) {
x -= P;
}
y = 1ll * t * w % P;
if (y < 0) {
y += P;
}
}
template <int P>
inline void applyIdft(int &x, int &y, int w) {
int t = 1ll * y * w % P;
y = x - t;
if (y < 0) {
y += P;
}
x = x + t;
if (x >= P) {
x -= P;
}
}
template <int P, void F(int &x, int &y, int w)>
inline void applyTrans(std::vector<MInt<P>> &a, int l) {
for (auto p = a.begin(), q = p + 2 * l; p != a.end(); p = q, q += 2 * l) {
for (auto i = p, j = p + l, w = roots<P>.begin() + l; j != q; ++i, ++j, ++w) {
F(i->x, j->x, w->x);
}
}
}
template <int P>
void dft(std::vector<MInt<P>> &a) {
const int n = int(a.size());
initRoots<P>(n);
for (int l = n / 2; l; l /= 2) {
applyTrans<P, applyDft<P>>(a, l);
}
}
template <int P>
void idft(std::vector<MInt<P>> &a) {
const int n = int(a.size());
initRoots<P>(n);
for (int l = 1; l < n; l *= 2) {
applyTrans<P, applyIdft<P>>(a, l);
}
std::reverse(std::next(a.begin()), a.end());
MInt<P> c = (1 - P) / n;
for (auto &x : a) {
x *= c;
}
}
template <int P>
struct IPoly : public std::vector<MInt<P>> {
using Z = MInt<P>;
IPoly() = default;
explicit IPoly(std::size_t n) : std::vector<Z>(n) {}
explicit IPoly(const std::vector<Z> &a) : std::vector<Z>{a} {}
IPoly(std::initializer_list<Z> a) : std::vector<Z>{a} {}
template <typename InputIt, typename = std::_RequireInputIter<InputIt>>
explicit IPoly(InputIt first, InputIt last) : std::vector<Z>(first, last) {}
template <typename F>
explicit IPoly(std::size_t n, F &&f) : IPoly(n) {
std::generate(this->begin(), this->end(), [&, i = 0]() mutable {
return f(i++);
});
}
IPoly shift(int k) const {
if (k >= 0) {
auto f = *this;
f.insert(f.begin(), k, 0);
return f;
} else if (int(this->size()) <= -k) {
return IPoly{};
} else {
return IPoly(this->begin() + -k, this->end());
}
}
IPoly trunc(int k) const {
if (k < int(this->size())) {
return IPoly(this->begin(), this->begin() + k);
} else {
auto f = *this;
f.resize(k);
return f;
}
}
Z get(int p) const {
if (p < 0 || int(this->size()) <= p) {
return 0;
}
return (*this)[p];
}
friend IPoly operator+(const IPoly &a, const IPoly &b) {
IPoly c(std::max(a.size(), b.size()));
for (int i = 0; i < int(c.size()); ++i) {
c[i] = a.get(i) + b.get(i);
}
return c;
}
friend IPoly operator-(const IPoly &a, const IPoly &b) {
IPoly c(std::max(a.size(), b.size()));
for (int i = 0; i < int(c.size()); ++i) {
c[i] = a.get(i) - b.get(i);
}
return c;
}
friend IPoly operator-(const IPoly &a) {
IPoly c(a.size());
for (int i = 0; i < int(a.size()); ++i) {
c[i] = -a[i];
}
return c;
}
friend IPoly operator*(const IPoly &f, const IPoly &g) {
static IPoly a, b;
if (f.empty() || g.empty()) {
return IPoly{};
}
int n = int(f.size()) + int(g.size()) - 1, len = bitceil(n);
if (n <= 128) {
IPoly c(n);
for (int i = 0; i < int(f.size()); ++i) {
for (int j = 0; j < int(g.size()); ++j) {
c[i + j] += f[i] * g[j];
}
}
return c;
}
bool eq = f == g;
a.resize(len);
std::copy(f.begin(), f.end(), a.begin());
std::fill(a.begin() + f.size(), a.end(), 0);
if (!eq) {
b.resize(len);
std::copy(g.begin(), g.end(), b.begin());
std::fill(b.begin() + g.size(), b.end(), 0);
}
assert(((P - 1) & (len - 1)) == 0);
dft(a);
if (eq) {
for (int i = 0; i < len; ++i) {
a[i] *= a[i];
}
} else {
dft(b);
for (int i = 0; i < len; ++i) {
a[i] *= b[i];
}
}
idft(a), a.resize(n);
return a;
}
friend IPoly operator*(IPoly a, Z b) {
for (int i = 0; i < int(a.size()); ++i) {
a[i] *= b;
}
return a;
}
friend IPoly operator*(Z a, const IPoly &b) {
return b * a;
}
friend IPoly operator/(IPoly a, Z b) {
return a * b.inv();
}
IPoly &operator+=(const IPoly &b) {
return *this = *this + b;
}
IPoly &operator-=(const IPoly &b) {
return *this = *this - b;
}
IPoly &operator*=(const IPoly &b) {
return *this = *this * b;
}
IPoly &operator*=(Z b) {
return *this = *this * b;
}
IPoly &operator/=(Z b) {
return *this = *this / b;
}
IPoly deriv() const {
if (this->empty()) {
return IPoly{};
}
IPoly f(this->size() - 1);
for (int i = 1; i < int(this->size()); ++i) {
f[i - 1] = (*this)[i] * i;
}
return f;
}
IPoly integr() const {
IPoly f(this->size() + 1);
icomb<P>.init(int(this->size()));
for (int i = 0; i < int(this->size()); ++i) {
f[i + 1] = (*this)[i] * icomb<P>.inv_[i + 1];
}
return f;
}
IPoly inv() const {
static IPoly a, b;
assert(!this->empty());
int len = bitceil(int(this->size()));
IPoly res{this->front().inv()};
res.resize(len);
a.reserve(len), b.reserve(len);
for (int l = 2; l <= len; l *= 2) {
a.resize(l);
std::copy(this->begin(), this->begin() + std::min(l, int(this->size())), a.begin());
dft(a);
b.resize(l);
std::copy(res.begin(), res.begin() + l, b.begin());
dft(b);
for (int i = 0; i < l; ++i) {
a[i] *= b[i];
}
idft(a);
std::fill(a.begin(), a.begin() + l / 2, 0);
dft(a);
for (int i = 0; i < l; ++i) {
a[i] *= -b[i];
}
idft(a);
std::copy(a.begin() + l / 2, a.end(), res.begin() + l / 2);
}
return res.trunc(int(this->size()));
}
IPoly log() const {
assert(!this->empty() && this->front() == 1);
return (deriv() * inv()).trunc(int(this->size()) - 1).integr();
}
template <typename F>
IPoly semiRelaxedConv(F &&relax) const {
static constexpr int Block = 64;
static IPoly a;
assert((Block & (Block - 1)) == 0);
int len = bitceil(int(this->size()));
IPoly res(len);
std::vector<IPoly> d(std::__lg(len));
a.reserve(len);
auto next = [&](int m) {
int l = m & -m;
if (l < Block) {
for (int i = m & -Block; i < m; ++i) {
res[m] += res[i] * (*this)[m - i];
}
} else {
a.resize(2 * l);
std::copy(res.begin() + m - l, res.begin() + m, a.begin());
std::fill(a.begin() + l, a.end(), 0);
dft(a);
auto &b = d[std::__lg(l)];
if (b.empty()) {
b = trunc(2 * l);
dft(b);
}
for (int i = 0; i < 2 * l; ++i) {
a[i] *= b[i];
}
idft(a);
for (int i = m; i < m + l; ++i) {
res[i] += a[i - m + l];
}
}
res[m] = relax(m, res[m]);
};
for (int i = 0; i < int(this->size()); ++i) {
next(i);
}
return res.trunc(int(this->size()));
}
IPoly exp() const {
assert(!this->empty() && this->front() == 0);
icomb<P>.init(int(this->size()));
return deriv().shift(1).semiRelaxedConv([&inv = icomb<P>.inv_](int p, Z x) {
return p == 0 ? 1 : x * inv[p];
});
}
IPoly pow(i64 k) const {
if (k == 0) {
return IPoly{1}.trunc(int(this->size()));
}
int i = std::find_if(this->begin(), this->end(), [](Z x) {
return x != 0;
}) - this->begin();
if (i >= (int(this->size()) - 1) / k + 1) {
return IPoly(int(this->size()));
}
Z x = (*this)[i];
auto f = shift(-i).trunc(int(this->size()) - i * k) / x;
return (f.log() * k).exp().shift(i * k) * power(x, k);
}
IPoly sqrt() const {
int i = std::find_if(this->begin(), this->end(), [](Z x) {
return x != 0;
}) - this->begin();
if (i == int(this->size())) {
return IPoly(this->size());
}
if (i % 2) {
return IPoly{};
}
auto f = shift(-i);
auto sq = sqrtMod(f.front());
if (sq.empty()) {
return IPoly{};
}
IPoly g{sq.front()};
int k = 1;
while (k < int(this->size())) {
k *= 2;
g = (g + (f.trunc(k) * g.trunc(k).inv()).trunc(k)) * CInv<2, P>;
}
return g.trunc(int(this->size()) - i / 2).shift(i / 2);
}
std::vector<Z> eval(std::vector<Z> x) const {
if (this->empty()) {
return std::vector<Z>(x.size());
}
std::vector<Z> ans(x.size());
const int n = int(std::max(x.size(), this->size()));
std::vector<IPoly> s(n << 2);
auto init = [&](auto self, int u, int l, int r) -> void {
s[u].reserve(bitceil(r - l));
if (r - l == 1) {
return;
}
int m = (l + r) / 2;
self(self, u << 1, l, m);
self(self, u << 1 | 1, m, r);
};
init(init, 1, 0, n);
x.resize(n);
auto build = [&](auto self, int u, int l, int r) -> void {
if (r - l == 1) {
s[u] = IPoly{1, -x[l]};
return;
}
int m = (l + r) / 2;
self(self, u << 1, l, m);
self(self, u << 1 | 1, m, r);
s[u] = s[u << 1] * s[u << 1 | 1];
};
build(build, 1, 0, n);
auto mulT = [&](const IPoly &a, IPoly b) {
if (b.empty()) {
return IPoly{};
}
int n = int(b.size());
std::reverse(b.begin(), b.end());
b.resize(a.size());
dft(b);
for (int i = 0; i < int(a.size()); ++i) {
b[i] *= a[i];
}
idft(b);
return b.shift(-(n - 1));
};
auto work = [&](auto self, int u, int l, int r, IPoly v) -> void {
v.resize(r - l);
if (r - l == 1) {
if (l < int(ans.size())) {
ans[l] = v[0];
}
return;
}
int m = (l + r) / 2;
v.resize(bitceil(v.size()));
dft(v);
self(self, u << 1, l, m, mulT(v, s[u << 1 | 1]));
self(self, u << 1 | 1, m, r, mulT(v, s[u << 1]));
};
auto d = *this;
d.resize(bitceil(d.size() + n + 1));
dft(d);
work(work, 1, 0, n, mulT(d, s[1].inv()));
return ans;
}
};
} // namespace Polynomial
using Polynomial::IPoly;
namespace MTT {
constexpr int M[3] = {167772161, 469762049, 998244353};
constexpr i64 M01 = 1ll * M[0] * M[1];
constexpr MInt<M[1]> inv0_1 = MInt<M[1]>(M[0]).inv();
constexpr MInt<M[2]> inv1_2 = MInt<M[2]>(M01).inv();
using Poly = std::vector<int>;
inline int CRT(int a, int b, int c, const int P) {
i64 d = 1ll * ((b - a) * inv0_1).val() * M[0] + a;
return (1ll * ((c - d) * inv1_2).val() * (M01 % P) % P + d) % P;
}
Poly convolution(const Poly &f, const Poly &g, const int P) {
auto res0 = IPoly<M[0]>(f.begin(), f.end()) * IPoly<M[0]>(g.begin(), g.end());
auto res1 = IPoly<M[1]>(f.begin(), f.end()) * IPoly<M[1]>(g.begin(), g.end());
auto res2 = IPoly<M[2]>(f.begin(), f.end()) * IPoly<M[2]>(g.begin(), g.end());
Poly res(f.size() + g.size() - 1);
for (int i = 0; i < int(res.size()); ++i) {
res[i] = CRT(res0[i].val(), res1[i].val(), res2[i].val(), P);
}
return res;
}
} // namespace MTT
constexpr int P = 998244353;
using Z = MInt<P>;
using Comb = IComb<P>;
using Poly = IPoly<P>;
#define comb icomb<P>
constexpr Z G = Polynomial::primitiveRoot<P>;
std::vector<int> getLog(int n) {
const int B = std::sqrt(P / n);
std::unordered_map<int, int> mp;
Z x = 1, coef = power(G, B);
for (int i = 0; i <= P / B + 1; ++i) {
mp[x.val()] = i * B;
x *= coef;
}
std::vector<int> lg(n + 1);
for (int a = 1; a <= n; ++a) {
Z x = a, coef = CInv<G.val(), P>;
for (int i = 0; i <= B; ++i) {
if (mp.count(x.val())) {
lg[a] = i + mp[x.val()];
break;
}
x *= coef;
}
}
return lg;
}
int main() {
std::cin.tie(nullptr)->sync_with_stdio(false);
int n;
std::cin >> n;
std::vector<Z> a(n);
for (int i = 0; i < n; ++i) {
std::cin >> a[i];
}
std::string s;
std::cin >> s;
auto lg = getLog(n - 1);
std::vector<int> cnt(n + 2);
for (int i = 0; i < n; ++i) {
cnt[i + 1 - (s[i] == '+' ? 1 : -1)] += 1;
}
auto f = MTT::convolution(lg, cnt, P - 1);
Z ans = 0;
for (int i = 1; i < n; ++i) {
Z res = a[i] * comb.ifac(i) * (s[i - 1] == '+' ? 1 : -1) * power(G, f[i]);
if (i >= 2 && s[i - 2] != '+') {
res = 0;
}
ans += res;
}
ans = (ans + a[0]) * comb.fac(n - 1);
std::cout << ans << "\n";
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 2ms
memory: 5816kb
input:
4 9 1 4 1 -+-
output:
46
result:
ok 1 number(s): "46"
Test #2:
score: 0
Accepted
time: 6ms
memory: 5760kb
input:
5 1 2 3 4 5 +-+-
output:
998244313
result:
ok 1 number(s): "998244313"
Test #3:
score: 0
Accepted
time: 4330ms
memory: 413896kb
input:
100000 664815434 205025136 871445392 797947979 379688564 336946672 231295524 401655676 526374414 670533644 156882283 372427821 700299596 166140732 677498490 44858761 185182210 559696133 813911251 842364231 681916958 114039865 222372111 784286397 437994571 152137641 650875922 613727135 209302742 5321...
output:
178167352
result:
ok 1 number(s): "178167352"
Test #4:
score: -100
Time Limit Exceeded
input:
200000 109044620 745578941 396599814 756923982 940933214 875346257 378089839 792684563 491924893 782192923 208569108 421583135 814903710 690275542 15773609 364566266 12890134 661702679 640270667 615999192 13352194 325560419 385152885 265008089 570536451 282429805 331946208 255056541 813809151 150995...