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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#244496 | #4483. Count Set | ucup-team203# | AC ✓ | 2496ms | 38132kb | C++20 | 5.7kb | 2023-11-09 10:19:50 | 2023-11-09 10:19:50 |
Judging History
answer
#include <bits/stdc++.h>
using i64 = long long;
using namespace std;
const int N = 5e5 + 5;
// const int B = 400;
// const int M = 4e6 + 5;
// const int base = 15171;
// const int mod = 998244353;
// const i64 mod = (i64)1e18 + 7;
// const double pi = acos(-1);
const int P = 998244353;
using i64 = long long;
using Poly = vector<int>;
/*---------------------------------------------------------------------------*/
#define MUL(a, b) (i64(a) * (b) % P)
#define ADD(a, b) (((a) += (b)) >= P ? (a) -= P : 0) // (a += b) %= P
#define SUB(a, b) (((a) -= (b)) < 0 ? (a) += P : 0) // ((a -= b) += P) %= P
Poly getInv(int L)
{
Poly inv(L);
inv[1] = 1;
for (int i = 2; i < L; i++)
inv[i] = MUL((P - P / i), inv[P % i]);
return inv;
}
int POW(i64 a, int b = P - 2, i64 x = 1)
{
for (; b; b >>= 1, a = a * a % P)
if (b & 1)
x = x * a % P;
return x;
}
auto inv = getInv(N);
namespace NTT
{
const int g = 3;
Poly Omega(int L)
{
int wn = POW(g, P / L);
Poly w(L);
w[L >> 1] = 1;
for (int i = L / 2 + 1; i < L; i++)
w[i] = MUL(w[i - 1], wn);
for (int i = L / 2 - 1; i >= 1; i--)
w[i] = w[i << 1];
return w;
}
auto W = Omega(1 << 20); // Length
void DIF(int *a, int n)
{
for (int k = n >> 1; k; k >>= 1)
for (int i = 0, y; i < n; i += k << 1)
for (int j = 0; j < k; ++j)
y = a[i + j + k], a[i + j + k] = MUL(a[i + j] - y + P, W[k + j]), ADD(a[i + j], y);
}
void IDIT(int *a, int n)
{
for (int k = 1; k < n; k <<= 1)
for (int i = 0, x, y; i < n; i += k << 1)
for (int j = 0; j < k; ++j)
x = a[i + j], y = MUL(a[i + j + k], W[k + j]),
a[i + j + k] = x - y < 0 ? x - y + P : x - y, ADD(a[i + j], y);
int Inv = P - (P - 1) / n;
for (int i = 0; i < n; i++)
a[i] = MUL(a[i], Inv);
reverse(a + 1, a + n);
}
}
/*---------------------------------------------------------------------------*/
namespace Polynomial
{
// basic operator
int norm(int n) { return 1 << (__lg(n - 1) + 1); }
void norm(Poly &a)
{
if (!a.empty())
a.resize(norm(a.size()), 0);
else
a = {0};
}
void DFT(Poly &a) { NTT::DIF(a.data(), a.size()); }
void IDFT(Poly &a) { NTT::IDIT(a.data(), a.size()); }
Poly &dot(Poly &a, Poly &b)
{
for (int i = 0; i < a.size(); i++)
a[i] = MUL(a[i], b[i]);
return a;
}
// mul / div int
Poly &operator*=(Poly &a, int b)
{
for (auto &x : a)
x = MUL(x, b);
return a;
}
Poly operator*(Poly a, int b) { return a *= b; }
Poly operator*(int a, Poly b) { return b * a; }
Poly &operator/=(Poly &a, int b) { return a *= POW(b); }
Poly operator/(Poly a, int b) { return a /= b; }
// Poly add / sub
Poly &operator+=(Poly &a, Poly b)
{
a.resize(max(a.size(), b.size()));
for (int i = 0; i < b.size(); i++)
ADD(a[i], b[i]);
return a;
}
Poly operator+(Poly a, Poly b) { return a += b; }
Poly &operator-=(Poly &a, Poly b)
{
a.resize(max(a.size(), b.size()));
for (int i = 0; i < b.size(); i++)
SUB(a[i], b[i]);
return a;
}
Poly operator-(Poly a, Poly b) { return a -= b; }
// Poly mul
Poly operator*(Poly a, Poly b)
{
int n = a.size() + b.size() - 1, L = norm(n);
if (a.size() <= 8 || b.size() <= 8)
{
Poly c(n);
for (int i = 0; i < a.size(); i++)
for (int j = 0; j < b.size(); j++)
c[i + j] = (c[i + j] + (i64)a[i] * b[j]) % P;
return c;
}
a.resize(L), b.resize(L);
DFT(a), DFT(b), dot(a, b), IDFT(a);
return a.resize(n), a;
}
}
using namespace Polynomial;
int n, k, fa[N], siz[N], fac[N], ifac[N];
int binom(int x, int y)
{
if (x < 0 || y < 0 || x < y)
return 0;
return (i64)fac[x] * ifac[y] % P * ifac[x - y] % P;
}
int find(int x)
{
if (x == fa[x])
return x;
else
return fa[x] = find(fa[x]);
}
void merge(int x, int y)
{
int fx = find(x), fy = find(y);
if (fx ^ fy)
{
fa[fy] = fx;
siz[fx] += siz[fy];
}
}
void solve()
{
cin >> n >> k;
iota(fa + 1, fa + n + 1, 1);
fill(siz + 1, siz + n + 1, 1);
for (int i = 1, x; i <= n; i++)
cin >> x, merge(i, x);
vector<Poly> tmp;
for (int i = 1; i <= n; i++)
{
if (find(i) != i)
continue;
int cur = siz[i];
Poly f(min(n / 2 + 1, cur + 1));
for (int j = 0; j < f.size(); j++)
f[j] = (binom(cur - j, j) + binom(cur - j - 1, j - 1)) % P;
tmp.push_back(f);
}
auto solve = [&](auto &solve, int l, int r) -> Poly
{
if (l == r)
return tmp[l];
int mid = l + r >> 1;
return solve(solve, l, mid) * solve(solve, mid + 1, r);
};
auto res = solve(solve, 0, tmp.size() - 1);
res.resize(n + 1);
cout << res[k] << '\n';
}
signed main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
fac[0] = 1;
for (int i = 1; i < N; i++)
fac[i] = (i64)fac[i - 1] * i % P;
ifac[N - 1] = POW(fac[N - 1]);
for (int i = N - 2; i >= 0; i--)
ifac[i] = (i64)ifac[i + 1] * (i + 1) % P;
int t = 1;
cin >> t;
// cout << fixed << setprecision(10);
while (t--)
solve();
}
Details
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Test #1:
score: 100
Accepted
time: 2496ms
memory: 38132kb
input:
14 5 1 5 3 2 1 4 5 2 2 5 1 3 4 10 3 10 9 3 8 6 4 5 7 2 1 30 5 1 16 28 30 27 23 2 20 10 12 7 13 11 15 17 24 14 25 21 4 22 29 3 6 19 18 8 26 9 5 30 5 29 6 21 30 14 18 24 26 3 11 23 13 2 12 16 9 4 22 25 20 28 19 5 17 8 10 15 1 7 27 500000 200000 293510 102358 252396 467703 280403 93120 462332 442364 31...
output:
5 5 40 51129 51359 371836159 565197945 0 0 844811446 803690398 638630160 14371218 1
result:
ok 14 lines