結果
| 問題 |
No.1621 Sequence Inversions
|
| コンテスト | |
| ユーザー |
 torisasami4
|
| 提出日時 | 2021-07-22 22:42:25 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 248 ms / 3,000 ms |
| コード長 | 8,467 bytes |
| コンパイル時間 | 2,086 ms |
| コンパイル使用メモリ | 189,808 KB |
| 実行使用メモリ | 200,704 KB |
| 最終ジャッジ日時 | 2024-07-17 19:01:46 |
| 合計ジャッジ時間 | 5,068 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 26 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb(x) push_back(x)
#define mp(a, b) make_pair(a, b)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define lscan(x) scanf("%I64d", &x)
#define lprint(x) printf("%I64d", x)
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define rep2(i, n) for (ll i = (ll)n - 1; i >= 0; i--)
#define REP(i, l, r) for (ll i = l; i < (r); i++)
#define REP2(i, l, r) for (ll i = (ll)r - 1; i >= (l); i--)
#define siz(x) (ll)x.size()
template <class T>
using rque = priority_queue<T, vector<T>, greater<T>>;
const ll mod = 998244353;
template <class T>
bool chmin(T &a, const T &b) {
if (b < a) {
a = b;
return 1;
}
return 0;
}
template <class T>
bool chmax(T &a, const T &b) {
if (b > a) {
a = b;
return 1;
}
return 0;
}
ll gcd(ll a, ll b)
{
if(a == 0)
return b;
if(b == 0)
return a;
ll cnt = a % b;
while (cnt != 0)
{
a = b;
b = cnt;
cnt = a % b;
}
return b;
}
long long extGCD(long long a, long long b, long long &x, long long &y)
{
if (b == 0)
{
x = 1;
y = 0;
return a;
}
long long d = extGCD(b, a % b, y, x);
y -= a / b * x;
return d;
}
struct UnionFind
{
vector<ll> data;
int num;
UnionFind(int sz)
{
data.assign(sz, -1);
num = sz;
}
bool unite(int x, int y)
{
x = find(x), y = find(y);
if (x == y)
return (false);
if (data[x] > data[y])
swap(x, y);
data[x] += data[y];
data[y] = x;
num--;
return (true);
}
int find(int k)
{
if (data[k] < 0)
return (k);
return (data[k] = find(data[k]));
}
ll size(int k)
{
return (-data[find(k)]);
}
bool same(int x, int y){
return find(x) == find(y);
}
};
ll M = 1000000007;
template <int mod>
struct ModInt
{
int x;
ModInt() : x(0) {}
ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
ModInt &operator+=(const ModInt &p)
{
if ((x += p.x) >= mod)
x -= mod;
return *this;
}
ModInt &operator-=(const ModInt &p)
{
if ((x += mod - p.x) >= mod)
x -= mod;
return *this;
}
ModInt &operator*=(const ModInt &p)
{
x = (int)(1LL * x * p.x % mod);
return *this;
}
ModInt &operator/=(const ModInt &p)
{
*this *= p.inverse();
return *this;
}
ModInt operator-() const { return ModInt(-x); }
ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
bool operator==(const ModInt &p) const { return x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inverse() const
{
int a = x, b = mod, u = 1, v = 0, t;
while (b > 0)
{
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return ModInt(u);
}
ModInt pow(int64_t n) const
{
ModInt ret(1), mul(x);
while (n > 0)
{
if (n & 1)
ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const ModInt &p)
{
return os << p.x;
}
friend istream &operator>>(istream &is, ModInt &a)
{
int64_t t;
is >> t;
a = ModInt<mod>(t);
return (is);
}
static int get_mod() { return mod; }
};
using mint = ModInt<mod>;
mint mpow(mint x, ll n)
{
mint ans = 1;
while (n != 0)
{
if (n & 1)
ans *= x;
x *= x;
n = n >> 1;
}
return ans;
}
ll mpow2(ll x, ll n, ll mod)
{
ll ans = 1;
while (n != 0)
{
if (n & 1)
ans = ans * x % mod;
x = x * x % mod;
n = n >> 1;
}
return ans;
}
vector<mint> fac;
vector<mint> ifac;
void setcomb(int sz = 2000010)
{
fac.assign(sz + 1, 0);
ifac.assign(sz + 1, 0);
fac[0] = 1;
for (ll i = 0; i < sz; i++)
{
fac[i + 1] = fac[i] * (i + 1); // n!(mod M)
}
ifac[sz] = fac[sz].inverse();
for (ll i = sz; i > 0; i--)
{
ifac[i - 1] = ifac[i] * i;
}
}
mint comb(ll a, ll b)
{
if(fac.size() == 0)
setcomb();
if (a == 0 && b == 0)
return 1;
if (a < b || a < 0 || b < 0)
return 0;
return ifac[a - b] * ifac[b] * fac[a];
}
mint perm(ll a, ll b)
{
if(fac.size() == 0)
setcomb();
if (a == 0 && b == 0)
return 1;
if (a < b || a < 0)
return 0;
return fac[a] * ifac[a - b];
}
long long modinv(long long a)
{
long long b = M, u = 1, v = 0;
while (b)
{
long long t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
u %= M;
if (u < 0)
u += M;
return u;
}
ll modinv2(ll a, ll mod)
{
ll b = mod, u = 1, v = 0;
while (b)
{
ll t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
u %= mod;
if (u < 0)
u += mod;
return u;
}
template <int mod>
struct NumberTheoreticTransform
{
vector<int> rev, rts;
int base, max_base, root;
NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1}
{
assert(mod >= 3 && mod % 2 == 1);
auto tmp = mod - 1;
max_base = 0;
while (tmp % 2 == 0)
tmp >>= 1, max_base++;
root = 2;
while (mod_pow(root, (mod - 1) >> 1) == 1)
++root;
assert(mod_pow(root, mod - 1) == 1);
root = mod_pow(root, (mod - 1) >> max_base);
}
inline int mod_pow(int x, int n)
{
int ret = 1;
while (n > 0)
{
if (n & 1)
ret = mul(ret, x);
x = mul(x, x);
n >>= 1;
}
return ret;
}
inline int inverse(int x)
{
return mod_pow(x, mod - 2);
}
inline unsigned add(unsigned x, unsigned y)
{
x += y;
if (x >= mod)
x -= mod;
return x;
}
inline unsigned mul(unsigned a, unsigned b)
{
return 1ull * a * b % (unsigned long long)mod;
}
void ensure_base(int nbase)
{
if (nbase <= base)
return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for (int i = 0; i < (1 << nbase); i++)
{
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
assert(nbase <= max_base);
while (base < nbase)
{
int z = mod_pow(root, 1 << (max_base - 1 - base));
for (int i = 1 << (base - 1); i < (1 << base); i++)
{
rts[i << 1] = rts[i];
rts[(i << 1) + 1] = mul(rts[i], z);
}
++base;
}
}
void ntt(vector<mint> &a)
{
const int n = (int)a.size();
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for (int i = 0; i < n; i++)
{
if (i < (rev[i] >> shift))
{
swap(a[i], a[rev[i] >> shift]);
}
}
for (int k = 1; k < n; k <<= 1)
{
for (int i = 0; i < n; i += 2 * k)
{
for (int j = 0; j < k; j++)
{
mint z = a[i + j + k] * rts[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
vector<mint> multiply(vector<mint> a, vector<mint> b)
{
int need = a.size() + b.size() - 1;
int nbase = 1;
while ((1 << nbase) < need)
nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
a.resize(sz, 0);
b.resize(sz, 0);
ntt(a);
ntt(b);
mint inv_sz = inverse(sz);
for (int i = 0; i < sz; i++)
{
a[i] = a[i] * b[i] * inv_sz;
}
reverse(a.begin() + 1, a.end());
ntt(a);
a.resize(need);
return a;
}
};
using NTT = NumberTheoreticTransform<mod>;
int main(){
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
ll n, k;
cin >> n >> k;
ll a[n];
rep(i, n) cin >> a[i];
map<ll, ll> cnt;
rep(i, n) cnt[a[i]]++;
mint dp[n + 1][k + 1][n + 1] = {};
rep(t, n + 1) dp[0][0][t] = 1;
REP(i,1,n+1)rep(j,k+1)rep(t,n+1){
if(j == 0){
dp[i][j][t] = 1;
continue;
}
if(t == 0)
continue;
dp[i][j][t] = dp[i][j][t - 1];
if(j >= t)
dp[i][j][t] += dp[i - 1][j - t][t];
}
NTT ntt;
vector<mint> d(1, 1);
ll sum = 0;
for(auto e: cnt){
ll ncnt = e.second;
vector<mint> nd(min(k, sum * ncnt) + 1);
rep(i, nd.size()) nd[i] = dp[ncnt][i][sum];
d = ntt.multiply(d, nd);
sum += ncnt;
}
cout << (d.size() > k ? d[k] : 0) << endl;
}