結果
| 問題 |
No.563 超高速一人かるた large
|
| コンテスト | |
| ユーザー |
 chocorusk
|
| 提出日時 | 2019-09-05 18:16:23 |
| 言語 | C++11（廃止可能性あり） (gcc 13.3.0) |
| 結果 |
AC
|
| 実行時間 | 64 ms / 3,000 ms |
| コード長 | 7,958 bytes |
| コンパイル時間 | 2,650 ms |
| コンパイル使用メモリ | 119,864 KB |
| 実行使用メモリ | 58,112 KB |
| 最終ジャッジ日時 | 2024-06-11 22:54:04 |
| 合計ジャッジ時間 | 2,811 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 18 |
ソースコード
#include <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <cassert>
#include <fstream>
#include <utility>
#include <functional>
#define popcount __builtin_popcount
using namespace std;
typedef long long int ll;
typedef pair<int, int> P;
const ll MOD=1e9+7;
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 modint = ModInt< MOD >;
namespace FastFourierTransform {
using real = double;
struct C {
real x, y;
C() : x(0), y(0) {}
C(real x, real y) : x(x), y(y) {}
inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }
inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }
inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }
inline C conj() const { return C(x, -y); }
};
const real PI = acosl(-1);
int base = 1;
vector< C > rts = { {0, 0},
{1, 0} };
vector< int > rev = {0, 1};
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));
}
while(base < nbase) {
real angle = PI * 2.0 / (1 << (base + 1));
for(int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
real angle_i = angle * (2 * i + 1 - (1 << base));
rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
}
++base;
}
}
void fft(vector< C > &a, int n) {
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++) {
C z = a[i + j + k] * rts[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {
int need = (int) a.size() + (int) b.size() - 1;
int nbase = 1;
while((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
vector< C > fa(sz);
for(int i = 0; i < sz; i++) {
int x = (i < (int) a.size() ? a[i] : 0);
int y = (i < (int) b.size() ? b[i] : 0);
fa[i] = C(x, y);
}
fft(fa, sz);
C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
for(int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
fa[i] = z;
}
for(int i = 0; i < (sz >> 1); i++) {
C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
fa[i] = A0 + A1 * s;
}
fft(fa, sz >> 1);
vector< int64_t > ret(need);
for(int i = 0; i < need; i++) {
ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
}
return ret;
}
};
template< typename T >
struct ArbitraryModConvolution {
using real = FastFourierTransform::real;
using C = FastFourierTransform::C;
ArbitraryModConvolution() = default;
vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {
if(need == -1) need = a.size() + b.size() - 1;
int nbase = 0;
while((1 << nbase) < need) nbase++;
FastFourierTransform::ensure_base(nbase);
int sz = 1 << nbase;
vector< C > fa(sz);
for(int i = 0; i < a.size(); i++) {
fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);
}
fft(fa, sz);
vector< C > fb(sz);
if(a == b) {
fb = fa;
} else {
for(int i = 0; i < b.size(); i++) {
fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);
}
fft(fb, sz);
}
real ratio = 0.25 / sz;
C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
for(int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C a1 = (fa[i] + fa[j].conj());
C a2 = (fa[i] - fa[j].conj()) * r2;
C b1 = (fb[i] + fb[j].conj()) * r3;
C b2 = (fb[i] - fb[j].conj()) * r4;
if(i != j) {
C c1 = (fa[j] + fa[i].conj());
C c2 = (fa[j] - fa[i].conj()) * r2;
C d1 = (fb[j] + fb[i].conj()) * r3;
C d2 = (fb[j] - fb[i].conj()) * r4;
fa[i] = c1 * d1 + c2 * d2 * r5;
fb[i] = c1 * d2 + c2 * d1;
}
fa[j] = a1 * b1 + a2 * b2 * r5;
fb[j] = a1 * b2 + a2 * b1;
}
fft(fa, sz);
fft(fb, sz);
vector< T > ret(need);
for(int i = 0; i < need; i++) {
int64_t aa = llround(fa[i].x);
int64_t bb = llround(fb[i].x);
int64_t cc = llround(fa[i].y);
aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
ret[i] = aa + (bb << 15) + (cc << 30);
}
return ret;
}
};
modint f[200020], invf[200020];
void fac(int n){
f[0]=1;
for(ll i=1; i<=n; i++) f[i]=f[i-1]*modint(i);
invf[n]=modint(1)/f[n];
for(ll i=n-1; i>=0; i--) invf[i]=invf[i+1]*modint(i+1);
}
modint comb(int x, int y){
if(!(0<=y && y<=x)) return 0;
return f[x]*invf[y]*invf[x-y];
}
struct node{
node* nxt[27];
int cnt;
bool exist;
node(){
fill(nxt, nxt+27, nullptr);
cnt=0;
exist=0;
}
};
void add(node* t, string p){
node* t0=t;
for(int i=0; i<p.size(); i++){
if(!t0->nxt[p[i]-'a']){
t0->nxt[p[i]-'a']=new node();
}
t0=t0->nxt[p[i]-'a'];
t0->cnt++;
}
t0->exist=1;
}
int n;
vector<modint> a, b;
void dfs(node* t, int d){
if(!t) return;
int x=t->cnt;
if(t->exist) a[x]+=modint(d);
else a[x]-=1;
for(int i=0; i<=26; i++){
if(!t->nxt[i]) continue;
dfs(t->nxt[i], d+1);
}
}
int main()
{
cin>>n;
node t;
int m=0;
for(int i=0; i<n; i++){
string s;
cin>>s;
s+='a'+26;
m=max(m, (int)s.size());
add(&t, s);
}
a.resize(n+1);
fac(n);
dfs(&t, 0);
a[0]=0;
for(int i=1; i<=n; i++) a[i]*=f[n-i];
b.resize(n+1);
for(int i=0; i<=n; i++) b[i]=invf[i];
ArbitraryModConvolution<modint> fft;
vector<modint> p=fft.multiply(a, b);
for(int i=1; i<=n; i++){
cout<<p[i]*f[i]*invf[n-i]<<endl;
}
return 0;
}