結果

問題 No.1978 Permutation Repetition
ユーザー milanis48663220milanis48663220
提出日時 2022-06-10 23:32:28
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 6,943 bytes
コンパイル時間 1,628 ms
コンパイル使用メモリ 125,828 KB
最終ジャッジ日時 2025-01-29 20:21:38
ジャッジサーバーID
(参考情報)
judge4 / judge3
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 * 35 WA * 9
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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

#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>
#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
using namespace std;
typedef long long ll;
template<typename T>
vector<vector<T>> vec2d(int n, int m, T v){
return vector<vector<T>>(n, vector<T>(m, v));
}
template<typename T>
vector<vector<vector<T>>> vec3d(int n, int m, int k, T v){
return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
}
template<typename T>
void print_vector(vector<T> v, char delimiter=' '){
if(v.empty()) {
cout << endl;
return;
}
for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter;
cout << v.back() << endl;
}
const ll MOD = 1000000007;
class ModInt{
public:
ll v;
ModInt(ll _v = 0){
if(_v < 0) _v = (_v%MOD)+MOD;
if(_v >= MOD) _v %= MOD;
v = _v;
}
ModInt operator+(ll n){
return ModInt((v+n)%MOD);
}
ModInt operator-(ll n){
return ModInt((v-n+MOD)%MOD);
}
ModInt operator*(ll n){
if(n >= MOD) n %= MOD;
return ModInt((v*n)%MOD);
}
ModInt operator/(ll n){
return ModInt((ModInt(n).inv()*v).v%MOD);
}
ModInt &operator+=(ll n){
v = (v+n)%MOD;
return *this;
}
ModInt &operator-=(ll n){
v = (v-n+MOD)%MOD;
return *this;
}
ModInt &operator*=(ll n){
v = (v*n+MOD)%MOD;
return *this;
}
ModInt operator+(ModInt n){
return ModInt((v+n.v)%MOD);
}
ModInt operator-(ModInt n){
return ModInt((v-n.v+MOD)%MOD);
}
ModInt operator*(ModInt n){
return ModInt((v*n.v)%MOD);
}
ModInt operator/(ModInt n){
return ModInt((n.inv()*v).v%MOD);
}
ModInt &operator+=(ModInt n){
v = (v+n.v)%MOD;
return *this;
}
ModInt &operator-=(ModInt n){
v = (v-n.v+MOD)%MOD;
return *this;
}
ModInt &operator*=(ModInt n){
v = (v*n.v)%MOD;
return *this;
}
bool operator==(ModInt n){
return v == n.v;
}
bool operator!=(ModInt n){
return v != n.v;
}
ModInt &operator=(ll n){
v = n%MOD;
return *this;
}
ModInt inv(){
if(v == 1) return ModInt(1);
else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD);
}
};
ostream& operator<<(ostream& os, const ModInt& m){
os << m.v;
return os;
}
istream & operator >> (istream &in, ModInt &m){
in >> m.v;
return in;
}
ModInt pow(ModInt a, ll n) {
assert(n >= 0);
ModInt ans = 1;
while (n > 0) {
if (n&1) ans = ans*a;
a = a*a;
n >>= 1;
}
return ans;
}
struct UnionFind {
vector<int> data;
UnionFind(int size) : data(size, -1) {}
bool unionSet(int x, int y) {
x = root(x); y = root(y);
if (x != y) {
if (data[y] < data[x]) swap(x, y);
data[x] += data[y]; data[y] = x;
}
return x != y;
}
bool findSet(int x, int y) {
return root(x) == root(y);
}
int root(int x) {
return data[x] < 0 ? x : data[x] = root(data[x]);
}
int size(int x) {
return -data[root(x)];
}
};
#define N_MAX 200002
ModInt inv[N_MAX],fac[N_MAX],finv[N_MAX];
void init(){
fac[0]=1;fac[1]=1;
finv[0]=1;finv[1]=1;
inv[1]=1;
for(int i=2;i<N_MAX;i++){
inv[i]=ModInt(MOD)-inv[MOD%i]*(MOD/i);
fac[i]=fac[i-1]*(ll) i;
finv[i]=finv[i-1]*inv[i];
}
}
ModInt comb(ll n, ll r){
if(n < r){
return ModInt(0);
}else{
return fac[n]*finv[r]*finv[n-r];
}
}
using mint = ModInt;
int naive(int n, int m, vector<int> a){
vector<int> p(n);
iota(p.begin(), p.end(), 0);
auto ok = [&](vector<int> p){
auto b = vector<int>(n);
iota(b.begin(), b.end(), 0);
for(int i = 0; i < m; i++){
for(int j = 0; j < n; j++){
b[j] = p[b[j]];
}
}
for(int i = 0; i < n; i++){
if(b[i] != a[i]) return false;
}
return true;
};
int ans = 0;
do{
if(ok(p)) {
// print_vector(p);
ans++;
}
}while(next_permutation(p.begin(), p.end()));
return ans;
}
mint solve(int n, int m, vector<int> a){
UnionFind uf(n);
for(int i = 0; i < n; i++) {
uf.unionSet(i, a[i]);
}
vector<int> cnt(n+1);
for(int i = 0; i < n; i++){
if(uf.root(i) != i) continue;
cnt[uf.size(i)]++;
}
mint ans = 1;
for(int x = 1; x <= n; x++) {
if(cnt[x] == 0) continue;
vector<mint> pattern(cnt[x]+1, 0);
for(int c = 1; c <= cnt[x]; c++){
int n_cycle = x*c;
if(x == 1){
if(m%n_cycle == 0) pattern[c] = fac[c-1].v;
continue;
}
if(m%n_cycle != 0){
int xx = m%n_cycle;
// debug_value(xx)
if(xx%c == 0){
int cc = xx/c;
if(gcd(cc, x) == 1) pattern[c] = 1;
}
}
}
auto dp = vec2d(cnt[x]+1, cnt[x]+1, mint(0));
// cout << x << ':';
// print_vector(pattern);
dp[0][0] = 1;
for(int c = 1; c <= cnt[x]; c++){
if(c >= 2){
pattern[c] *= pow(mint(x), c-1);
}
for(int j = 0; j <= cnt[x]; j++){
mint select = 1;
int rem = cnt[x]-j;
for(int k = 0; j+k*c <= cnt[x]; k++){
if(k > 0) select *= comb(rem, c)*pattern[c];
dp[c][j+k*c] += dp[c-1][j]*select*finv[k];
if(k > 0) rem -= c;
}
}
// print_vector(dp[c]);
}
// debug_value(cnt[x])
// debug_value(dp[cnt[x]][cnt[x]])
ans *= dp[cnt[x]][cnt[x]];
}
return ans;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
cout << setprecision(10) << fixed;
init();
int n, m; cin >> n >> m;
vector<int> a(n);
for(int i = 0; i < n; i++) {
cin >> a[i]; a[i]--;
}
cout << solve(n, m, a) << endl;
// cout << naive(n, m, a) << endl;
// iota(a.begin(), a.end(), 0);
// do{
// if(solve(n, m, a).v != naive(n, m, a)) print_vector(a);
// }while(next_permutation(a.begin(), a.end()));
}
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