結果
問題 | No.1978 Permutation Repetition |
ユーザー | milanis48663220 |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 35 WA * 9 |
ソースコード
#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 200002ModInt 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()));}