結果
問題 | No.1392 Don't be together |
ユーザー |
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提出日時 | 2021-02-12 21:53:28 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 192 ms / 2,000 ms |
コード長 | 2,619 bytes |
コンパイル時間 | 2,082 ms |
コンパイル使用メモリ | 188,244 KB |
実行使用メモリ | 5,376 KB |
最終ジャッジ日時 | 2024-07-19 21:09:02 |
合計ジャッジ時間 | 4,597 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 27 |
ソースコード
#include <bits/stdc++.h>using namespace std;const long long MOD = 998244353;long long modpow(long long a, long long b){long long ans = 1;while (b > 0){if (b % 2 == 1){ans *= a;ans %= MOD;}a *= a;a %= MOD;b /= 2;}return ans;}long long modinv(long long a){return modpow(a, MOD - 2);}vector<long long> mf = {1};vector<long long> mfi = {1};long long modfact(int n){if (mf.size() > n){return mf[n];} else {for (int i = mf.size(); i <= n; i++){long long next = mf.back() * i % MOD;mf.push_back(next);mfi.push_back(modinv(next));}return mf[n];}}long long modfactinv(int n){if (mfi.size() > n){return mfi[n];} else {return modinv(modfact(n));}}long long modbinom(int n, int k){if (n < 0 || k < 0 || k > n){return 0;} else {return modfact(n) * modfactinv(k) % MOD * modfactinv(n - k) % MOD;}}vector<vector<long long>> matmul(vector<vector<long long>> A, vector<vector<long long>> B){int N = A.size();vector<vector<long long>> ans(N, vector<long long>(N, 0));for (int i = 0; i < N; i++){for (int j = 0; j < N; j++){for (int k = 0; k < N; k++){ans[i][k] += A[i][j] * B[j][k] % MOD;ans[i][k] %= MOD;}}}return ans;}vector<vector<long long>> matexp(vector<vector<long long>> A, long long b){int N = A.size();vector<vector<long long>> ans(N, vector<long long>(N, 0));for (int i = 0; i < N; i++){ans[i][i] = 1;}while (b > 0){if (b % 2 == 1){ans = matmul(ans, A);}A = matmul(A, A);b /= 2;}return ans;}int main(){int N, M;cin >> N >> M;vector<int> P(N);for (int i = 0; i < N; i++){cin >> P[i];P[i]--;}vector<int> s;vector<bool> used(N, false);for (int i = 0; i < N; i++){if (!used[i]){int cnt = 0;for (int j = i; !used[j]; j = P[j]){used[j] = true;cnt++;}s.push_back(cnt);}}int cnt = s.size();long long ans = 0;for (int i = M; i >= 2; i--){long long add = 1;unordered_map<int, long long> mp;for (int j = 0; j < cnt; j++){if (!mp.count(s[j])){vector<vector<long long>> mat(2, vector<long long>(2));mat[0][0] = 0;mat[0][1] = i - 1;mat[1][0] = 1;mat[1][1] = i - 2;mat = matexp(mat, s[j]);mp[s[j]] = mat[0][0] * i % MOD;}add *= mp[s[j]];add %= MOD;}add *= modbinom(M, i);add %= MOD;if ((M - i) % 2 == 1){add = (MOD - add) % MOD;}ans += add;ans %= MOD;}ans *= modfactinv(M);ans %= MOD;cout << ans << endl;}