結果

問題 No.590 Replacement
ユーザー koyumeishikoyumeishi
提出日時 2017-11-04 00:14:35
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
TLE  
実行時間 -
コード長 7,654 bytes
コンパイル時間 1,736 ms
コンパイル使用メモリ 134,072 KB
実行使用メモリ 151,424 KB
最終ジャッジ日時 2024-11-23 15:27:52
合計ジャッジ時間 13,395 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
10,496 KB
testcase_01 AC 2 ms
13,008 KB
testcase_02 AC 2 ms
10,496 KB
testcase_03 AC 2 ms
5,248 KB
testcase_04 AC 2 ms
5,248 KB
testcase_05 AC 2 ms
5,248 KB
testcase_06 AC 2 ms
5,248 KB
testcase_07 AC 12 ms
5,248 KB
testcase_08 AC 6 ms
5,248 KB
testcase_09 AC 10 ms
5,248 KB
testcase_10 AC 7 ms
5,248 KB
testcase_11 AC 6 ms
5,248 KB
testcase_12 AC 10 ms
5,248 KB
testcase_13 AC 49 ms
5,248 KB
testcase_14 AC 98 ms
5,504 KB
testcase_15 AC 5 ms
5,248 KB
testcase_16 AC 37 ms
5,248 KB
testcase_17 AC 34 ms
5,248 KB
testcase_18 AC 114 ms
7,296 KB
testcase_19 AC 142 ms
6,828 KB
testcase_20 AC 537 ms
5,248 KB
testcase_21 AC 227 ms
7,580 KB
testcase_22 AC 122 ms
8,796 KB
testcase_23 AC 139 ms
8,192 KB
testcase_24 AC 139 ms
8,064 KB
testcase_25 AC 125 ms
7,936 KB
testcase_26 AC 250 ms
7,924 KB
testcase_27 AC 135 ms
8,064 KB
testcase_28 AC 184 ms
7,552 KB
testcase_29 AC 146 ms
7,680 KB
testcase_30 AC 164 ms
7,424 KB
testcase_31 AC 146 ms
8,064 KB
testcase_32 AC 156 ms
8,252 KB
testcase_33 AC 2 ms
5,248 KB
testcase_34 AC 2 ms
5,248 KB
testcase_35 AC 2 ms
5,248 KB
testcase_36 AC 97 ms
9,044 KB
testcase_37 AC 97 ms
9,048 KB
testcase_38 AC 102 ms
8,912 KB
testcase_39 AC 101 ms
9,040 KB
testcase_40 TLE -
testcase_41 TLE -
testcase_42 AC 103 ms
8,556 KB
testcase_43 AC 102 ms
8,044 KB
testcase_44 AC 253 ms
151,424 KB
testcase_45 AC 96 ms
8,920 KB
testcase_46 AC 95 ms
16,676 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
#include <tuple>
#include <utility>
using namespace std;

namespace {
  using Integer = long long; //__int128;
  template<class T, class S> istream& operator >> (istream& is, pair<T,S>& p){return is >> p.first >> p.second;}
  template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
  template<class T> istream& operator ,  (istream& is, T& val){ return is >> val;}
  template<class T, class S> ostream& operator << (ostream& os, const pair<T,S>& p){return os << p.first << " " << p.second;}
  template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(size_t i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;}
  template<class T> ostream& operator ,  (ostream& os, const T& val){ return os << " " << val;}

  template<class H> void print(const H& head){ cout << head; }
  template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
  template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }

  template<class H> void eprint(const H& head){ cerr << head; }
  template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); }
  template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; }

  class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator   end(){ return range_iterator(  end_, step_); } };

  inline string operator "" _s (const char* str, size_t size){ return move(string(str)); }
  constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
  constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);}
  constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }

  inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed

  mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());

  template<class T> string join(const vector<T>& v, const string& sep){ stringstream ss; for(size_t i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str(); }

  inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; }
}
constexpr long long mod = 9_ten + 7;

long long gcd(long long a, long long b){ return (b==0)?a:gcd(b,a%b); }
template<class ... T> long long gcd(long long a, long long b, T ... c){ return gcd(gcd(a,b), c...);}
long long lcm(long long a, long long b){ if(a<b) swap(a,b); return (b==1)?a:a*(b/gcd(a,b)); }
template<class ... T> long long lcm(long long a, long long b, T ... c){ return lcm(lcm(a,b), c...);}

long long extgcd(long long a, long long b, long long &x, long long &y){
  long long d=a;
  if(b!=0){
    d = extgcd(b, a%b, y, x);
    y -= (a/b) * x;
  }else{
    x = 1;
    y = 0;
  }
  return d;
}

long long mod_inverse(long long a, long long m){
  long long x,y;
  extgcd(a,m,x,y);
  return (m+x%m)%m;
}


long long Chinese_Remainder_Theorem_Garner(vector<long long> x, vector<long long> y){
  int N = x.size();
  bool valid = true;
  //前処理
  //gcd(Yi,Yj) == 1 (i!=j) でなくてはならないので、
  //共通の因数 g = gcd(Yi,Yj) を見つけたら片側に寄せてしまう
  for(int i=0; i<N; i++){
    for(int j=i+1; j<N; j++){
      if(i == j) continue;
      long long g = gcd(y[i], y[j]);

      if( x[i]%g != x[j]%g ) valid = false; //解が存在しない

      if(g != 1){
        y[i] /= g; y[j] /= g;
        long long g_ = gcd(y[i], g);
        while(g_ != 1){
          y[i] *= g_;
          g /= g_;
          g_ = gcd(y[i], g);
        }
        y[j] *= g;

        x[i] %= y[i];
        x[j] %= y[j];
      }
    }
  }

  if(!valid){
    // cerr << -1 << endl;
    return -1;
  }

  //Garner's algorithm
  vector<long long> z(N);
  for(int i=0; i<N; i++){
    z[i] = x[i];
    for(int j=0; j<i; j++){
      z[i] = mod_inverse(y[j], y[i]) % y[i] * (z[i] - z[j]) % y[i];

      z[i] = (z[i]+y[i])%y[i];
    }
  }

  long long ans = 0;
  long long tmp = 1;
  for(int i=0; i<N; i++){
    // ans = (ans + z[i] * tmp)%mod;
    // tmp = (tmp * y[i])%mod;
    ans = (ans + z[i] * tmp);
    tmp = (tmp * y[i]);
  }

  return ans;
}

int main(){
  int n;
  cin >> n;
  vector<int> a(n),b(n);
  cin >> a,b;
  for(int i=0; i<n; i++){
    a[i]--;
    b[i]--;
  }

  vector<deque<int>> x,y;
  vector<int> d_a(n, -1), d_b(n, -1);
  vector<int> i_a(n, -1), i_b(n, -1);
  for(int i=0; i<n; i++){
    if(d_a[i] != -1) continue;
    deque<int> tmp;
    int pos = i;
    int k = x.size();
    while( d_a[pos] == -1 ){
      tmp.push_back( pos );
      d_a[pos] = k;
      i_a[pos] = tmp.size()-1;
      pos = a[pos];
    }
    reverse(tmp.begin(), tmp.end());
    for(int j=0; j<tmp.size(); j++){
      i_a[tmp[j]] = j;
    }
    x.push_back( tmp );
  }

  for(int i=0; i<n; i++){
    if(d_b[i] != -1) continue;
    deque<int> tmp;
    int pos = i;
    int k = y.size();
    while( d_b[pos] == -1 ){
      tmp.push_back( pos );
      d_b[pos] = k;
      i_b[pos] = tmp.size()-1;
      pos = b[pos];
    }
    reverse(tmp.begin(), tmp.end());
    for(int j=0; j<tmp.size(); j++){
      i_b[tmp[j]] = j;
    }
    y.push_back( tmp );
  }

  // eprintln( join(x, "\n") );
  // eprintln("");
  // eprintln( join(y, "\n") );

  map<pair<int,int>, vector<int>> unko;
  for(int i=0; i<n; i++){
    unko[{d_a[i], d_b[i]}].push_back( i );
  }

  long long inv2 = my_pow_mod(2, mod-2, mod);

  vector<int> checked(n, 0);
  long long ans = 0;
  for(int i=0; i<n; i++){
    if(checked[i]) continue;
    auto& A = x[d_a[i]];
    auto& B = y[d_b[i]];

    int la = A.size();
    int lb = B.size();

    int ia = i_a[i];
    int ib = i_b[i];

    pair<int,int> pp = {d_a[i], d_b[i]};
    auto& nums = unko[pp];

    vector<long long> hoge;

    checked[ i ] = true;
    hoge.push_back(0);
    for(auto j : nums){
      if(j == i) continue;
      int ja = i_a[j];
      int jb = i_b[j];

      int dist_a = ja - ia;
      int dist_b = jb - ib;

      if(dist_a < 0) dist_a += la;
      if(dist_b < 0) dist_b += lb;

      long long dist = Chinese_Remainder_Theorem_Garner( vector<long long>{dist_a, dist_b}, vector<long long>{la,lb} );
      if(dist == -1) continue;

      hoge.push_back( dist );
      checked[ j ] = true;
    }

    hoge.push_back( lcm(la,lb) );

    sort(hoge.begin(), hoge.end());

    for(int k=0; k+1<hoge.size(); k++){
      long long m = hoge[k+1] - hoge[k];
      m %= mod;
      long long tmp = m * ((m-1+mod)%mod) % mod * inv2 % mod;
      ans += tmp;
      ans %= mod;
    }
  }

  println(ans);

  return 0;
}
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