oj.uz

Submission #786530

# Submission time Handle Problem Language Result Execution time Memory
786530 2023-07-18T08:47:06 Z PCTprobability Fish (IOI08_fish) C++17
85 / 100
 715 ms 65536 KB 
#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using ll = long long;
using ld = long double;
using ull = unsigned long long;
#define endl "\n"
typedef pair<int, int> Pii;
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define REP3(i, m, n) for (int i = (m); (i) < int(n); ++ (i))
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(x) begin(x), end(x)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define fore(i,a) for(auto &i:a)
#define all(s) (s).begin(),(s).end()
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define FOR_(n) for (ll _ = 0; (_) < (ll)(n); ++(_))
#define FOR(i, n) for (ll i = 0; (i) < (ll)(n); ++(i))
#define se second
#define pb push_back
#define P pair<ll,ll>
#define PQminll priority_queue<ll, vector<ll>, greater<ll>>
#define PQmaxll priority_queue<ll,vector<ll>,less<ll>>
#define PQminP priority_queue<P, vector<P>, greater<P>>
#define PQmaxP priority_queue<P,vector<P>,less<P>>
#define NP next_permutation
//const ll mod = 1000000009;
const ll mod = 998244353;
//const ll mod = 1000000007;
const ll inf = 4100000000000000000ll;
const ld eps = ld(0.00000000001);
static const long double pi = 3.141592653589793;
template<class T>void vcin(vector<T> &n){for(int i=0;i<int(n.size());i++) cin>>n[i];}
template<class T,class K>void vcin(vector<T> &n,vector<K> &m){for(int i=0;i<int(n.size());i++) cin>>n[i]>>m[i];}
template<class T>void vcout(vector<T> &n){for(int i=0;i<int(n.size());i++){cout<<n[i]<<" ";}cout<<endl;}
template<class T>void vcin(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cin>>n[i][j];}}}
template<class T>void vcout(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cout<<n[i][j]<<" ";}cout<<endl;}cout<<endl;}
void yes(bool a){cout<<(a?"yes":"no")<<endl;}
void YES(bool a){cout<<(a?"YES":"NO")<<endl;}
void Yes(bool a){cout<<(a?"Yes":"No")<<endl;}
void possible(bool a){ cout<<(a?"possible":"impossible")<<endl; }
void Possible(bool a){ cout<<(a?"Possible":"Impossible")<<endl; }
void POSSIBLE(bool a){ cout<<(a?"POSSIBLE":"IMPOSSIBLE")<<endl; }
#define FOR_R(i, n) for (ll i = (ll)(n)-1; (i) >= 0; --(i))
template<class T>auto min(const T& a){ return *min_element(all(a)); }
template<class T>auto max(const T& a){ return *max_element(all(a)); }
template<class T,class F>void print(pair<T,F> a){cout<<a.fi<<" "<<a.se<<endl;}
template<class T>bool chmax(T &a,const T b) { if (a<b) { a=b; return 1; } return 0;}
template<class T>bool chmin(T &a,const T b) { if (b<a) { a=b; return 1; } return 0;}
template<class T> void ifmin(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<class T> void ifmax(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
ll fastgcd(ll u,ll v){ll shl=0;while(u&&v&&u!=v){bool eu=!(u&1);bool ev=!(v&1);if(eu&&ev){++shl;u>>=1;v>>=1;}else if(eu&&!ev){u>>=1;}else if(!eu&&ev){v>>=1;}else if(u>=v){u=(u-v)>>1;}else{ll tmp=u;u=(v-u)>>1;v=tmp;}}return !u?v<<shl:u<<shl;}
ll modPow(ll a, ll n, ll mod) { if(mod==1) return 0;ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
vector<ll> divisor(ll x){ vector<ll> ans; for(ll i = 1; i * i <= x; i++){ if(x % i == 0) {ans.push_back(i); if(i*i!=x){ ans.push_back(x / ans[i]);}}}sor(ans); return ans; }
ll pop(ll x){return __builtin_popcountll(x);}
ll poplong(ll x){ll y=-1;while(x){x/=2;y++;}return y;}
P hyou(P a){ll x=fastgcd(abs(a.fi),abs(a.se));a.fi/=x;a.se/=x;if(a.se<0){a.fi*=-1;a.se*=-1;}return a;}
P Pplus(P a,P b){ return hyou({a.fi*b.se+b.fi*a.se,a.se*b.se});}
P Ptimes(P a,ll b){ return hyou({a.fi*b,a.se});}
P Ptimes(P a,P b){ return hyou({a.fi*b.fi,a.se*b.se});}
P Pminus(P a,P b){ return hyou({a.fi*b.se-b.fi*a.se,a.se*b.se});}
P Pgyaku(P a){ return hyou({a.se,a.fi});}
template<class T>
struct Sum{
  vector<T> data;
  Sum(const vector<T>& v):data(v.size()+1){
    for(ll i=0;i<v.size();i++) data[i+1]=data[i]+v[i];
  }
  T get(ll l,ll r) const {
    return data[r]-data[l];
  }
};
template<class T>
struct Sum2{
  vector<vector<T>> data;
  Sum2(const vector<vector<T>> &v):data(v.size()+1,vector<T>(v[0].size()+1)){
    for(int i=0;i<v.size();i++) for(int j=0;j<v[i].size();j++) data[i+1][j+1]=data[i][j+1]+v[i][j];
    for(int i=0;i<v.size();i++) for(int j=0;j<v[i].size();j++) data[i+1][j+1]+=data[i+1][j];
  }
  T get(ll x1,ll y1,ll x2,ll y2) const {
    return data[x2][y2]+data[x1][y1]-data[x1][y2]-data[x2][y1];
  }
};
 
void cincout(){
  ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
  cout<< fixed << setprecision(15);
}
ll m;
vector<ll> p,ex;
ll Inv[100000];
struct mint{
  ll v=1;
  vector<ll> c;
  mint(){
  }
  mint(ll x){
    c.resize(int(p.size()));
    for(int i=0;i<int(p.size());i++){
      while(x%p[i]==0){
        x/=p[i];
        c[i]++;
      }
    }
    v=x%m;
  }
  ll val(){
    ll ret=v;
    for(int i=0;i<int(p.size());i++){
      ret*=modPow(p[i],c[i],m);
      ret%=m;
    }
    return ret;
  }
  void mul(ll x){
    for(int i=0;i<int(p.size());i++){
      while(x%p[i]==0){
        x/=p[i];
        c[i]++;
      }
    }
    v*=x;
    v%=m;
  }
  void mul(mint x){
    for(int i=0;i<int(p.size());i++) c[i]+=x.c[i];
    v*=x.v;
    v%=m;
  }
  void inv(mint x){
    for(int i=0;i<int(p.size());i++) c[i]-=x.c[i];
    v*=Inv[x.v];
    v%=m;
  }
  void inv(ll x){
    for(int i=0;i<int(p.size());i++){
      while(x%p[i]==0){
        x/=p[i];
        c[i]--;
      }
    }
    v*=Inv[x%m];
    v%=m;
  }
};
struct Segtree{
  ll n;
  vector<mint> node;
  Segtree(vector<ll> f){
    ll N=f.size();
    n=1;
    while(n<N) n*=2;
    node.resize(2*n);
    for(int i=0;i<f.size();i++) node[i+n]=mint(f[i]);
    for(int i=f.size();i<n;i++) node[i+n]=mint(1);
    for(int j=n-1;j>=1;j--){
      node[j]=node[2*j];
      node[j].mul(node[2*j+1]);
    }
  }
  void mul(int i,mint x){
    i+=n;
    while(i){
      node[i].mul(x);
      i/=2;
    }
  }
  void inv(int i,mint x){
    i+=n;
    while(i){
      node[i].inv(x);
      i/=2;
    }
  }
  mint prod(ll l,ll r,ll a,ll b,ll k){
    if(r<=a||b<=l) return mint(1);
    if(l<=a&&b<=r) return node[k];
    mint x=prod(l,r,a,(a+b)/2,2*k);
    x.mul(prod(l,r,(a+b)/2,b,2*k+1));
    return x;
  }
  mint prod(ll l,ll r){
    return prod(l,r,0,n,1);
  }
};
int main() {
  cincout();
  ll n,k;
  cin>>n>>k>>m;
  ll C=-1;
  for(int i=1;i<=m;i++) if(gcd(i,m)==1) C++;
  for(int i=0;i<m;i++){
    Inv[i]=modPow(i,C,m);
  }
  ll memo=m;
  for(int i=2;i<=30000;i++){
    ll cnt=0;
    while(m%i==0){
      m/=i;
      cnt++;
    }
    if(cnt){
      p.pb(i);
      ex.pb(cnt);
    }
  }
  m=memo;
  vector<P> a(n);
  for(int i=0;i<n;i++){
    cin>>a[i].fi>>a[i].se;
    a[i].se--;
  }
  sor(a);
  rever(a);
  vector<ll> c(k),d(k);
  ll x=0;
  for(int i=0;i<n;i++){
    if(c[a[i].se]==0){
      d[a[i].se]=x;
      x++;
      c[a[i].se]=1;
    }
  }
  for(auto &e:a) e.se=d[e.se];
  vector<vector<ll>> b;
  for(auto &e:c) e=0;
  ll ans=0;
  multiset<pair<int,int>> ms;
  for(int i=0;i<n;i++){
    ms.insert({a[i].fi,-i});
  }
  ms.insert({1000000000,1000000000});
  ll q=0;
  //今 q 以降が f に含まれている
  vector<ll> f(k);
  for(int j=q;j<n;j++){
    f[a[j].se]++;
  }
  mint ret2(1);
  for(int i=1;i<k;i++){
    ret2.mul(f[i]+1);
  }
  ll l=0;
  //今 l の部分までかけている
  vector<ll> ld(k);
  for(auto &e:f) e++;
  Segtree seg(f);
  for(auto &e:f) e--;
  multiset<pair<int,int>> idx;
  idx.insert({n+n+n,n+n+n});
  vector<vector<int>> A(k);
  for(int i=0;i<n;i++) A[a[i].se].pb(i);
  for(int i=0;i<n;i++){
    if(c[a[i].se]==0){
      ld[a[i].se]=i;
      auto itr=ms.lower_bound({a[i].fi/2+1,-n-n-n});
      //itr より手前の要素を使える -> itr 以下は無理
      for(int j=q;j<=-(*itr).se;j++){
        if(a[j].se>=a[i].se+1) ret2.inv(f[a[j].se]+1);
        seg.inv(a[j].se,f[a[j].se]+1);
        f[a[j].se]--;
        seg.mul(a[j].se,f[a[j].se]+1);
        if(a[j].se>=a[i].se+1) ret2.mul(f[a[j].se]+1);
      }
      q=-(*itr).se+1;
      mint ret(1); 
      //A[a[i].se] にある要素のうち、q-1 以下のもの
      int OK=0,NG=A[a[i].se].size();
      while(abs(OK-NG)>1){
        int MID=(OK+NG)/2;
        if(A[a[i].se][MID]<=q-1) OK=MID;
        else NG=MID;
      }
      OK=A[a[i].se][OK];
      //2*a[i].fi 以上の最小の idx
      if(a[0].fi<a[OK].fi*2){
        ret.mul(seg.prod(0,a[i].se));
      }
      else{
        int ok=0,ng=a[i].se;
        while(abs(ok-ng)/2){
          int mid=(ok+ng)/2;
          if(a[ld[mid]].fi<a[OK].fi*2) ng=mid;
          else ok=mid;
        }
        ret.mul(seg.prod(ng,a[i].se));
      }
      ans+=(ret.val()+f[a[i].se])*(ret2.val());
      ans%=m;
      c[a[i].se]=1;
      ret2.inv(f[a[i].se+1]+1);
    }
  }
  cout<<ans<<endl;
}

Compilation message

fish.cpp: In constructor 'Segtree::Segtree(std::vector<long long int>)':
fish.cpp:162:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  162 |     for(int i=0;i<f.size();i++) node[i+n]=mint(f[i]);
      |                 ~^~~~~~~~~
fish.cpp: In function 'int main()':
fish.cpp:251:6: warning: unused variable 'l' [-Wunused-variable]
  251 |   ll l=0;
      |      ^

Subtask #1
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 468 KB Output is correct

Subtask #2
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 468 KB Output is correct

Subtask #3
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 496 KB Output is correct

Subtask #4
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 468 KB Output is correct

Subtask #5
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 468 KB Output is correct
2 Correct 7 ms 596 KB Output is correct

Subtask #6
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 596 KB Output is correct
2 Correct 256 ms 34500 KB Output is correct

Subtask #7
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 596 KB Output is correct

Subtask #8
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 724 KB Output is correct

Subtask #9
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 139 ms 14580 KB Output is correct
2 Correct 145 ms 17628 KB Output is correct

Subtask #10
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 1108 KB Output is correct
2 Correct 7 ms 852 KB Output is correct
3 Correct 11 ms 1108 KB Output is correct

Subtask #11
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 205 ms 21720 KB Output is correct
2 Correct 338 ms 34952 KB Output is correct
3 Correct 307 ms 35328 KB Output is correct

Subtask #12
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 467 ms 35000 KB Output is correct
2 Correct 330 ms 35676 KB Output is correct

Subtask #13
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 318 ms 22128 KB Output is correct
2 Correct 364 ms 36032 KB Output is correct

Subtask #14
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 415 ms 34852 KB Output is correct

Subtask #15
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 426 ms 40404 KB Output is correct

Subtask #16
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 456 ms 41004 KB Output is correct
2 Correct 715 ms 59484 KB Output is correct

Subtask #17
0 / 5.0

# Verdict Execution time Memory Grader output
1 Runtime error 196 ms 65536 KB Execution killed with signal 9
2 Halted 0 ms 0 KB -

Subtask #18
0 / 5.0

# Verdict Execution time Memory Grader output
1 Runtime error 213 ms 65536 KB Execution killed with signal 9
2 Halted 0 ms 0 KB -

Subtask #19
0 / 5.0

# Verdict Execution time Memory Grader output
1 Runtime error 220 ms 65536 KB Execution killed with signal 9
2 Halted 0 ms 0 KB -