結果

問題 No.1691 Badugi
ユーザー PCTprobabilityPCTprobability
提出日時 2021-09-24 22:28:05
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 144 ms / 2,000 ms
コード長 8,621 bytes
コンパイル時間 7,201 ms
コンパイル使用メモリ 333,812 KB
実行使用メモリ 73,928 KB
最終ジャッジ日時 2024-07-05 10:55:27
合計ジャッジ時間 9,698 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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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 91 ms
73,768 KB
testcase_01 AC 92 ms
73,864 KB
testcase_02 AC 92 ms
73,764 KB
testcase_03 AC 87 ms
73,872 KB
testcase_04 AC 96 ms
73,684 KB
testcase_05 AC 93 ms
73,808 KB
testcase_06 AC 86 ms
73,852 KB
testcase_07 AC 89 ms
73,904 KB
testcase_08 AC 91 ms
73,928 KB
testcase_09 AC 87 ms
73,868 KB
testcase_10 AC 88 ms
73,772 KB
testcase_11 AC 90 ms
73,820 KB
testcase_12 AC 142 ms
73,816 KB
testcase_13 AC 144 ms
73,900 KB
testcase_14 AC 140 ms
73,828 KB
testcase_15 AC 140 ms
73,816 KB
testcase_16 AC 144 ms
73,788 KB
testcase_17 AC 132 ms
73,760 KB
testcase_18 AC 137 ms
73,808 KB
testcase_19 AC 130 ms
73,748 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 # 

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#include <unistd.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 FOR(i,a,b) for(ll i=a;i<=(ll)(b);i++)
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(x) begin(x), end(x)
#define all(s) (s).begin(),(s).end()
//#define rep2(i, m, n) for (int i = (m); i < (n); ++i)
//#define rep(i, n) rep2(i, 0, n)
#define PB push_back 
#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 FOR(i,a,b) for(ll i=a;i<=(ll)(b);i++)
#define fi first
#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; }
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;}}
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}
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;}
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(10);
}
class UnionFind{
public:
  vector<ll> par;
  vector<ll> siz;
  UnionFind(ll sz_):par(sz_),siz(sz_,1ll){
    for(int i=0;i<sz_;i++) par[i]=i;
  }
  void init(ll sz_){
    par.resize(sz_);
    siz.assign(sz_,1ll);
    for(int i=0;i<sz_;i++) par[i]=i;
  }
  ll root(ll x){
    while(par[x]!=x){
      x=par[x]=par[par[x]];
    }
    return x;
  }
  bool merge(ll x,ll y){
    x=root(x);
    y=root(y);
    if(x==y) return false;
    if(siz[x]<siz[y]) swap(x,y);
    siz[x]+=siz[y];
    par[y]=x;
    return true;
  }
  bool issame(ll x,ll y){
    return root(x)==root(y);
  }
  ll size(ll x){
    return siz[root(x)];
  }
};
constexpr ll MAX = 3000000;
ll fac[MAX],finv[MAX],inv[MAX];
void COMinit(){
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for(int i=2;i<MAX;i++){
    fac[i]=fac[i-1]*i%mod;
    inv[i]=mod-inv[mod%i]*(mod/i)%mod;
    finv[i]=finv[i-1]*inv[i]%mod;
  }
}
ll binom(ll n,ll k){
  if(n<k) return 0;
  if(n<0||k<0) return 0;
  return fac[n]*(finv[k]*finv[n-k]%mod)%mod;
}
ll HOM(ll n,ll k){
  if(n+k-1>=n-1&&n-1>=0){
  return binom(n+k-1,n-1);
  }
  else{
    return 0;
  }
}
int main() {
  cincout();
  COMinit();
  map<pair<P,P>,ll> M;
  for(ll t=1;t<=3;t++){
    for(ll s=1;s<=3;s++){
    vector<P> a;
    for(int j=0;j<s;j++){
      for(int k=0;k<t;k++){
        a.pb({j,k});
      }
    }
    ll n=a.size();
    for(int j=0;j<(1<<n);j++){
      mcf_graph<ll,ll> g(s+t+2);
      for(int k=0;k<n;k++){
        if((j>>k)&1){
          g.add_edge(a[k].fi,a[k].se+s,1,0);
        }
      }
      for(int k=0;k<s;k++){
        g.add_edge(s+t,k,1,0);
       // g.add_edge(k+s,s+t+1,1,0);
      }
      for(int k=0;k<t;k++){
        g.add_edge(s+k,s+t+1,1,0);
      }
      auto p=g.flow(s+t,s+t+1);
      if(pop(j)-p.fi<=2&&pop(j)!=p.fi){
        UnionFind uf(s+t);
        for(int k=0;k<n;k++){
          if((j>>k)&1) uf.merge(a[k].fi,a[k].se+s);
        }
        if(uf.size(0)!=s+t) continue;
      //  cout<<t<<endl;
      //  cout<<"P"<<" "<<pop(j)<<" "<<p.fi<<endl;
        M[{{t,s},{pop(j),p.fi}}]++;
      }
    }
    }
  }
 /* for(auto e:M){
    cout<<e.fi.fi.fi<<" "<<e.fi.fi.se<<" "<<e.fi.se.fi<<" "<<e.fi.se.se<<" "<<e.se<<endl;
  }*/
  ll ans=0;
  ll n,m,k;
  cin>>n>>m>>k;
  for(auto e:M){
    if(e.fi.se.fi-e.fi.se.se==2&&k-e.fi.se.se-2>=0){
    //  cout<<e.fi.fi.fi<<" "<<e.fi.fi.se<<" "<<e.fi.se.fi<<" "<<e.fi.se.se<<" "<<e.se<<" "<<binom(n,e.fi.fi.fi)*binom(m,e.fi.fi.se)%mod*e.se%mod*binom(n-e.fi.fi.fi,k-e.fi.se.se-2)%mod*binom(m-e.fi.fi.se,k-e.fi.se.se-2)%mod*fac[k-e.fi.se.se-2]%mod<<endl;
      ans+=binom(n,e.fi.fi.fi)*binom(m,e.fi.fi.se)%mod*e.se%mod*binom(n-e.fi.fi.fi,k-e.fi.se.se-2)%mod*binom(m-e.fi.fi.se,k-e.fi.se.se-2)%mod*fac[k-e.fi.se.se-2]%mod;
      ans%=mod;
    }
  }
  ll x=0;
  for(auto e:M){
    ll y=0;
    for(auto f:M){
     // cout<<"X"<<" "<<x<<" "<<y<<endl;
      if(x<y){
        y++;
        continue;
      }
      ll G=1;
      if(x==y) G*=modPow(2,mod-2,mod);
      if(e.fi.se.fi-e.fi.se.se==1&&f.fi.se.fi-f.fi.se.se==1&&k-e.fi.se.se-f.fi.se.se-2>=0){
      //  cout<<e.fi.fi.fi<<" "<<e.fi.fi.se<<" "<<e.fi.se.fi<<" "<<e.fi.se.se<<" "<<e.se<<endl;
        //cout<<f.fi.fi.fi<<" "<<f.fi.fi.se<<" "<<f.fi.se.fi<<" "<<f.fi.se.se<<" "<<f.se<<endl;
        //cout<<binom(n,e.fi.fi.fi)*binom(m,e.fi.fi.se)%mod*e.se%mod*binom(n-e.fi.fi.fi,f.fi.fi.fi)%mod*binom(m-e.fi.fi.se,f.fi.fi.se)%mod*f.se%mod*binom(n-e.fi.fi.fi-f.fi.fi.fi,k-e.fi.se.se-f.fi.se.se-2)%mod*binom(m-e.fi.fi.se-f.fi.fi.se,k-e.fi.se.se-f.fi.se.se-2)%mod*fac[k-e.fi.se.se-f.fi.se.se-2]%mod*G%mod<<endl;
        ans+=binom(n,e.fi.fi.fi)*binom(m,e.fi.fi.se)%mod*e.se%mod*binom(n-e.fi.fi.fi,f.fi.fi.fi)%mod*binom(m-e.fi.fi.se,f.fi.fi.se)%mod*f.se%mod*binom(n-e.fi.fi.fi-f.fi.fi.fi,k-e.fi.se.se-f.fi.se.se-2)%mod*binom(m-e.fi.fi.se-f.fi.fi.se,k-e.fi.se.se-f.fi.se.se-2)%mod*fac[k-e.fi.se.se-f.fi.se.se-2]%mod*G%mod;
        ans%=mod;
      }
      y++;
    }
    x++;
  }
  cout<<ans<<endl;
}
0