結果
問題 | No.1193 Penguin Sequence |
ユーザー |
👑 ![]() |
提出日時 | 2020-08-22 15:38:22 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,002 ms / 2,000 ms |
コード長 | 7,046 bytes |
コンパイル時間 | 2,946 ms |
コンパイル使用メモリ | 214,320 KB |
最終ジャッジ日時 | 2025-01-13 09:44:45 |
ジャッジサーバーID (参考情報) |
judge2 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 38 |
ソースコード
//#define _GLIBCXX_DEBUG #include<bits/stdc++.h> using namespace std; #define endl '\n' #define lfs cout<<fixed<<setprecision(10) #define ALL(a) (a).begin(),(a).end() #define ALLR(a) (a).rbegin(),(a).rend() #define spa << " " << #define fi first #define se second #define MP make_pair #define MT make_tuple #define PB push_back #define EB emplace_back #define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++) #define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--) using ll = long long; using ld = long double; const ll MOD1 = 1e9+7; const ll MOD9 = 998244353; const ll INF = 1e18; using P = pair<ll, ll>; template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;} template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;} ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});} void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;} void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;} void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;} template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;} template<typename T>void debug(vector<vector<T>>&v,ll h,ll w){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout spa v[i][j];cout<<endl;}}; void debug(vector<string>&v,ll h,ll w){for(ll i=0;i<h;i++){for(ll j=0;j<w;j++)cout<<v[i][j];cout<<endl;}}; template<typename T>void debug(vector<T>&v,ll n){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout spa v[i];cout<<endl;}; template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;} ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;} vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1}; template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);} template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));} template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << p.first << " " << p.second;} template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;} //mt19937 mt(chrono::steady_clock::now().time_since_epoch().count()); template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; template< typename T > struct Combination { vector< T > _fact, _rfact, _inv; Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) { _fact[0] = _rfact[sz] = _inv[0] = 1; for(ll i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i; _rfact[sz] /= _fact[sz]; for(ll i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1); for(ll i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1]; } inline T fact(ll k) const { return _fact[k]; } inline T rfact(ll k) const { return _rfact[k]; } inline T inv(ll k) const { return _inv[k]; } T P(ll n, ll r) const { if(r < 0 || n < r) return 0; return fact(n) * rfact(n - r); } T C(ll p, ll q) const { if(q < 0 || p < q) return 0; return fact(p) * rfact(q) * rfact(p - q); } T RC(ll p, ll q) const { if(q < 0 || p < q) return 0; return rfact(p) * fact(q) * fact(p - q); } T H(ll n, ll r) const { if(n < 0 || r < 0) return (0); return r == 0 ? 1 : C(n + r - 1, r); } }; template<typename T> struct BIT{ ll n; ll k=1; vector<T>data; BIT() = default; BIT(ll size):n(size){ data.assign(n,0); while(k*2<=n)k*=2; } void add(ll a,T w){ for(ll i=a+1;i<=n;i+=i&-i)data[i-1]+=w; } T sum(ll a){ if(a<0)return 0; T ret = 0; for(ll i=a+1;i>0;i-=i&-i)ret+=data[i-1]; return ret; } T sum(ll a,ll b){return a>b?0:sum(b)-sum(a-1);} T operator[](ll pos){ return sum(pos,pos); } ll lower_bound(ll x){ ll ret=0; for(ll i=k;i>0;i/=2){ if(ret+i<=n&&data[ret+i-1]<x){ x-=data[ret+i-1]; ret+=i; } } return ret; } void print(){ for(ll i=0;i<n;i++){ if(i!=0)cout<<" "; cout<<(*this)[i]; } cout<<endl; } }; template<typename T> map<T,ll> compress(vector<T> &v){ sort(ALL(v)); v.erase(unique(ALL(v)),v.end()); map<T, ll> ret; for(ll i=0;i<(ll)v.size();i++) ret[v[i]]=i; return ret; } using modint = ModInt< MOD9 >;modint pow(ll n, ll x){return modint(n).pow(x);}modint pow(modint n, ll x){return n.pow(x);} //using modint=ld; using Comb=Combination<modint>; int main(){ cin.tie(nullptr); ios_base::sync_with_stdio(false); ll res=0,buf=0; bool judge = true; ll n;cin>>n; vector<ll>a(n); rep(i,0,n)cin>>a[i]; vector<ll>val=a; auto mp=compress(val); modint ret=0; Comb comb(500005);//cout<<"naosu"<<endl; { modint inv=0; ll sz=mp.size(); BIT<modint>bit(sz); rep(i,0,n){ inv+=bit.sum(mp[a[i]]+1,sz-1); bit.add(mp[a[i]],1); } //cout<<inv<<endl; rep(i,1,n+1){ auto t1=comb.C(n-2,i-2); auto t0=comb.C(n,i); //cout<<t1 spa t0 spa ret<<endl; ret+=inv*t1/t0; } //cout<<ret<<endl; modint low=0; rep(i,0,n){ low+=bit.sum(mp[a[i]]-1); } modint now=0; //cout<<low<<endl; rep(i,1,n+1){ //cout<<now spa ret<<endl; modint prob=modint(1)-comb.C(n-1,i)/comb.C(n,i); //cout<<prob<<endl; ret+=low*now*prob; now+=prob; } rep(i,1,n+1){ ret*=comb.C(n,i); } } cout<<ret<<endl; return 0; }