結果
| 問題 |
No.3123 Inversion
|
| ユーザー |
 GOTKAKO
|
| 提出日時 | 2025-04-20 11:51:56 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,522 ms / 10,000 ms |
| コード長 | 10,094 bytes |
| コンパイル時間 | 2,596 ms |
| コンパイル使用メモリ | 212,892 KB |
| 実行使用メモリ | 329,676 KB |
| 最終ジャッジ日時 | 2025-04-20 11:52:38 |
| 合計ジャッジ時間 | 37,356 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 21 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
long long mod = 998244353;
//入力が必ず-mod<a<modの時.
struct mint{
long long v = 0;
mint(){} mint(int a){v = a<0?a+mod:a;} mint(long long a){v = a<0?a+mod:a;}
mint(unsigned long long a){v = a;}
long long val(){return v;}
mint &operator=(const mint &b) = default;
mint operator-() const {return mint(0)-(*this);}
mint operator+(const mint b){return mint(v)+=b;}
mint operator-(const mint b){return mint(v)-=b;}
mint operator*(const mint b){return mint(v)*=b;}
mint operator/(const mint b){return mint(v)/=b;}
mint operator+=(const mint b){
v += b.v; if(v >= mod) v -= mod;
return *this;
}
mint operator-=(const mint b){
v -= b.v; if(v < 0) v += mod;
return *this;
}
mint operator*=(const mint b){v = v*b.v%mod; return *this;}
mint operator/=(mint b){
if(b == 0) assert(false);
int left = mod-2;
while(left){if(left&1) *this *= b; b *= b; left >>= 1;}
return *this;
}
mint operator++(){*this += 1; return *this;}
mint operator--(){*this -= 1; return *this;}
mint operator++(int){*this += 1; return *this;}
mint operator--(int){*this -= 1; return *this;}
bool operator==(const mint b){return v == b.v;}
bool operator!=(const mint b){return v != b.v;}
bool operator>(const mint b){return v > b.v;}
bool operator>=(const mint b){return v >= b.v;}
bool operator<(const mint b){return v < b.v;}
bool operator<=(const mint b){return v <= b.v;}
mint pow(long long n){
mint ret = 1,p = v;
if(n < 0) p = p.inv(),n = -n;
while(n){
if(n&1) ret *= p;
p *= p; n >>= 1;
}
return ret;
}
mint inv(){return mint(1)/v;}
};
class UnionFind{
private:
vector<int> par,siz;
public:
UnionFind(int N){
par.resize(N,-1);
siz.resize(N,1);
}
int root(int x){ //連結成分の代表頂点を返す.
if(par.at(x) == -1) return x;
else return par.at(x) = root(par.at(x));
}
bool unite(int u, int v){ //u,vを連結する 連結してた->false,した->trueを返す.
u = root(u),v = root(v);
if(u == v) return false;
if(siz.at(u) < siz.at(v)) swap(u,v); //Union by size.
par.at(v) = u;
siz.at(u) += siz.at(v);
return true;
}
bool issame(int u, int v){ //同じ連結成分ならtrue.
if(root(u) == root(v)) return true;
else return false;
}
int size(int pos){return siz.at(root(pos));} //posの連結成分の大きさを返す.
};
long long inv(vector<int> P){
int N = P.size();
long long ret = 0;
for(int i=0; i<N; i++) for(int k=i+1; k<N; k++) ret += P.at(i)>P.at(k);
return ret;
}
using SS = mint;
class SegmentTree{
public:
int siz = -1,n = -1;
vector<SS> dat;
SS op(SS a, SS b){return a*b;}
SS e(){return 1;}
void renew (SS &a,SS x){
a = op(a,x);
//a = x; //set(pos,x)で可能.
//その他.
}
SegmentTree(int N){init(N);}
SegmentTree(const vector<SS> &A){//長さ配列サイズに合わせる.
siz = 1; n = A.size();
while(siz < n) siz *= 2;
dat.resize(siz*2,e());
for(int i=0; i<n; i++) dat.at(i+siz) = A.at(i);
for(int i=siz-1; i>0; i--) dat.at(i) = op(dat.at(i*2),dat.at(i*2+1));
}
void init(int N){
//全要素単位元に初期化.
siz = 1; n = N;
while(siz < n) siz *= 2;
dat.assign(siz*2,e());
}
void init(const vector<SS> &A){//長さ配列サイズに合わせる.
siz = 1; n = A.size();
dat.resize(siz*2,e());
for(int i=0; i<n; i++) dat.at(i+siz) = A.at(i);
for(int i=siz-1; i>0; i--) dat.at(i) = op(dat.at(i*2),dat.at(i*2+1));
}
void set(int pos,SS x){
pos = pos+siz;
dat.at(pos) = x;
while(pos != 1){
pos = pos/2;
dat.at(pos) = op(dat.at(pos*2),dat.at(pos*2+1));
}
}
void update(int pos,SS x){
pos = pos+siz;
renew(dat.at(pos),x);
while(pos != 1){
pos = pos/2;
dat.at(pos) = op(dat.at(pos*2),dat.at(pos*2+1));
}
}
SS findans(int l, int r){
SS retl = e(),retr = e();
l += siz,r += siz;
while(l < r){
if(l&1) retl = op(retl,dat.at(l++));
if(r&1) retr = op(dat.at(--r),retr);
l >>= 1; r >>= 1;
}
return op(retl,retr);
}
SS get(int pos){return dat.at(pos+siz);}
SS rangeans(int l, int r){return findans(l,r);}
SS allrange(){return dat.at(1);}
//rightは) leftは[で 渡す&返す.
int maxright(const function<bool(SS)> f,int l = 0){
//fを満たさない最小の箇所を返す なければn.
l += siz; int r = n+siz;
vector<int> ls,rs;
while(l < r){
if(l&1) ls.push_back(l++);
if(r&1) rs.push_back(--r);
l >>= 1; r >>= 1;
}
SS okl = e();
for(int i=0; i<ls.size(); i++){
l = ls.at(i);
SS now = op(okl,dat.at(l));
if(!f(now)){
while(l < siz){
l <<= 1;
now = op(okl,dat.at(l));
if(f(now)){okl = now; l++;}
}
return l-siz;
}
okl = now;
}
for(int i=rs.size()-1; i>=0; i--){
l = rs.at(i);
SS now = op(okl,dat.at(l));
if(!f(now)){
while(l < siz){
l <<= 1;
now = op(okl,dat.at(l));
if(f(now)){okl = now; l++;}
}
return l-siz;
}
okl = now;
}
return n;
}
int minleft(const function<bool(SS)> f,int r = -1){
//fを満たす最小の箇所を返す なければ0.
if(r == -1) r = n;
int l = siz; r += siz;
vector<int> ls,rs;
while(l < r){
if(l&1) ls.push_back(l++);
if(r&1) rs.push_back(--r);
l >>= 1; r >>= 1;
}
SS okr = e();
for(int i=0; i<rs.size(); i++){
r = rs.at(i);
SS now = op(dat.at(r),okr);
if(!f(now)){
while(r < siz){
r <<= 1; r++;
now = op(dat.at(r),okr);
if(f(now)){okr = now; r--;}
}
return r+1-siz;
}
okr = now;
}
for(int i=ls.size()-1; i>=0; i--){
r = ls.at(i);
SS now = op(dat.at(r),okr);
if(!f(now)){
while(r < siz){
r <<= 1; r++;
now = op(dat.at(r),okr);
if(f(now)){okr = now; r--;}
}
return r+1-siz;
}
okr = now;
}
return 0;
}
};
int main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int T; cin >> T;
cin >> mod;
if(mod == 1){
while(T--) cout << "0\n";
return 0;
}
int n = 5000000;
vector<mint> fac(n+1,1); for(int i=1; i<=n; i++) fac.at(i) = fac.at(i-1)*i;
vector<mint> give(n+1);
for(int i=0; i<=n; i++) give.at(i) = i%mod;
SegmentTree Seg(give);
//OEIS最高！→え～何が違うの→mod合成数の時facの逆元が悪さしてる.
//連結成分サイズ2 逆順列=revとなる数 A037224->A001813 2n!/n!->(n+1)*(n+2)*...*2nなのでセグ木.
//連結成分サイズ2 それ以外 A000898.
//連結成分サイズ8 A000899*8. n!-2Xn-Y[n/2]+2*Two[n/2]
vector<mint> Two(n/2+1),Eight(n+1),X(n+1),Y(n/2+1);
Two.at(0) = 1; Two.at(1) = 2%mod; X.at(0) = 1; X.at(1) = 1; X.at(2) = 2%mod;
for(int i=2; i<=n/2; i++) Two.at(i) = (Two.at(i-1)+Two.at(i-2)*(i-1))*2;
for(int i=3; i<=n; i++) X.at(i) = X.at(i-1)+X.at(i-2)*(i-1);
mint p2 = 1;
for(int i=0; i<=n/2; i++) Y.at(i) = fac.at(i)*p2,p2 += p2;
for(int i=1; i<=n; i++) Eight.at(i) = fac.at(i)-X.at(i)*2-Y.at(i/2)+Two.at(i/2)*2;
while(T--){
int N; cin >> N;
if(N == 1){cout << 1 << "\n"; continue;}
mint two = Two.at(N/2),answer = 0,eight = Eight.at(N),four = 0;
if(N%4 == 0 || N%4 == 1){
int M = N/4;
two += Seg.rangeans(M+1,2*M+1);
}
four = fac.at(N)-two-eight;
answer = two*2+four*4+eight*8;
answer.v %= mod;
cout << answer.v << "\n"; continue;
long long f = 1;
for(int i=1; i<=N; i++) f *= i;
UnionFind Z(f);
map<vector<int>,long long> name;
vector<int> P(N);
iota(P.begin(),P.end(),0);
do{
name[P] = name.size();
}while(next_permutation(P.begin(),P.end()));
iota(P.begin(),P.end(),0);
vector<int> Q(N);
int idx = -1;
do{
idx++;
reverse(P.begin(),P.end());
Z.unite(idx,name[P]);
reverse(P.begin(),P.end());
for(int i=0; i<N; i++) Q.at(P.at(i)) = i;
Z.unite(idx,name[Q]);
}while(next_permutation(P.begin(),P.end()));
map<long long,long long> ap;
for(auto [K,v] : name){
ap[Z.size(v)]++;
if(Z.size(v) == 2) continue;
//continue;
vector<int> S(N);
for(int i=0; i<N; i++) S[i] = K.at(i)+K.at(N-1-i);
for(auto p : K) cout << p+1 << " ";
cout << " ";
for(auto p : S) cout << p+1 << " ";
cout << " ";
//cout << " " << inv(K);
cout << " " << Z.size(v) << endl;
vector<bool> B(N);
}
//cout << N << endl;
long long ans = 0;
for(auto [k,v] : ap) cout << k << "->" << v << endl,ans += k*v;
cout << ans << endl;
cout << endl;
}
}