#980771 (C++11) No.2755 行列の共役類

提出ソース

結果

問題	No.2755 行列の共役類
ユーザー	leaf_1415
提出日時	2024-05-10 22:32:44
言語	C++11 (gcc 11.4.0)
結果	WA
実行時間	-
コード長	13,882 bytes
コンパイル時間	1,719 ms
コンパイル使用メモリ	139,464 KB
実行使用メモリ	47,800 KB
最終ジャッジ日時	2024-05-10 22:33:05
合計ジャッジ時間	18,937 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

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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 13,756 KB
testcase_01	AC	1 ms 6,940 KB
testcase_02	AC	2 ms 6,944 KB
testcase_03	AC	6 ms 6,940 KB
testcase_04	AC	8 ms 6,944 KB
testcase_05	AC	5 ms 6,940 KB
testcase_06	AC	3 ms 6,944 KB
testcase_07	AC	8 ms 6,944 KB
testcase_08	AC	4 ms 6,944 KB
testcase_09	AC	3 ms 6,944 KB
testcase_10	AC	3 ms 6,944 KB
testcase_11	AC	3 ms 6,940 KB
testcase_12	AC	2 ms 6,944 KB
testcase_13	AC	13 ms 6,944 KB
testcase_14	AC	4 ms 6,944 KB
testcase_15	AC	3 ms 6,940 KB
testcase_16	AC	2 ms 6,940 KB
testcase_17	AC	19 ms 6,944 KB
testcase_18	AC	6 ms 6,940 KB
testcase_19	AC	3 ms 6,940 KB
testcase_20	AC	39 ms 6,940 KB
testcase_21	WA	-
testcase_22	AC	4 ms 6,944 KB
testcase_23	AC	4 ms 6,944 KB
testcase_24	AC	4 ms 6,940 KB
testcase_25	AC	3 ms 6,940 KB
testcase_26	AC	3 ms 6,944 KB
testcase_27	AC	56 ms 6,944 KB
testcase_28	AC	21 ms 6,944 KB
testcase_29	AC	6 ms 6,944 KB
testcase_30	AC	27 ms 6,940 KB
testcase_31	AC	20 ms 6,944 KB
testcase_32	AC	9 ms 6,940 KB
testcase_33	AC	4 ms 6,944 KB
testcase_34	AC	5 ms 6,944 KB
testcase_35	AC	4 ms 6,940 KB
testcase_36	AC	2 ms 6,940 KB
testcase_37	AC	4 ms 6,940 KB
testcase_38	AC	9 ms 6,944 KB
testcase_39	AC	13 ms 6,944 KB
testcase_40	AC	12 ms 6,940 KB
testcase_41	AC	20 ms 6,944 KB
testcase_42	AC	52 ms 6,944 KB
testcase_43	AC	19 ms 6,940 KB
testcase_44	AC	4 ms 6,944 KB
testcase_45	AC	4 ms 6,940 KB
testcase_46	AC	2 ms 6,940 KB
testcase_47	AC	3 ms 6,940 KB
testcase_48	AC	22 ms 6,940 KB
testcase_49	AC	2 ms 6,944 KB
testcase_50	AC	4 ms 6,940 KB
testcase_51	AC	2 ms 6,944 KB
testcase_52	AC	3 ms 6,944 KB
testcase_53	AC	1,566 ms 14,316 KB
testcase_54	AC	639 ms 8,680 KB
testcase_55	AC	271 ms 6,940 KB
testcase_56	AC	2,716 ms 20,520 KB
testcase_57	AC	1,207 ms 11,884 KB
testcase_58	AC	3,041 ms 21,580 KB
testcase_59	AC	1,318 ms 12,008 KB
testcase_60	TLE	-
testcase_61	--	-
testcase_62	--	-
testcase_63	--	-
testcase_64	--	-
testcase_65	--	-

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ソースコード

raw source code

#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstdlib>
#include <cassert>
#include <vector>
#include <list>
#include <stack>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <bitset>
#include <string>
#include <algorithm>
#include <utility>
#include <complex>
#include <array>
#include <unordered_set>
#include <unordered_map>
#define rep(x, s, t) for(ll x = (s); (x) <= (t); (x)++)
#define per(x, s, t) for(ll x = (s); (x) >= (t); (x)--)
#define reps(x, s) for(ll x = 0; (x) < (ll)(s).size(); (x)++)
#define pers(x, s) for(ll x = (ll)(s).size()-1; (x) >= 0; (x)--)
#define chmin(x, y) (x) = min((x), (y))
#define chmax(x, y) (x) = max((x), (y))
#define sz(x) ((ll)(x).size())
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define outl(...) dump_func(__VA_ARGS__)
#define outf(x) cout << fixed << setprecision(16) << (x) << endl
#define pb push_back
#define fi first
#define se second
#define inf 2e18
#define eps 1e-9
const double PI = 3.1415926535897932384626433;

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;

struct edge{
	ll to, cost;
	edge(){}
	edge(ll a, ll b){ to = a, cost = b;}
};
const int dx[] = {1, 0, -1, 0}, dy[] = {0, -1, 0, 1};
const int dx8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dy8[] = {0, -1, -1, -1, 0, 1, 1, 1};

const int mod = 998244353;
//const int mod = 1000000007;

struct mint{
	int x;
	mint(ll y = 0){if(y < 0 || y >= mod) y = (y%mod+mod)%mod; x = y;}
	mint(const mint &ope) {x = ope.x;}
	mint operator-(){return mint(-x);}
	mint operator+(const mint &ope){return mint(x) += ope;}
	mint operator-(const mint &ope){return mint(x) -= ope;}
	mint operator*(const mint &ope){return mint(x) *= ope;}
	mint operator/(const mint &ope){return mint(x) /= ope;}
	mint& operator+=(const mint &ope){x += ope.x; if(x >= mod) x -= mod; return *this;}
	mint& operator-=(const mint &ope){x += mod - ope.x; if(x >= mod) x -= mod; return *this;}
	mint& operator*=(const mint &ope){ll tmp = x; tmp *= ope.x, tmp %= mod; x = tmp; return *this;}
	mint& operator/=(const mint &ope){
		ll n = mod-2; mint mul = ope;
		while(n){if(n & 1) *this *= mul; mul *= mul; n >>= 1;}
		return *this;
	}
	mint inverse(){return mint(1) / *this;}
	bool operator ==(const mint &ope){return x == ope.x;}
	bool operator !=(const mint &ope){return x != ope.x;}
	bool operator <(const mint &ope)const{return x < ope.x;}
};
mint modpow(mint a, ll n){
	if(n == 0) return mint(1);
	if(n % 2) return a * modpow(a, n-1);
	else return modpow(a*a, n/2);
}
istream& operator >>(istream &is, mint &ope){ll t; is >> t, ope = mint(t); return is;}
ostream& operator <<(ostream &os, mint &ope){return os << ope.x;}
ostream& operator <<(ostream &os, const mint &ope){return os << ope.x;}

ll modpow(ll a, ll n, ll mod){
	if(n == 0) return 1;
	if(n % 2) return ((a%mod) * (modpow(a, n-1, mod)%mod)) % mod;
	else return modpow((a*a)%mod, n/2, mod) % mod;
}

vector<mint> fact, fact_inv;
void make_fact(int n){
	fact.resize(n+1), fact_inv.resize(n+1);
	fact[0] = mint(1); rep(i, 1, n) fact[i] = fact[i-1] * mint(i);
	fact_inv[n] = fact[n].inverse(); per(i, n-1, 0) fact_inv[i] = fact_inv[i+1] * mint(i+1);
}
mint comb(int n, int k){ if(n < 0 || k < 0 || n < k) return mint(0); return fact[n] * fact_inv[k] * fact_inv[n-k];}
mint perm(int n, int k){ return comb(n, k) * fact[k]; }
mint divide(int n, int k){ if(n == 0 && k == 0) return 1; return comb(n+k-1, k-1); }
template<typename T> T comb2(ll n, ll k){ if(n < 0 || k < 0 || n < k) return T(0); T ret = 1; rep(i, 1, k) ret *= n-k+i, ret /= i; return ret;}

vector<ll> prime, pvec, qrime;
void make_prime(int n){
	prime.resize(n+1);
	rep(i, 2, n){
		if(prime[i] == 0) pvec.push_back(i), prime[i] = i;
		for(auto p : pvec){ if(i*p > n || p > prime[i]) break; prime[i*p] = p;}
	}
}
void make_qrime(int n){
	qrime.resize(n+1);
	rep(i, 2, n){int ni = i / prime[i]; if(prime[i] == prime[ni]) qrime[i] = qrime[ni] * prime[i]; else qrime[i] = prime[i];}
}
void factorize(ll n, map<ll, ll> &mp){
	mp.clear();
	for(auto p : pvec) while(n % p == 0) mp[p]++, n /= p;
	if(n > 1) mp[n]++;
}

bool exceed(ll x, ll y, ll m){return y > 0 && x >= m / y + 1;}
void mark(){ cout << "*" << endl; }
void yes(){ cout << "Yes" << endl; }
void no(){ cout << "No" << endl; }
ll floor(ll a, ll b){ if(b < 0) a *= -1, b *= -1; if(a >= 0) return a/b; else return -((-a+b-1)/b); }
ll ceil(ll a, ll b){ if(b < 0) a *= -1, b *= -1; if(a >= 0) return (a+b-1)/b; else return -((-a)/b); }
ll modulo(ll a, ll b){ b = abs(b); return a - floor(a, b) * b;}
ll sgn(ll x){ if(x > 0) return 1; if(x < 0) return -1; return 0;}
ll gcd(ll a, ll b){if(b == 0) return a; return gcd(b, a%b);}
ll lcm(ll a, ll b){return a/gcd(a, b)*b;}
template<typename T> T arith(T x){return x*(x+1)/2;}
template<typename T> T arith2(T x){return x*(x+1)*(x*2+1)/6;}
ll digitnum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret++; return ret;}
ll digitsum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret += x % b; return ret;}
string lltos(ll x, ll b = 10){if(x == 0) return "0"; string ret; for(;x;x/=b) ret += x % b + '0'; reverse(all(ret)); return ret;}
ll stoll(string &s, ll b = 10){ll ret = 0; for(auto c : s) ret *= b, ret += c - '0'; return ret;}
template<typename T> void uniq(T &vec){sort(all(vec)); vec.erase(unique(all(vec)), vec.end());}
int popcount(ull x){
	x -= ((x>>1)&0x5555555555555555ULL), x = (x & 0x3333333333333333ULL) + ((x>>2) & 0x3333333333333333ULL);
	return (((x + (x>>4)) & 0x0F0F0F0F0F0F0F0FULL) * 0x0101010101010101ULL) >> 56;
}
template<typename T> vector<pair<T, ll>> rle(vector<T> vec){
	vector<pair<T, ll>> ret;
	for(auto x : vec){if(sz(ret) == 0 || ret.back().first != x) ret.push_back(P(x, 1)); else ret.back().second++;}
	return ret;
}
vector<pair<char, ll>> rle(string s){ vector<char> vec; for(auto c : s) vec.push_back(c); return rle(vec);}

template<class S, class T> pair<S, T>& operator+=(pair<S, T> &s, const pair<S, T> &t){s.first += t.first, s.second += t.second; return s;}
template<class S, class T> pair<S, T>& operator-=(pair<S, T> &s, const pair<S, T> &t){s.first -= t.first, s.second -= t.second; return s;}
template<class S, class T> pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t){return pair<S,T>(s.first+t.first, s.second+t.second);}
template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t){return pair<S,T>(s.first-t.first, s.second-t.second);}
template<class T> T dot(const pair<T, T> &s, const pair<T, T> &t){return s.first*t.first + s.second*t.second;}
template<class T> T cross(const pair<T, T> &s, const pair<T, T> &t){return s.first*t.second - s.second*t.first;}
template<class T> T mdist(pair<T, T> s, pair<T, T> t){return abs(s.first-t.first) + abs(s.second-t.second);}
template<class T> T cdist(pair<T, T> s, pair<T, T> t){return max(abs(s.first-t.first), abs(s.second-t.second));}
template<class T> T edist2(pair<T, T> s, pair<T, T> t){return (s.first-t.first)*(s.first-t.first) + (s.second-t.second)*(s.second-t.second);}

template<typename T> ostream& operator << (ostream& os, vector<T>& vec){reps(i, vec) os << vec[i] << " "; return os;}
template<typename T> ostream& operator << (ostream& os, const vector<T>& vec){reps(i, vec) os << vec[i] << " "; return os;}
template<typename T> ostream& operator << (ostream& os, list<T>& ls){for(auto x : ls) os << x << " "; return os;}
template<typename T> ostream& operator << (ostream& os, const list<T>& ls){for(auto x : ls) os << x << " "; return os;}
template<typename T> ostream& operator << (ostream& os, deque<T>& deq){reps(i,  deq) os << deq[i] << " "; return os;}
template<typename T, typename U> ostream& operator << (ostream& os, pair<T, U>& ope){ os << "(" << ope.first << ", " << ope.second << ")"; return os;}
template<typename T, typename U> ostream& operator << (ostream& os, const pair<T, U>& ope){ os << "(" << ope.first << ", " << ope.second << ")"; return os;}
template<typename T, typename U> ostream& operator << (ostream& os, map<T, U>& ope){ for(auto p : ope) os << "(" << p.first << ", " << p.second << "),";return os;}
template<typename T> ostream& operator << (ostream& os, set<T>& ope){for(auto x : ope) os << x << " "; return os;}
template<typename T> ostream& operator << (ostream& os, multiset<T>& ope){for(auto x : ope) os << x << " "; return os;}
template<typename T> void outa(T a[], ll s, ll t){rep(i, s, t){ cout << a[i]; if(i < t) cout << " ";} cout << endl;}
template<typename T, size_t N> ostream& operator << (ostream& os, array<T, N>& arr){reps(i, arr) os << arr[i] << " "; return os;}
template<typename T, size_t N> ostream& operator << (ostream& os, const array<T, N>& arr){reps(i, arr) os << arr[i] << " "; return os;}
void dump_func(){cout << endl;}
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&... tail){cout << head; if(sizeof...(Tail) > 0) cout << " "; dump_func(std::move(tail)...);}
template<typename T> void bssert(bool b, T t){ if(!b) cout << t << endl, exit(0); }

struct UnionFind{
	int size;
	vector<int> parent;
	vector<int> rank;
	vector<ll> v, e;

	UnionFind(){}
	UnionFind(int size){
		this->size = size;
		parent.resize(size+1);
		rank.resize(size+1);
		v.resize(size+1);
		e.resize(size+1);
		init();
	}
	void init(){
		for(int i = 0; i <= size; i++){
			parent[i] = i, rank[i] = 0;
			v[i] = 1, e[i] = 0;
		}
	}
	int root(int i){
		if(parent[i] == i) return i;
		return parent[i] = root(parent[i]);
	}
	bool same(int i, int j){
		return root(i) == root(j);
	}
	void merge(int i, int j){ // j will become new root
		parent[i] = j;
		v[j] += v[i];
		e[j] += e[i] + 1;
	}
	void unite(int i, int j){
		int root_i = root(i), root_j = root(j);
		if(root_i == root_j){
			e[root_i]++;
			return;
		}
		if(rank[root_i] < rank[root_j]) merge(root_i, root_j);
		else merge(root_j, root_i);
		if(rank[root_i] == rank[root_j]) rank[root_i]++;
	}
};

struct Matrix{
	typedef ll T;

	int h, w;
	array<T, 4> mat;
	Matrix(){h = w = 0;}
	Matrix(int h, int w){
		this->h = h, this->w = w;
		//mat.resize(h*w);
	}

	T addope(T a, T b){ return a+b; } //addtive operator
	static T addIdent(){ return 0;} //additive identity
	T mulope(T a, T b){ return a*b; } //multiplicative operator
	static T mulIdent(){ return 1; } //multiplicative identity

	T& at(int i, int j){ return mat[w*(i-1)+(j-1)];}
	static Matrix Ident(int size){
		Matrix ret(size, size);
		rep(i, 1, size) rep(j, 1, size){
			if(i == j) ret.at(i, j) = mulIdent();
			else ret.at(i, j) = addIdent();
		}
		return ret;
	}
	Matrix operator+(Matrix& ope){
		Matrix ret(h, w);
		rep(i, 1, h) rep(j, 1, w) ret.at(i, j) = at(i, j) + ope.at(i, j);
		return ret;
	}
	Matrix operator*(Matrix& ope){
		Matrix ret(h, ope.w);
		rep(i, 1, h) rep(j, 1, ope.w){
			ret.at(i, j) = addIdent();
			rep(k, 1, w) ret.at(i, j) = addope(ret.at(i, j), mulope(at(i, k), ope.at(k, j)));
		}
		return ret;
	}
	Matrix pow(ll n){
		if(n == 0) return Ident(h);
		if(n % 2) return pow(n-1) * (*this);
		else{
			Matrix tmp = pow(n/2);
			return tmp * tmp;
		}
	}
};
ostream& operator << (ostream& os, Matrix& mat) {
	rep(i, 1, mat.h){rep(j, 1, mat.w) os << mat.mat[mat.w*(i-1)+(j-1)] << " "; cout << endl;}
	return os;
}
ostream& operator << (ostream& os, const Matrix& mat) {
	rep(i, 1, mat.h){rep(j, 1, mat.w) os << mat.mat[mat.w*(i-1)+(j-1)] << " "; cout << endl;}
	return os;
}


struct Congruence{
	//find (x, y) such that ax+by = gcd(a, b), and return gcd(a, b)
	static ll extgcd(ll a, ll b, ll &x, ll &y)
	{
		if(b == 0){
			x = 1, y = 0;
			return a;
		}
		ll xx, yy;
		ll d = extgcd(b, a%b, xx, yy);
		x = yy, y = xx-(a/b)*yy;
		return d;
	}

	//return a^{-1} (mod m); if not exists (gcd(a, m)!=1), then return -1
	static ll mod_inverse(ll a, ll m)
	{
		ll x, y;
		if(extgcd(a, m, x, y) != 1) return -1;
		return (x%m + m) % m;
	}

	static ll mul(ll a, ll n, ll mod){
		if(n == 0) return 0;
		if(n % 2) return (mul(a, n-1, mod) + a) % mod;
		else return mul(a, n/2, mod) * 2 % mod;
	}
	//return x(mod m/gcd(a, m)) such that ax = b (mod m); if not exists (b%gcd(a, m)!=0), then return (0, -1)
	static P congruence(ll a, ll b, ll m)
	{
		ll d = gcd(a, m);
		if(b % d) return make_pair(0, -1);
		a /= d, b /= d, m /= d;
		return P(mul(b%m, mod_inverse(a, m)%m, m), m);
	}

	//return a solution (x, M) of system of congruence a_i*x = b_i (mod m_i)(i = 1, 2, ..., n; if not exists, then return (0, -1)
	static P simultaneous(ll a[], ll b[], ll m[], ll n)
	{
		ll x = 0, M = 1;
		for(int i = 1; i <= n; i++){
			P res = congruence(a[i]*M, (b[i]-a[i]*x%m[i]+m[i])%m[i], m[i]);
			if(res.second == -1) return res;
			x += M*res.first, M *= res.second;
		}
		return make_pair(x, M);
	}
};

ll b, c;
ll inv[605];

int main(void)
{
	ios::sync_with_stdio(0);
	cin.tie(0);

	cin >> b >> c;

	vector<P> vec;
	rep(i, 1, b-1){
		if(gcd(i, b) > 1) continue;
		rep(j, 0, b-1){
			if(j % c) continue;
			vec.pb(P(i, j));
		}
	}
	//for(auto p : vec) outl(p);

	rep(i, 1, b-1) inv[i] = Congruence::mod_inverse(i, b);
	map<P, ll> mp;
	reps(i, vec) mp[vec[i]] = i;

	UnionFind uf(sz(vec)+5); ll cnt = 0;
	reps(i, vec){
		if(uf.v[uf.root(i)] >= 2) continue;
		cnt++;
		if(cnt > 100){
			outl("100+");
			return 0;
		}
		rep(j, i+1, sz(vec)-1){
			Matrix p = Matrix(2, 2), r = Matrix(2, 2), rinv = Matrix(2, 2);

			p.at(1, 1) = vec[i].fi, p.at(1, 2) = vec[i].se, p.at(2, 1) = 0, p.at(2, 2) = 1;
			r.at(1, 1) = vec[j].fi, r.at(1, 2) = vec[j].se, r.at(2, 1) = 0, r.at(2, 2) = 1;
			rinv = r, rinv.at(1, 2) *= -1, rinv.at(2, 1) *= -1, swap(rinv.at(1, 1), rinv.at(2, 2));
			ll ainv = inv[modulo(r.at(1, 1), b)];

			rep(k, 1, 2) rep(l, 1, 2) rinv.at(k, l) *= ainv;

			Matrix q = rinv * p * r;
			uf.unite(i, mp[P(modulo(q.at(1, 1), b), modulo(q.at(1, 2), b))]);
		}
	}

	set<ll> S;
	reps(i, vec) S.insert(uf.root(i));
	ll ans = sz(S);
	chmax(ans, 1LL);
	if(ans > 100) outl("100+");
	else outl(ans);

	return 0;
}

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結果

テストケース

ソースコード