結果

問題 No.1436 Rgaph
コンテスト
ユーザー heno239
提出日時 2021-03-20 01:30:53
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 621 ms / 2,000 ms
コード長 5,480 bytes
コンパイル時間 3,545 ms
コンパイル使用メモリ 160,516 KB
最終ジャッジ日時 2025-01-19 20:07:04
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 28
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 optimize("Ofast")
//#pragma GCC target ("sse4")

#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acosl(-1.0);

ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 24;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}


void solve() {
	int n, m; cin >> n >> m;
	vector<P> memo(m);
	vector<vector<int>> G(n);
	rep(i, m) {
		int a, b; cin >> a >> b; a--; b--;
		G[a].push_back(b);
		memo[i] = { a,b };
	}
	rep(i, n) {
		vector<bool> used(n);
		queue<int> q; q.push(i); used[i] = true;
		while (!q.empty()) {
			int v = q.front(); q.pop();
			for (int to : G[v]) {
				if (!used[to]) {
					used[to] = true; q.push(to);
				}
			}
		}
		rep(j, n)if (!used[j]) {
			cout << -1 << "\n"; return;
		}
	}
	vector<bool> can(2 * n);
	queue<int> q;
	can[0] = true; q.push(0);
	while (!q.empty()) {
		int v = q.front(); q.pop();
		int id = v % n;
		int col = v / n;
		for (int to : G[id]) {
			int nex = n * (col ^ 1) + to;
			if (!can[nex]) {
				can[nex] = true; q.push(nex);
			}
		}
	}
	rep(i, 2 * n)if (!can[i]) {
		cout << -1 << "\n"; return;
	}
	if (n == m) {
		cout << -1 << "\n"; return;
	}
	auto find_loop = [&](P p)->vector<P> {
		int fr = p.first;
		int sc = p.second;
		vector<bool> used(n);
		vector<P> res;
		res.push_back(p);
		function<bool(int)> dfs = [&](int id)->bool {
			used[id] = true;
			for (int to : G[id]) {
				if (to == fr) {
					res.push_back({ id,to });
					return true;
				}
				if (!used[to]) {
					if (dfs(to)) {
						res.push_back({ id,to });
						return true;
					}
				}
			}
			return false;
		};
		dfs(sc);
		return res;
	};
	vector<P> loop1 = find_loop(memo[0]);
	//cout << loop1.size() << "\n";
	//rep(i, loop1.size())cout << loop1[i].first << " " << loop1[i].second << "\n";
	vector<P> loop2;
	rep(i, m) {
		bool exi = false;
		rep(j, loop1.size())if (loop1[j] == memo[i])exi = true;
		if (!exi) {
			loop2 = find_loop(memo[i]);
			break;
		}
	}
	//cout << "?? "<<loop2.size() << "\n";
	if (loop1.size() > loop2.size())swap(loop1, loop2);
	vector<P> vexi, nexi;
	rep(i, loop1.size()) {
		bool exi = false;
		rep(j, loop2.size())if (loop1[i] == loop2[j])exi = true;
		if (exi) {
			vexi.push_back(loop1[i]);
		}
		else {
			nexi.push_back(loop1[i]);
		}
	}
	rep(i, nexi.size())vexi.push_back(nexi[i]);
	int sz = loop1.size();
	//cout << "?? " << sz << "\n";
	vector<char> c(sz);
	rep(i, sz) {
		if (i % 2 == 0)c[i] = 'R';
		else c[i] = 'G';
	}
	if (sz % 2 == 0)c.back() = 'R';
	vector<char> ans(m, 'G');
	rep(i, vexi.size()) {
		rep(j, m) {
			if (vexi[i] == memo[j]) {
				ans[j] = c[i];
			}
		}
	}
	rep(i, m)cout << ans[i]; cout << "\n";
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//init_f();
	//init();
	//expr();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
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