結果

問題 No.470 Inverse S+T Problem
ユーザー SHIJOUSHIJOU
提出日時 2020-10-27 18:48:21
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 72 ms / 2,000 ms
コード長 6,743 bytes
コンパイル時間 2,732 ms
コンパイル使用メモリ 232,408 KB
実行使用メモリ 12,616 KB
最終ジャッジ日時 2024-06-01 23:05:57
合計ジャッジ時間 4,119 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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 2 ms
5,248 KB
testcase_01 AC 1 ms
5,248 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 70 ms
12,616 KB
testcase_07 AC 70 ms
12,564 KB
testcase_08 AC 72 ms
12,544 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 AC 1 ms
5,376 KB
testcase_12 AC 2 ms
5,376 KB
testcase_13 AC 2 ms
5,376 KB
testcase_14 AC 2 ms
5,376 KB
testcase_15 AC 1 ms
5,376 KB
testcase_16 AC 2 ms
5,376 KB
testcase_17 AC 2 ms
5,376 KB
testcase_18 AC 1 ms
5,376 KB
testcase_19 AC 2 ms
5,376 KB
testcase_20 AC 2 ms
5,376 KB
testcase_21 AC 2 ms
5,376 KB
testcase_22 AC 2 ms
5,376 KB
testcase_23 AC 2 ms
5,376 KB
testcase_24 AC 2 ms
5,376 KB
testcase_25 AC 2 ms
5,376 KB
testcase_26 AC 2 ms
5,376 KB
testcase_27 AC 2 ms
5,376 KB
testcase_28 AC 9 ms
5,376 KB
testcase_29 AC 3 ms
5,376 KB
testcase_30 AC 6 ms
5,376 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 # 

//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
#define rep(i, n) for(int i=0; i<n; ++i)
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
using namespace std;
using ll = int64_t;
using ld = long double;
using P = pair<int, int>;
using vs = vector<string>;
using vi = vector<int>;
using vvi = vector<vi>;
template<class T> using PQ = priority_queue<T>;
template<class T> using PQG = priority_queue<T, vector<T>, greater<T> >;
const int INF = 0xccccccc;
const ll LINF = 0xcccccccccccccccLL;
template<typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {return a < b && (a = b, true);}
template<typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {return a > b && (a = b, true);}
template<typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) { return is >> p.first >> p.second;}
template<typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) { return os << p.first << ' ' << p.second;}

struct SCC {
	struct csr {
		vector<int> start, elist;
		csr(int n, const vector<pair<int, int>> &edges)
			: start(n+1), elist(edges.size()) {
				for(pair<int, int> e:edges) {
					start[e.first+1]++;
				}
				for(int i = 1; i <= n; i++) {
					start[i] += start[i-1];
				}
				vector<int> counter = start;
				for(pair<int, int> e:edges) {
					elist[counter[e.first]++] = e.second;
				}
		}
	};
	int n;
	vector<pair<int, int>> edges;
	SCC(int n_) : n(n_) {}
	void add(int from, int to) {edges.emplace_back(from, to);}
	pair<int, vector<int>> scc_ids() {
		csr g(n, edges);
		int now_ord = 0, group_num = 0;
		vector<int> used, low(n), ord(n, -1), ids(n);
		used.reserve(n);
		auto dfs = [&](auto self, int v)->void {
			low[v] = ord[v] = now_ord++;
			used.push_back(v);
			for(int i = g.start[v]; i < g.start[v+1]; i++) {
				int to = g.elist[i];
				if(ord[to] == -1) {
					self(self, to);
					low[v] = min(low[v], low[to]);
				}
				else {
					low[v] = min(low[v], ord[to]);
				}
			}
			if(low[v] == ord[v]) {
				while(true) {
					int u = used.back();
					used.pop_back();
					ord[u] = n;
					ids[u] = group_num;
					if(u == v) break;
				}
				group_num++;
			}
		};
		for(int i = 0; i < n; i++) {
			if(ord[i] == -1) dfs(dfs, i);
		}
		for(int &x:ids) {
			x = group_num - 1 - x;
		}
		return {group_num, ids};
	}
	vector<vector<int>> scc() {
		pair<int, vector<int>> ids = scc_ids();
		int group_num = ids.first;
		vector<int> counts(group_num);
		for(int x:ids.second) counts[x]++;
		vector<vector<int>> groups(group_num);
		for(int i = 0; i < group_num; i++) {
			groups[i].reserve(counts[i]);
		}
		for(int i = 0; i < n; i++) {
			groups[ids.second[i]].push_back(i);
		}
		return groups;
	}
};

//SCC is needed

struct two_sat {
	int n;
	vector<bool> boolean_val;
	SCC scc;
	two_sat():n(0), scc(0) {}
	two_sat(int n_):n(n_), boolean_val(n_), scc(n_<<1) {}

	void add(int i, bool ii, int j, bool jj) {
		scc.add(i + (ii?0:n), j + (jj?n:0));
		scc.add(j + (jj?0:n), i + (ii?n:0));
	}
	bool satisfiable() {
		vector<int> id = scc.scc_ids().second;
		for(int i = 0; i < n; i++) {
			if(id[i] == id[i+n]) return false;
			boolean_val[i] = id[i] < id[i+n];
		}
		return true;
	}
};

#undef _GLIBCXX_DEBUG
string to_string(const string &s) {return '"' + s + '"';}
string to_string(const char *s) {return to_string(string(s));}
string to_string(bool b) {return b?"true":"false";}
string to_string(vector<bool> v) {
	string res = "{";
	for(int i = 0; i < int(v.size()); i++) {
		if(i) res += ", ";
		res += to_string(v[i]);
	}
	res += "}";
	return res;
}
template<size_t N>
string to_string(bitset<N> v) {
	string res;
	for(size_t i = 0; i < N; i++) res += char('0' + v[i]);
	return res;
}
template<class A, class B>
string to_string(pair<A, B>);
template<class A, class B, class C>
string to_string(tuple<A, B, C>);
template<class A, class B, class C, class D>
string to_string(tuple<A, B, C, D>);
template<class A>
string to_string(A v) {
	bool first = true;
	string res = "{";
	for(const auto &x:v) {
		if(!first) res += ", ";
		first = false;
		res += to_string(x);
	}
	res += "}";
	return res;
}
template<class A, class B>
string to_string(pair<A, B> p) {
	return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template<class A, class B, class C>
string to_string(tuple<A, B, C> t) {
	return "(" + to_string(get<0>(t)) + ", " + to_string(get<1>(t)) + ", " + to_string(get<2>(t)) + ")";
}
template<class A, class B, class C, class D>
string to_string(tuple<A, B, C, D> t) {
	return "(" + to_string(get<0>(t)) + ", " + to_string(get<1>(t)) + ", " + to_string(get<2>(t)) + ", " + to_string(get<3>(t)) + ")";
}
void debug_out() {cerr << endl;}
template<typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
	cerr << ' ' << to_string(H);
	debug_out(T...);
}
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 822
#endif

//head

void imp() {
	cout << "Impossible\n";
}

int pl(vs::iterator itb, vs::iterator ite, string s) {
	auto itr = upper_bound(itb, ite, s);
	itr--;
	int res = itr-itb;
	(*itr).back()++;
	return res;
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	int n;
	cin >> n;
	vs s(n), s_(n), s__(n);
	rep(i, n) {
		cin >> s[i];
		s_[i] = s[i];
		s__[i] = s[i];
		reverse(all(s__[i]));
	}
	sort(all(s_));
	sort(all(s__));
	rep(i, n) {
		auto it = equal_range(all(s_), s_[i]);
		if(it.second-it.first > 2 or n > 52) {
			imp();
			return 0;
		}
	}
	two_sat ts(n);
	vector<P> p(n);
	vi _(n), __(n);
	rep(i, n) {
		string x = s[i];
		int u = pl(all(s_), x);
		reverse(all(x));
		int v = pl(all(s__), x);
		p[i] = {u, v};
		_[u] = i;
		__[v] = i;
	}
	//debug(_);//debug(__);
	rep(i, n) {
		int j = p[i].first+1;
		while(j < n and s_[j][0] == s[i][0]) {
			ts.add(i, true, _[j++], true);
		}
		auto itr = lower_bound(all(s_), s[i].substr(2));
		j = itr-s_.begin();
		while(j < n and s_[j][0] == s[i][2]) {
			//debug(i, _[j], s[i], s[_[j]]);
			ts.add(i, false, _[j++], true);
		}
		j = p[i].second+1;
		while(j < n and s__[j][0] == s[i][2]) {
			ts.add(i, false, __[j++], false);
		}
		
		string ss = s[i].substr(0, 2);
		j = p[i].first+1;
		while(j < n and s_[j].substr(0, 2) == ss) {
			ts.add(i, false, _[j++], false);
		}
		ss = s[i].substr(1);
		itr = lower_bound(all(s_), ss);
		j = itr-s_.begin();
		while(j < n and s_[j].substr(0, 2) == ss) {
			ts.add(i, true, _[j++], false);
		}
		reverse(all(ss));
		j = p[i].second+1;
		while(j < n and s__[j].substr(0, 2) == ss) {
			ts.add(i, true, __[j++], true);
		}
	}
	if(!ts.satisfiable()) {
		imp();
		return 0;
	}
	rep(i, n) {
		if(ts.boolean_val[i]) {
			cout << s[i].substr(0, 2) << ' ' << s[i][2] << '\n';
		}
		else {
			cout << s[i][0] << ' ' << s[i].substr(1) << '\n';
		}
	}
}
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