結果

問題 No.470 Inverse S+T Problem
ユーザー snteasntea
提出日時 2017-02-20 19:04:04
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 10,102 bytes
コンパイル時間 3,034 ms
コンパイル使用メモリ 215,108 KB
実行使用メモリ 17,864 KB
最終ジャッジ日時 2024-06-01 22:49:19
合計ジャッジ時間 4,530 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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 WA -
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 WA -
testcase_04 AC 1 ms
5,376 KB
testcase_05 WA -
testcase_06 AC 8 ms
6,400 KB
testcase_07 AC 7 ms
6,272 KB
testcase_08 AC 8 ms
6,400 KB
testcase_09 WA -
testcase_10 WA -
testcase_11 WA -
testcase_12 WA -
testcase_13 WA -
testcase_14 WA -
testcase_15 AC 2 ms
5,376 KB
testcase_16 WA -
testcase_17 WA -
testcase_18 WA -
testcase_19 AC 2 ms
5,376 KB
testcase_20 WA -
testcase_21 AC 2 ms
5,376 KB
testcase_22 AC 2 ms
5,376 KB
testcase_23 WA -
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 3 ms
5,376 KB
testcase_29 AC 410 ms
17,864 KB
testcase_30 AC 2 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 # 

#ifdef LOCAL111
	#define _GLIBCXX_DEBUG
#else
	#define NDEBUG
#endif
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
const int INF = 1e9;
using namespace std;
template<typename T, typename U> ostream& operator<< (ostream& os, const pair<T,U>& p) { cout << '(' << p.first << ' ' << p.second << ')'; return os; }

#define endl '\n'
#define ALL(a)  (a).begin(),(a).end()
#define SZ(a) int((a).size())
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define REP(i,n)  FOR(i,0,n)
#define RREP(i,n) for (int i=(n)-1;i>=0;i--)
#ifdef LOCAL111
	#define DEBUG(x) cout<<#x<<": "<<(x)<<endl
	template<typename T> void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
#else
	#define DEBUG(x) true
	template<typename T> void dpite(T a, T b){ return; }
#endif
#define F first
#define S second
#define SNP string::npos
#define WRC(hoge) cout << "Case #" << (hoge)+1 << ": "
template<typename T> void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
template<typename T> bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;}
template<typename T> bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;}


// 検証しなおしたい

//library
typedef long long cost_t;

// class Edge {
// public:
// 	int to = -1, from = -1, rev = -1;
// 	cost_t cost = -1;
	
// 	Edge(){
// 	}

// 	Edge(int x,cost_t y){
// 		to = x;
// 		cost = y;
// 	}

// 	Edge(int x, int y, cost_t z){
// 		from = x;
// 		to = y;
// 		cost = z;
// 	}

// 	Edge(int x, int y, int r, cost_t z){
// 		from = x;
// 		to = y;
// 		cost = z;
// 		rev = r;
// 	}

// 	bool operator< (const Edge& x) const {
// 		if(cost != x.cost) return cost < x.cost;
// 		return to < x.to;
// 	}

// 	bool operator> (const Edge& x) const {
// 		if(cost != x.cost) return cost > x.cost;
// 		return to > x.to;
// 	}
// };

class Edge {
public:
	int to = -1;
	cost_t cost = -1;
	
	Edge(){
	}

	Edge(int x,cost_t y){
		to = x;
		cost = y;
	}

	// Edge(int x, int y, cost_t z){
	// 	// from = x;
	// 	to = y;
	// 	cost = z;
	// }

	// Edge(int x, int y, int r, cost_t z){
	// 	// from = x;
	// 	to = y;
	// 	cost = z;
	// 	// rev = r;
	// }

	bool operator< (const Edge& x) const {
		if(cost != x.cost) return cost < x.cost;
		return to < x.to;
	}

	bool operator> (const Edge& x) const {
		if(cost != x.cost) return cost > x.cost;
		return to > x.to;
	}
};

class Graph {
private:
	typedef vector<Edge> Edges;
	//const long long int INF = (long long)1e18;
	vector<Edges> v; 
	int n;
public:
	Graph(int x){
		n = x;
		v = vector<Edges>(x);
	}

	Graph(){}

	Edges& operator[](int x){
		return v[x];
	}

	const Edges& operator[](int x) const {
		return v[x];
	}

	int size() const {
		return n;
	}

	void add_edge(int from, const Edge &e){
		v[from].push_back(e);
	}

	void add_edge(int from, int to, cost_t cost = -1){
		add_edge(from,Edge(to,cost));
	}

	// void add_edge(int from, int to, cost_t cost = -1, int rev = -1){
	// 	add_edge(from,Edge(from,to,rev,cost));
	// }

	void add_uedge(int from, int to, cost_t cost = -1){
		add_edge(from,to,cost);
		add_edge(to,from,cost);
	}
};


vector<cost_t> dijkstra(int from, const Graph& v)
{
	vector<cost_t> dist(v.size(),INF);
	priority_queue<Edge,vector<Edge>,greater<Edge>> que;
	que.push(Edge(from,0));
	while(!que.empty()){
		Edge e = que.top();
		que.pop();
		if(dist[e.to] == INF){
			dist[e.to] = e.cost;
			for(auto to : v[e.to]){
				if(dist[to.to] == INF)
					que.push(Edge(to.to, e.cost+to.cost));
			}
		}
	}
	return dist;
}

vector<cost_t> bellmanford(int from, const Graph& g)
{
	vector<cost_t> res(g.size(),INF);
	res[from] = 0;
	bool conf = true;
	int cnt = 0;
	while(conf){
		conf = false;
		for(int i = 0; i < g.size(); i++){
			if(res[i] != INF)
			for(const auto& e : g[i]){
				if(res[e.to] > res[i]+e.cost){
					conf = true;
					res[e.to] = res[i]+e.cost;
				}
			}
		}
		if(cnt > g.size()+5) return vector<cost_t>();
		cnt++;
	}
	return res;
}

Graph prim(const Graph g)
{
	using T = tuple<cost_t, int, int>;
	priority_queue<T, vector<T>, greater<T>> qu;
	int n = g.size();
	assert(n != 0);
	vector<bool> added(n,false);
	qu.emplace(0,0,0);
	Graph res(n);
	while(!qu.empty()){
		int from, to;
		cost_t cost;
		tie(cost, from, to) = qu.top();
		qu.pop();
		if(!added[to]){
			added[to] = true;
			res.add_edge(from, to, cost);
			res.add_edge(to, from, cost);
			for(const auto &e : g[to]){
				if(!added[e.to]){
					qu.emplace(e.cost, to, e.to);
				}
			}
		}
	}
	return res;
}

vector<int> getTreeOrder(const Graph &g, int root)
{
	vector<int> res;
	function<void(int p, int pre)> func = [&](int p, int pre){
		for(auto &e : g[p]){
			if(e.to != pre){
				func(e.to,p);
			}
		}
		res.push_back(p);
	};
	func(root,-1);
	return res;
}

vector<int> getTreePar(const Graph &g, int root)
{
	vector<int> par(g.size(),root);
	function<void(int p, int pre)> func = [&](int p, int pre){
		par[p] = pre;
		for(auto &e : g[p]){
			if(e.to != pre){
				func(e.to,p);
			}
		}
	};
	func(root,root);
	return par;
}


vector<int> toposort(const Graph &g)
{
	int n = g.size();
	vector<int> res;
	res.reserve(n);
	vector<bool> used(n,false);
	function<void(int)> rec = [&](int p){
		if(used[p]) return;
		used[p] = true;
		for(auto&& e : g[p]) {
			rec(e.to);
		}
		res.push_back(p);
	};
	for(int i = 0; i < n; ++i) {
		if(!used[i]) rec(i);
	}
	reverse(res.begin(), res.end());
	return res;
}

//0からの連結成分をたどる
tuple<cost_t,int,int> getTreeDiameter(const Graph &g){
	using P = pair<cost_t,int>;
	
	function<P(int,int)> dfs = [&](int p, int par) -> P{
		P res = {0,p};
		for(auto&& e : g[p]) {
			if(e.to == par) continue;
			auto v = dfs(e.to,p);
			v.first += e.cost;
			res = max(res,v);
		}
		return res;
	};	
	auto ap1 = dfs(0,-1);
	auto ap2 = dfs(ap1.second,-1);
	return make_tuple(ap2.first,ap2.second,ap1.second);
}

// res.secondはなければ-1
pair<int,int> getTreeCenter(const Graph& g){
	cost_t di;
	int x, y;
	tie(di, x, y) = getTreeDiameter(g);
	pair<int,int> res(-1,-1);
	cost_t mi;
	function<cost_t(int,int)> rec 
	 = [&](int p, int par) -> cost_t{
		if(p == y){
			return 0;
		}
		cost_t ress = -1;
		for(auto&& e : g[p]) if(e.to != par){
			cost_t v = rec(e.to,p);
			if(v != -1){
				v += e.cost;
				ress = v;
				v = max(v, di-(v));
				if(mi > v){
					mi = v;
					res = {p,-1};
				}else if(mi == v){
					res.second = p;
				}
			}
		}
		return ress;
	};
	rec(x,-1);
	return res;
}
//liblary

//liblary

tuple<vector<int>,int> SCC(const Graph &g)
{
	int n = g.size();
	vector<bool> used(n,false);
	vector<int> cmp(g.size());
	Graph rg(n);
	for(int i = 0; i < n; ++i) {
		for(auto&& e : g[i]) {
			rg.add_edge(e.to,i,e.cost);
		}
	}
	vector<int> vs;
	vs.reserve(g.size());
	
	function<void(int)> dfs = [&](int v){
		used[v] = true;
		for(auto&& e : g[v]) {
			if(!used[e.to]) dfs(e.to);
		}
		vs.push_back(v);
	};

	function<void(int,int)> rdfs = [&](int v, int k){
		used[v] = true;
		cmp[v] = k;
		for(auto&& e : rg[v]) {
			if(!used[e.to]) rdfs(e.to,k); 
		}
	};

	for(int v = 0; v < n; ++v) {
		if(!used[v]) dfs(v);
	}
	fill(used.begin(), used.end(), false);
	int k = 0;
	for(int i = n-1; i >= 0; --i) {
		if(!used[vs[i]]) rdfs(vs[i], k++);
	}
	return make_tuple(cmp,k);
}

Graph getSCCGraph(const Graph &g, vector<int> cmp, int k){
	Graph res(k);
	for(int p = 0; p < (int)g.size(); ++p) {
		for(auto&& e : g[p]) {
			res.add_edge(cmp[p],e);
		}
	}
	return res;
}

//liblary

void vizGraph(const Graph &g, bool with_dir = false, bool with_cap = false){
	ofstream ofs("./out.dot");
	if(with_dir) ofs << "graph graph_name {" << endl;
	else ofs << "digraph graph_name {" << endl;
	for(int i = 0; i < (int)g.size(); i++){
		if (!g[i].size())
			continue;
		for(const auto &e : g[i]){
			if(with_dir){
				if(e.to > i) ofs << "    \"" << i << "\" -- \"" << e.to << '"'; 
			}else ofs << "    \"" << i << "\" -> \"" << e.to << '"'; 
			
			if (with_cap) {
				ofs << " [ label = \"" << (e.cost  == INF ? "inf" : to_string(e.cost)) << "\"];"; 
			}
			if(!with_dir or e.to > i)ofs << endl;
		}
	}
	ofs << "}" << endl;
	ofs.close();
	system("dot -T png out.dot > sample.png");	
}


//library
//Graph, scc に依存
class TwoSATsolver{
private:
	Graph g;
	int center;

public:
	TwoSATsolver(int n){
		center = n;
		g = Graph(2*n+1);
	}

	int f(int x){
		return center+x;
	}

	void add_clause(int x, int y){
		g.add_edge(f(-y),f(x));
		g.add_edge(f(-x),f(y));
	}

	//充足不可能なら空のvectorを返す
	vector<bool> solve(){
		vector<int> cmp;
		int k;
		tie(cmp,k) = SCC(g);
		Graph retg = getSCCGraph(g,cmp,k);

		for(int i = 1; i <= center; ++i) {
			if(cmp[f(i)] == cmp[f(-i)]){
				return vector<bool>();
			}
		}

		vector<bool> res(center+1);
		for(int i = 1; i <= center; ++i) {
			int cmpi = cmp[f(i)];
			int cmpni = cmp[f(-i)];
			assert(cmpi != cmpni);
			if(cmpi > cmpni){
				res[i] = false;
			}else{
				res[i] = true;
			}
		}
		return res;
	}
};
//library

typedef long long int LL;
typedef unsigned long long ULL;
typedef pair<int,int> P;

void ios_init(){
	//cout.setf(ios::fixed);
	//cout.precision(12);
#ifdef LOCAL111
	return;
#endif
	ios::sync_with_stdio(false); cin.tie(0);	
}

int main()
{
	ios_init();
	int n;
	while(cin >> n) {
		vector<string> u(n);
		REP(i,n) cin >> u[i];
		if(n > 3000){
			cout << "Impossible" << endl;
		}else{
			TwoSATsolver sat(n);
			REP(i,n) REP(j,i){
				REP(ci,2) REP(cj,2){
					array<string,4> ar;
					ar[0] = u[i].substr(0,ci+1);
					ar[1] = u[i].substr(ci+1,3-ci-1);
					ar[2] = u[j].substr(0,cj+1);
					ar[3] = u[j].substr(cj+1,3-cj-1);
					// dpite(ALL(ar));
					REP(a,4) REP(b,a){
						if(ar[a] == ar[b]){
							int p = i+1, q = j+1;
							if(ci) p = -p;
							if(cj) q = -q;
							DEBUG(p); DEBUG(q);
							sat.add_clause(p,q);
							break;
						}
					}
				}
			}
			auto res = sat.solve();
			if(SZ(res) == 0){
				cout << "Impossible" << endl;
			}else{
				REP(i,n){
					cout << u[i].substr(0,res[i]+1) << ' ';
					cout << u[i].substr(res[i]+1,3-res[i]-1) << endl;
				}
			}
		}
	}
	return 0;
}
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