結果

問題 No.470 Inverse S+T Problem
ユーザー Coki628Coki628
提出日時 2020-12-16 17:16:32
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 7,916 bytes
コンパイル時間 2,589 ms
コンパイル使用メモリ 235,400 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-06-01 23:06:09
合計ジャッジ時間 3,676 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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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 1 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 2 ms
5,376 KB
testcase_09 AC 1 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 AC 2 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 2 ms
5,376 KB
testcase_16 AC 2 ms
5,376 KB
testcase_17 AC 2 ms
5,376 KB
testcase_18 AC 2 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 1 ms
5,376 KB
testcase_24 AC 2 ms
5,376 KB
testcase_25 AC 2 ms
5,376 KB
testcase_26 AC 1 ms
5,376 KB
testcase_27 AC 2 ms
5,376 KB
testcase_28 AC 1 ms
5,376 KB
testcase_29 AC 1 ms
5,376 KB
testcase_30 AC 1 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 # 

// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ld = long double;
using pll = pair<ll, ll>;
using pii = pair<int, int>;
using vvl = vector<vector<ll>>;
using vvi = vector<vector<int>>;
using vvpll = vector<vector<pll>>;
#define rep(i, a, b) for (ll i=(a); i<(b); i++)
#define rrep(i, a, b) for (ll i=(a); i>(b); i--)
#define pb push_back
#define tostr to_string
#define ALL(A) A.begin(), A.end()
constexpr ll INF = LONG_LONG_MAX;
constexpr ll MOD = 1000000007;

template<typename T> vector<vector<T>> list2d(int N, int M, T init) { vector<vector<T>> res(N, vector<T>(M, init)); return res; }
template<typename T> vector<vector<vector<T>>> list3d(int N, int M, int L, T init) { vector<vector<vector<T>>> res(N, vector<vector<T>>(M, vector<T>(L, init))); return res; }

void print(ld out) { cout << fixed << setprecision(15) << out << '\n'; }
void print(double out) { cout << fixed << setprecision(15) << out << '\n'; }
template<typename T> void print(T out) { cout << out << '\n'; }
template<typename T1, typename T2> void print(pair<T1, T2> out) { cout << out.first << ' ' << out.second << '\n'; }
template<typename T> void print(vector<T> A) { rep(i, 0, A.size()) { cout << A[i]; cout << (i == A.size()-1 ? '\n' : ' '); } }
template<typename T> void print(set<T> S) { vector<T> A(S.begin(), S.end()); print(A); }

void Yes() { print("Yes"); }
void No() { print("No"); }
void YES() { print("YES"); }
void NO() { print("NO"); }

ll floor(ll a, ll b) { if (a < 0) { return (a-b+1) / b; } else { return a / b; } }
ll ceil(ll a, ll b) { if (a >= 0) { return (a+b-1) / b; } else { return a / b; } }
pll divmod(ll a, ll b) { ll d = a / b; ll m = a % b; return {d, m}; }
template<typename T> bool chmax(T &x, T y) { return (y > x) ? x = y, true : false; }
template<typename T> bool chmin(T &x, T y) { return (y < x) ? x = y, true : false; }

template<typename T> T sum(vector<T> A) { T res = 0; for (T a: A) res += a; return res; }
template<typename T> T max(vector<T> A) { return *max_element(ALL(A)); }
template<typename T> T min(vector<T> A) { return *min_element(ALL(A)); }

ll toint(string s) { ll res = 0; for (char c : s) { res *= 10; res += (c - '0'); } return res; }
int toint(char num) { return num - '0'; }
char tochar(int num) { return '0' + num; }
int ord(char c) { return (int)c; }
char chr(int a) { return (char)a; }

ll pow(int x, ll n) { ll res = 1; rep(_, 0, n) res *= x; return res; }
ll pow(ll x, ll n, int mod) { ll res = 1; while (n > 0) { if (n & 1) { res = (res * x) % mod; } x = (x * x) % mod; n >>= 1; } return res; }

int popcount(ll S) { return __builtin_popcountll(S); }
ll gcd(ll a, ll b) { return __gcd(a, b); }

#ifndef ATCODER_INTERNAL_SCC_HPP
#define ATCODER_INTERNAL_SCC_HPP 1
#include <algorithm>
#include <utility>
#include <vector>
namespace atcoder {
namespace internal {
template <class E> struct csr {
    std::vector<int> start;
    std::vector<E> elist;
    csr(int n, const std::vector<std::pair<int, E>>& edges)
        : start(n + 1), elist(edges.size()) {
        for (auto e : edges) {
            start[e.first + 1]++;
        }
        for (int i = 1; i <= n; i++) {
            start[i] += start[i - 1];
        }
        auto counter = start;
        for (auto e : edges) {
            elist[counter[e.first]++] = e.second;
        }
    }
};
// Reference:
// R. Tarjan,
// Depth-First Search and Linear Graph Algorithms
struct scc_graph {
  public:
    scc_graph(int n) : _n(n) {}
    int num_vertices() { return _n; }
    void add_edge(int from, int to) { edges.push_back({from, {to}}); }
    // @return pair of (# of scc, scc id)
    std::pair<int, std::vector<int>> scc_ids() {
        auto g = csr<edge>(_n, edges);
        int now_ord = 0, group_num = 0;
        std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
        visited.reserve(_n);
        auto dfs = [&](auto self, int v) -> void {
            low[v] = ord[v] = now_ord++;
            visited.push_back(v);
            for (int i = g.start[v]; i < g.start[v + 1]; i++) {
                auto to = g.elist[i].to;
                if (ord[to] == -1) {
                    self(self, to);
                    low[v] = std::min(low[v], low[to]);
                } else {
                    low[v] = std::min(low[v], ord[to]);
                }
            }
            if (low[v] == ord[v]) {
                while (true) {
                    int u = visited.back();
                    visited.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 (auto& x : ids) {
            x = group_num - 1 - x;
        }
        return {group_num, ids};
    }
    std::vector<std::vector<int>> scc() {
        auto ids = scc_ids();
        int group_num = ids.first;
        std::vector<int> counts(group_num);
        for (auto x : ids.second) counts[x]++;
        std::vector<std::vector<int>> groups(ids.first);
        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;
    }
  private:
    int _n;
    struct edge {
        int to;
    };
    std::vector<std::pair<int, edge>> edges;
};
}  // namespace internal
}  // namespace atcoder
#endif  // ATCODER_INTERNAL_SCC_HPP
#ifndef ATCODER_TWOSAT_HPP
#define ATCODER_TWOSAT_HPP 1
#include <cassert>
#include <vector>
namespace atcoder {
// Reference:
// B. Aspvall, M. Plass, and R. Tarjan,
// A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean
// Formulas
struct two_sat {
  public:
    two_sat() : _n(0), scc(0) {}
    two_sat(int n) : _n(n), _answer(n), scc(2 * n) {}
    void add_clause(int i, bool f, int j, bool g) {
        assert(0 <= i && i < _n);
        assert(0 <= j && j < _n);
        scc.add_edge(2 * i + (f ? 0 : 1), 2 * j + (g ? 1 : 0));
        scc.add_edge(2 * j + (g ? 0 : 1), 2 * i + (f ? 1 : 0));
    }
    bool satisfiable() {
        auto id = scc.scc_ids().second;
        for (int i = 0; i < _n; i++) {
            if (id[2 * i] == id[2 * i + 1]) return false;
            _answer[i] = id[2 * i] < id[2 * i + 1];
        }
        return true;
    }
    std::vector<bool> answer() { return _answer; }
  private:
    int _n;
    std::vector<bool> _answer;
    internal::scc_graph scc;
};
}  // namespace atcoder
#endif  // ATCODER_TWOSAT_HPP
using namespace atcoder;

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

    map<string, vector<pair<ll, bool>>> cond;
    ll N;
    cin >> N;

    if (N > 52) {
        print("Impossible");
        return 0;
    }
    vector<string> A(N);
    rep(i, 0, N) {
        string s;
        cin >> s;
        cond[s.substr(0, 2)].pb({i, 1});
        cond[s.substr(2)].pb({i, 1});
        cond[s.substr(0, 1)].pb({i, 0});
        cond[s.substr(1)].pb({i, 0});
        A[i] = s;
    }

    // ts[i] := i番目の文字列を前2,後ろ1で切る
    two_sat ts(N);
    for (auto& [s, li] : cond) {
        ll m = li.size();
        rep(i, 0, m) {
            auto [idx1, flag1] = li[i];
            rep(j, i+1, m) {
                auto [idx2, flag2] = li[j];
                ts.add_clause(idx1, 1-flag1, idx2, 1-flag2);
            }
        }
    }

    if (ts.satisfiable()) {
        auto ans = ts.answer();
        rep(i, 0, N) {
            if (ans[i]) {
                cout << A[i].substr(0, 2) << ' ' << A[i].substr(2) << '\n';
            } else {
                cout << A[i].substr(0, 1) << ' ' << A[i].substr(1) << '\n';
            }
        }
    } else {
        print("Impossible");
    }
    return 0;
}
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