結果

問題 No.1078 I love Matrix Construction
ユーザー iiljjiiljj
提出日時 2020-06-13 20:31:42
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 348 ms / 2,000 ms
コード長 11,269 bytes
コンパイル時間 3,212 ms
コンパイル使用メモリ 221,112 KB
実行使用メモリ 71,196 KB
最終ジャッジ日時 2024-06-25 20:19:09
合計ジャッジ時間 7,877 ms
ジャッジサーバーID
（参考情報） 		judge2 / 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 AC 2 ms
6,816 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 31 ms
13,056 KB
testcase_03 AC 103 ms
29,132 KB
testcase_04 AC 156 ms
39,008 KB
testcase_05 AC 133 ms
32,908 KB
testcase_06 AC 30 ms
12,672 KB
testcase_07 AC 11 ms
6,948 KB
testcase_08 AC 119 ms
33,116 KB
testcase_09 AC 6 ms
6,940 KB
testcase_10 AC 348 ms
71,196 KB
testcase_11 AC 159 ms
41,004 KB
testcase_12 AC 276 ms
59,576 KB
testcase_13 AC 325 ms
66,944 KB
testcase_14 AC 199 ms
47,040 KB
testcase_15 AC 299 ms
63,220 KB
testcase_16 AC 10 ms
6,944 KB
testcase_17 AC 2 ms
6,944 KB
testcase_18 AC 25 ms
10,368 KB
testcase_19 AC 58 ms
19,752 KB
testcase_20 AC 53 ms
19,340 KB
testcase_21 AC 3 ms
6,940 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 # 

/* #region Head */

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

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                                                        \
    sort(ALL(c));                                                                                                      \
    for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());

#define endl '\n'
#define sqrt sqrtl
#define floor floorl
#define log2 log2l

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
    for (T &x : vec) is >> x;
    return is;
}
template <typename T> ostream &operator<<(ostream &os, vc<T> &vec) { // vector 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}
template <typename T> ostream &operator>>(ostream &os, vc<T> &vec) { // vector 出力 (inline)
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
    return os;
}

template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
    is >> pair_var.first >> pair_var.second;
    return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, pair<T, U> &pair_var) { // pair 出力
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, T &map_var) {
    os << "{";
    REPI(itr, map_var) {
        os << *itr;
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, map<T, U> &map_var) { return out_iter(os, map_var); }
template <typename T, typename U> ostream &operator<<(ostream &os, um<T, U> &map_var) {
    os << "{";
    REPI(itr, map_var) {
        auto [key, value] = *itr;
        os << "(" << key << ", " << value << ")";
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, pq<T> &pq_var) {
    pq<T> pq_cp(pq_var);
    os << "{";
    if (!pq_cp.empty()) {
        os << pq_cp.top(), pq_cp.pop();
        while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
    }
    return os << "}";
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) > 0) DUMPOUT << ", ";
    dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
    if (comp(xmax, x)) {
        xmax = x;
        return true;
    }
    return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
    if (comp(x, xmin)) {
        xmin = x;
        return true;
    }
    return false;
}

// ローカル用
#define DEBUG_

#ifdef DEBUG_
#define DEB
#define dump(...)                                                                                                      \
    DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                                                                    \
            << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl                                        \
            << "    ",                                                                                                 \
        dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

struct AtCoderInitialize {
    static constexpr int IOS_PREC = 15;
    static constexpr bool AUTOFLUSH = false;
    AtCoderInitialize() {
        ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
        cout << fixed << setprecision(IOS_PREC);
        if (AUTOFLUSH) cout << unitbuf;
    }
} ATCODER_INITIALIZE;

string yes = "Yes", no = "No";
// string yes = "YES", no = "NO";
void yn(bool p) { cout << (p ? yes : no) << endl; }

/* #endregion */

/* #region Graph */

// エッジ（本来エッジは双方向だが，ここでは単方向で管理）
template <class weight_t, class flow_t> struct Edge {
    ll src;          // エッジ始点となる頂点
    ll dst;          // エッジ終点となる頂点
    weight_t weight; // 重み
    flow_t cap;
    Edge() : src(0), dst(0), weight(0) {}
    Edge(ll src, ll dst, weight_t weight) : src(src), dst(dst), weight(weight) {}
    Edge(ll src, ll dst, weight_t weight, flow_t cap) : src(src), dst(dst), weight(weight), cap(cap) {}
    // Edge 標準出力
    friend ostream &operator<<(ostream &os, Edge &edge) {
        os << "(" << edge.src << " -> " << edge.dst << ", " << edge.weight << ")";
        return os;
    }
};
// 同じ頂点を始点とするエッジ集合
template <class weight_t, class flow_t> class Node : public vc<Edge<weight_t, flow_t>> {
  public:
    ll idx;
    Node() : vc<Edge<weight_t, flow_t>>() {}
    // void add(int a, int b, weight_t w, flow_t cap) { this->emplace_back(a, b, w, cap); };
};
// graph[i] := 頂点 i を始点とするエッジ集合
template <class weight_t, class flow_t> class Graph : public vc<Node<weight_t, flow_t>> {
  public:
    Graph() : vc<Node<weight_t, flow_t>>() {}
    Graph(int n) : vc<Node<weight_t, flow_t>>(n) { REP(i, 0, n)(*this)[i].idx = i; }
    // 単方向
    void add_arc(int a, int b, weight_t w = 1, flow_t cap = 1) { (*this)[a].emplace_back(a, b, w, cap); }
    // 双方向
    void add_edge(int a, int b, weight_t w = 1, flow_t cap = 1) { add_arc(a, b, w, cap), add_arc(b, a, w, cap); }
};
// using Array = vc<Weight>;
// using Matrix = vc<Array>;

/* #endregion */

/* #region scc */

// 強連結成分分解
template <class weight_t, class flow_t> vll scc(const Graph<weight_t, flow_t> &g) {
    ll n = SIZE(g);                // ノード数
    Graph<weight_t, flow_t> rg(n); // 逆向きのグラフ
    for (const Node<weight_t, flow_t> &es : g)
        for (Edge<weight_t, flow_t> e : es) {
            swap(e.src, e.dst);
            rg[e.src].emplace_back(e);
        }

    vll order;
    order.reserve(n);

    { // dfs 1回目
        vc<bool> visited(n), added(n);
        REP(i, 0, n) {
            if (visited[i]) continue;
            stack<ll> stk;
            stk.push(i);
            while (!stk.empty()) {
                ll cur = stk.top();
                visited[cur] = true;
                bool pushed = false;
                for (const Edge<weight_t, flow_t> &e : g[cur])
                    if (!visited[e.dst]) stk.push(e.dst), pushed = true;
                if (!pushed) { // カレントノードからは未訪問ノードへ到達できない
                    ll t = stk.top();
                    stk.pop(); // 未訪問ノードへ到達できないノードは除いていく
                    if (!added[t]) added[t] = true, order.push_back(t);
                }
            }
        }
        reverse(ALL(order));
    }

    vll ret(n, -1);
    { // dfs 2回目
        ll groupnum = 0;
        for (ll &v : order) {
            if (ret[v] != -1) continue;
            stack<ll> stk;
            stk.push(v);
            while (!stk.empty()) {
                ll cur = stk.top();
                stk.pop(), ret[cur] = groupnum;
                for (Edge<weight_t, flow_t> &e : rg[cur])
                    if (ret[e.dst] == -1) stk.push(e.dst);
            }
            ++groupnum;
        }
    }
    return ret;
}

/* #endregion */

/* #region TwoSat */

// 2-SAT
struct TwoSat {
    using G = Graph<int, int>;
    int _var_cnt;   // 命題論理式に含まれる変数の個数
    int _sz;        // グラフのサイズ
    G graph;        // graph[i] <-> not(graph[i+_var_cnt])
    vc<int> result; // 結果格納用，外からアクセスする前提
    // var_cnt: 変数の個数，P と ¬P あわせて1個．
    TwoSat(int var_cnt) : _var_cnt(var_cnt), _sz(var_cnt * 2), graph(_sz), result(var_cnt) {}
    // (x ∨ y) の形の節を追加する．¬x は x+_var_cnt に変えておく．
    void add_arcs(int x, int y) {
        graph.add_arc((x + _var_cnt) % _sz, y); // ¬x -> y
        graph.add_arc((y + _var_cnt) % _sz, x); // ¬y -> x
    }
    // 充足可能性を判定する．不能なら false. 可能なら result に変数の T/F を入れる．
    bool sat() {
        vll groups = scc(graph);
        // dump(groups);
        REP(i, 0, _var_cnt) if (groups[i] == groups[i + _var_cnt]) return false;
        REP(i, 0, _var_cnt) result[i] = groups[i] > groups[i + _var_cnt];
        return true;
    }
};

/* #endregion */

// Problem
void solve() {
    ll n;
    cin >> n;
    vll s(n), t(n), u(n);
    cin >> s >> t >> u;

    ll var_cnt = n * n;
    TwoSat ts(var_cnt);
    auto idx = [&n](ll row, ll col) -> ll { return n * row + col; };
    REP(i, 0, n) {
        // i 個目の条件
        s[i]--, t[i]--;
        bool on_sj = !(u[i] & 1), on_jt = !((u[i] >> 1) & 1);
        int offset_sj = on_sj ? 0 : var_cnt;
        int offset_jt = on_jt ? 0 : var_cnt;
        // dump(offset_sj, offset_jt);
        REP(j, 0, n) {
            int p1 = idx(s[i], j) + offset_sj;
            int p2 = idx(j, t[i]) + offset_jt;
            // dump(p1, p2);
            ts.add_arcs(p1, p2);
        }
    }

    if (ts.sat()) {
        REP(row, 0, n) {
            REP(col, 0, n) cout << ts.result[idx(row, col)] << (col == n - 1 ? "" : " ");
            cout << endl;
        }
    } else {
        cout << -1 << endl;
    }
}

// entry point
int main() {
    solve();
    return 0;
}
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