#674015 (C++17) No.1587 012 Matrix

提出ソース
結果

問題	No.1587 012 Matrix
ユーザー	iiljj
提出日時	2021-07-08 22:50:08
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	TLE
実行時間	-
コード長	16,418 bytes
コンパイル時間	2,133 ms
コンパイル使用メモリ	163,540 KB
実行使用メモリ	41,600 KB
最終ジャッジ日時	2024-07-01 13:01:08
合計ジャッジ時間	8,046 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 13,760 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	3 ms 6,940 KB
testcase_08	AC	5 ms 6,944 KB
testcase_09	AC	11 ms 6,944 KB
testcase_10	AC	35 ms 6,940 KB
testcase_11	AC	105 ms 8,044 KB
testcase_12	AC	270 ms 11,368 KB
testcase_13	AC	694 ms 16,236 KB
testcase_14	TLE	-
testcase_15	TLE	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
testcase_19	--	-
testcase_20	--	-
testcase_21	--	-
testcase_22	--	-
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ソースコード

raw source code
/* #region Head */

// #include <bits/stdc++.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert> // assert.h
#include <cmath>   // math.h
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
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 TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i))
#define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i))
#define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i))
#define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d))
#define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d))

#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 REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); 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 CEIL(a, b) (((a) + (b)-1) / (b))

#define endl '\n'

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
// constexpr ll MOD = 998244353;
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, const 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, const 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, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr) { // array 入力
    REP(i, 0, SIZE(arr)) is >> arr[i];
    return is;
}
template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr) { // array 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    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, const 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, const 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, const map<T, U> &map_var) {
    return out_iter(os, map_var);
}
template <typename T, typename U> ostream &operator<<(ostream &os, const 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, const set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const 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 << "}";
}

void pprint() { cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {
    cout << head;
    if (sizeof...(Tail) > 0) cout << ' ';
    pprint(move(tail)...);
}

// 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
#ifndef ONLINE_JUDGE
#define DEBUG_
#endif

#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

#define VAR(type, ...)                                                                                                 \
    type __VA_ARGS__;                                                                                                  \
    cin >> __VA_ARGS__;

template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }
template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }

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;

void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }

/* #endregion */

// #include <atcoder/all>
// using namespace atcoder;

/* #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 = int, class flow_t = int> 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 = int, class flow_t = int> 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 = int, class flow_t = int> 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 DINIC_SPARSE */

// using flow_type = int;

template <class flow_type> struct dinic_sparse {
    struct edge {
        int src, dst;
        flow_type cap, flow;
        int rev_idx;
        bool is_rev;
    };
    int n, s, t;
    std::vector<std::vector<edge>> g;
    std::vector<int> level, prog, que;
    std::vector<std::pair<std::pair<int, int>, flow_type>> edges;

    dinic_sparse(int n_ = 0) : n(n_) {}

    // Compute the maximum-flow from `s_` to `t_` by Dinic's algorithm.
    flow_type maximum_flow(int s_, int t_) {
        s = s_;
        t = t_;
        make_graph();
        que.resize(n);
        flow_type res = 0;
        while (levelize()) {
            prog.assign(n, 0);
            res += augment(s, std::numeric_limits<flow_type>::max());
        }
        return res;
    }

    // Add an edge from `u` to `v` with capacity `c`. Note that it will be added
    // to `g` when `make_graph` is called instead of just after calling this
    // function.
    void add_edge(int u, int v, flow_type c) {
        if (u != v && c != 0) {
            edges.emplace_back(std::make_pair(u, v), c);
        }
    }

    void make_graph() {
        g.assign(n, {});
        if (true) {
            std::sort(edges.begin(), edges.end());
            for (auto it = edges.begin(); it != edges.end();) {
                flow_type c = 0;
                auto uv = it->first;
                while (it != edges.end() && it->first == uv) {
                    c += it->second;
                    ++it;
                }
                int u = uv.first, v = uv.second;
                g[u].push_back({u, v, c, 0, (int)g[v].size(), false});
                g[v].push_back({v, u, c, c, (int)g[u].size() - 1, true});
            }
        } else {
            for (auto &e : edges) {
                auto uv = e.first;
                int u = uv.first, v = uv.second;
                flow_type c = e.second;
                g[u].push_back({u, v, c, 0, (int)g[v].size(), false});
                g[v].push_back({v, u, c, c, (int)g[u].size() - 1, true});
            }
        }
    }

    bool levelize() {
        int fst = 0, lst = 0;
        que[lst++] = s;
        level.assign(n, -1);
        level[s] = 0;
        while (fst != lst) {
            int v = que[fst++];
            if (v == t) break;
            for (auto &e : g[v]) {
                if (level[e.dst] == -1 && residue(e) != 0) {
                    level[e.dst] = level[v] + 1;
                    que[lst++] = e.dst;
                }
            }
        }
        return level[t] != -1;
    }

    flow_type augment(int v, flow_type lim) {
        flow_type res = 0;
        if (v == t) return lim;
        for (int &i = prog[v]; i < (int)g[v].size(); ++i) {
            if (lim == 0) break;
            auto &e = g[v][i];
            if (level[v] < level[e.dst] && residue(e) != 0) {
                flow_type aug = augment(e.dst, std::min(lim, residue(e)));
                if (aug == 0) continue;
                e.flow += aug;
                reverse(e).flow -= aug;
                res += aug;
                lim -= aug;
            }
        }
        return res;
    }

    flow_type residue(const edge &e) { return e.cap - e.flow; }

    edge &reverse(const edge &e) { return g[e.dst][e.rev_idx]; }

    // Output current flow by graphviz dot language.
    // Run `dot $filename -o out.png -T png` on shell.
    void show(const std::string &filename = "out.dot") {
        int fst = 0, lst = 0;
        que[lst++] = s;
        level.assign(n, -1);
        level[s] = 0;
        while (fst != lst) {
            int v = que[fst++];
            for (auto &e : g[v]) {
                if (!e.is_rev && level[e.dst] == -1 && e.flow) {
                    level[e.dst] = level[v] + 1;
                    que[lst++] = e.dst;
                }
            }
        }
        std::map<int, std::vector<int>> rank_to_vertices;
        for (int i = 0; i < n; ++i) {
            rank_to_vertices[level[i]].push_back(i);
        }

        std::ostringstream oss;
        oss << "digraph {" << '\n';
        for (int i = 0; i < n; ++i) {
            oss << "\t" << i;
            if (i == s || i == t) {
                oss << " [ peripheries = 2 ]";
            }
            oss << ";\n";
            for (auto &e : g[i]) {
                if (!e.is_rev) {
                    const char *color = e.flow ? "black" : "gray";
                    oss << "\t" << e.src << " -> " << e.dst << "\t[ "
                        << "label = \"" << e.flow << "/" << e.cap << "\", "
                        << "color = \"" << color << "\", "
                        << "fontcolor = \"" << color << "\"];\n";
                }
            }
        }

        for (auto &p : rank_to_vertices) {
            const char *rank = p.first != -1 ? "same" : "sink";
            oss << "\t{ rank = " << rank << "; ";
            for (int v : p.second) {
                if (v != s && v != t) {
                    oss << v << "; ";
                }
            }
            oss << "}\n";
        }
        oss << "\t{ rank = same; " << s << "; }\n";
        oss << "\t{ rank = same; " << t << "; }\n";
        oss << "}\n";

        std::ofstream ofs(filename);
        ofs << oss.str();
    }
};

/* #endregion */

// Problem
void solve() {
    VAR(ll, n); //

    vll row_caps, col_caps;
    REPM(i, 1, 2 * n) {
        if (i % 4 == 1 || i % 4 == 0) {
            row_caps.push_back(i);
        } else {
            col_caps.push_back(i);
        }
    }
    ll sum = accumulate(ALL(row_caps), 0LL);
    // dump(rows, cols);

    using Flow = ll;
    dinic_sparse<Flow> dn(n * n + 2 * n + 2);
    auto idx = [&](ll r, ll c) -> ll { return n * r + c; };
    auto row = [&](ll r) -> ll { return n * n + r; };
    auto col = [&](ll c) -> ll { return n * n + n + c; };
    ll S = n * n + 2 * n;
    ll T = S + 1;

    REP(i, 0, n) REP(j, 0, n) {
        dn.add_edge(row(i), idx(i, j), 2);
        dn.add_edge(idx(i, j), col(j), 2);
    }
    REP(i, 0, n) dn.add_edge(S, row(i), row_caps[i]);
    REP(j, 0, n) dn.add_edge(col(j), T, col_caps[j]);

    ll f = dn.maximum_flow(S, T);
    // dump(f);
    if (f != sum) {
        Yn(false);
        return;
    }

    vvll ans(n, vll(n, INF));
    for (auto &edges : dn.g) {
        for (auto &edge : edges) {
            if (edge.src < n * n) {
                ll i = edge.src / n;
                ll j = edge.src % n;
                if (edge.dst != col(j)) continue;
                // dump(i, j, edge.src, edge.dst, edge.flow);
                ans[i][j] = edge.flow;
            }
        }
    }
    // dump(ans);

    REP(i, 0, n) {
        REP(j, 0, n) cout << ans[i][j];
        cout << endl;
    }
}

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

結果

テストケース

ソースコード
