#461983 (C++14) No.1023 Cyclic Tour

提出ソース

結果

問題	No.1023 Cyclic Tour
ユーザー	hitonanode
提出日時	2020-04-10 21:49:03
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	121 ms / 2,000 ms
コード長	7,904 bytes
コンパイル時間	2,461 ms
コンパイル使用メモリ	180,792 KB
実行使用メモリ	20,212 KB
最終ジャッジ日時	2024-09-15 20:08:52
合計ジャッジ時間	8,332 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
（要ログイン）

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	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	27 ms 5,376 KB
testcase_05	AC	27 ms 5,376 KB
testcase_06	AC	28 ms 5,376 KB
testcase_07	AC	27 ms 5,376 KB
testcase_08	AC	45 ms 12,356 KB
testcase_09	AC	56 ms 13,104 KB
testcase_10	AC	56 ms 13,364 KB
testcase_11	AC	57 ms 13,776 KB
testcase_12	AC	58 ms 15,200 KB
testcase_13	AC	62 ms 14,516 KB
testcase_14	AC	52 ms 14,256 KB
testcase_15	AC	60 ms 14,524 KB
testcase_16	AC	103 ms 17,652 KB
testcase_17	AC	121 ms 17,780 KB
testcase_18	AC	103 ms 17,196 KB
testcase_19	AC	99 ms 16,944 KB
testcase_20	AC	61 ms 12,240 KB
testcase_21	AC	61 ms 12,392 KB
testcase_22	AC	79 ms 13,540 KB
testcase_23	AC	82 ms 13,912 KB
testcase_24	AC	100 ms 15,728 KB
testcase_25	AC	63 ms 12,252 KB
testcase_26	AC	62 ms 12,232 KB
testcase_27	AC	59 ms 11,432 KB
testcase_28	AC	94 ms 15,316 KB
testcase_29	AC	95 ms 15,956 KB
testcase_30	AC	98 ms 15,352 KB
testcase_31	AC	87 ms 14,832 KB
testcase_32	AC	103 ms 16,188 KB
testcase_33	AC	91 ms 15,444 KB
testcase_34	AC	21 ms 5,376 KB
testcase_35	AC	46 ms 5,376 KB
testcase_36	AC	71 ms 12,764 KB
testcase_37	AC	82 ms 14,808 KB
testcase_38	AC	90 ms 15,672 KB
testcase_39	AC	86 ms 13,900 KB
testcase_40	AC	85 ms 13,972 KB
testcase_41	AC	84 ms 14,028 KB
testcase_42	AC	57 ms 10,588 KB
testcase_43	AC	64 ms 12,872 KB
testcase_44	AC	34 ms 10,196 KB
testcase_45	AC	61 ms 20,088 KB
testcase_46	AC	65 ms 20,212 KB
testcase_47	AC	33 ms 10,324 KB
testcase_48	AC	60 ms 12,664 KB
testcase_49	AC	64 ms 12,660 KB
testcase_50	AC	61 ms 12,432 KB
testcase_51	AC	58 ms 9,968 KB
testcase_52	AC	58 ms 10,488 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

raw source code

#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template<typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/tag_and_trait.hpp>
using namespace __gnu_pbds; // find_by_order(), order_of_key()
template<typename TK> using pbds_set = tree<TK, null_type, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename TK, typename TV> using pbds_map = tree<TK, TV, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;
*/

// UnionFind Tree (0-indexed), based on size of each disjoint set
struct UnionFind
{
    std::vector<int> par, cou;
    UnionFind(int N = 0) : par(N), cou(N, 1) {
        iota(par.begin(), par.end(), 0);
    }
    int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); }
    bool unite(int x, int y) {
        x = find(x), y = find(y);
        if (x == y) return false;
        if (cou[x] < cou[y]) std::swap(x, y);
        par[y] = x, cou[x] += cou[y];
        return true;
    }
    int count(int x) { return cou[find(x)]; }
    bool same(int x, int y) { return find(x) == find(y); }
};

// Directed graph library to find strongly connected components （強連結成分分解）
// 0-indexed directed graph
// Complexity: O(V + E)
struct DirectedGraphSCC {
    int V; // # of Vertices
    std::vector<std::vector<int>> to, from;
    std::vector<int> used;  // Only true/false
    std::vector<int> vs;
    std::vector<int> cmp;
    int scc_num = -1;

    DirectedGraphSCC(int V = 0) : V(V), to(V), from(V), cmp(V) {}

    void _dfs(int v) {
        used[v] = true;
        for (auto t : to[v]) if (!used[t]) _dfs(t);
        vs.push_back(v);
    }
    void _rdfs(int v, int k) {
        used[v] = true;
        cmp[v] = k;
        for (auto t : from[v]) if (!used[t]) _rdfs(t, k);
    }

    void add_edge(int from_, int to_) {
        assert(from_ >= 0 and from_ < V and to_ >= 0 and to_ < V);
        to[from_].push_back(to_);
        from[to_].push_back(from_);
    }

    // Detect strongly connected components and return # of them.
    // Also, assign each vertex `v` the scc id `cmp[v]` (0-indexed)
    int FindStronglyConnectedComponents() {
        used.assign(V, false);
        vs.clear();
        for (int v = 0; v < V; v++) if (!used[v]) _dfs(v);
        used.assign(V, false);
        scc_num = 0;
        for (int i = (int)vs.size() - 1; i >= 0; i--) if (!used[vs[i]]) _rdfs(vs[i], scc_num++);
        return scc_num;
    }

    // After calling `FindStronglyConnectedComponents()`, generate a new graph by uniting all vertices
    // belonging to the same component(The resultant graph is DAG).
    DirectedGraphSCC GenerateTopologicalGraph() {
        DirectedGraphSCC newgraph(scc_num);
        for (int s = 0; s < V; s++) for (auto t : to[s]) {
            if (cmp[s] != cmp[t]) newgraph.add_edge(cmp[s], cmp[t]);
        }
        return newgraph;
    }
};

// 2-SAT solver: Find a solution for  `(Ai v Aj) ^ (Ak v Al) ^ ... = true`
// - `nb_sat_vars`: Number of variables
// - Considering a graph with `2 * nb_sat_vars` vertices
// - Vertices [0, nb_sat_vars) means `Ai`
// - vertices [nb_sat_vars, 2 * nb_sat_vars) means `not Ai`
struct SATSolver : DirectedGraphSCC {
    int nb_sat_vars;
    std::vector<int> solution;
    SATSolver(int nb_variables = 0) : DirectedGraphSCC(nb_variables * 2), nb_sat_vars(nb_variables), solution(nb_sat_vars) {}
    void add_x_or_y_constraint(bool is_x_true, int x, bool is_y_true, int y) {
        assert(x >= 0 and x < nb_sat_vars);
        assert(y >= 0 and y < nb_sat_vars);
        if (!is_x_true) x += nb_sat_vars;
        if (!is_y_true) y += nb_sat_vars;
        add_edge((x + nb_sat_vars) % (nb_sat_vars * 2), y);
        add_edge((y + nb_sat_vars) % (nb_sat_vars * 2), x);
    }
    // Solve the 2-SAT problem. If no solution exists, return `false`.
    // Otherwise, dump one solution to `solution` and return `true`.
    bool run() {
        FindStronglyConnectedComponents();
        for (int i = 0; i < nb_sat_vars; i++) {
            if (cmp[i] == cmp[i + nb_sat_vars]) return false;
            solution[i] = cmp[i] > cmp[i + nb_sat_vars];
        }
        return true;
    }
};

int main()
{
    int N, M;
    cin >> N >> M;
    vector<pint> v;
    UnionFind uf(N);
    while (M--)
    {
        int a, b, c;
        cin >> a >> b >> c;
        a--, b--;
        if (c == 2)
        {
            v.emplace_back(a, b);
        }
        else
        {
            if (!uf.unite(a, b))
            {
                puts("Yes");
                return 0;
            }
        }
    }
    DirectedGraphSCC graph(N);
    for (auto p : v)
    {
        int s = uf.find(p.first), t = uf.find(p.second);
        if (s == t)
        {
            puts("Yes");
            return 0;
        }
        graph.add_edge(uf.find(p.first), uf.find(p.second));
    }
    graph.FindStronglyConnectedComponents();
    vector<int> deg(N);
    for (auto x : graph.cmp) deg[x]++;
    if (*max_element(deg.begin(), deg.end()) > 1) puts("Yes");
    else puts("No");
}

yukicoder

結果

テストケース

ソースコード