#1049971 (C++23) No.2780 The Bottle Imp

提出ソース
結果

問題	No.2780 The Bottle Imp
ユーザー	noya2
提出日時	2025-03-07 01:41:10
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	47 ms / 2,000 ms
コード長	20,233 bytes
コンパイル時間	5,003 ms
コンパイル使用メモリ	302,500 KB
実行使用メモリ	25,476 KB
最終ジャッジ日時	2025-03-07 01:41:18
合計ジャッジ時間	6,716 ms
ジャッジサーバーID （参考情報）	judge1 / judge5
このコードへのチャレンジ
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ファイルパターン	結果
sample	AC * 4
other	AC * 40
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ソースコード

raw source code
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

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

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/graph/graph_query.hpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
#include<ranges>
#line 7 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"

namespace noya2::internal {

template<class E>
struct csr {
    csr () {}
    csr (int _n) : n(_n) {}
    csr (int _n, int m) : n(_n){
        start.reserve(m);
        elist.reserve(m);
    }
    // ACL style constructor (do not have to call build)
    csr (int _n, const std::vector<std::pair<int,E>> &idx_elem) : n(_n), start(_n + 2), elist(idx_elem.size()) {
        for (auto &[i, e] : idx_elem){
            start[i + 2]++;
        }
        for (int i = 1; i < n; i++){
            start[i + 2] += start[i + 1];
        }
        for (auto &[i, e] : idx_elem){
            elist[start[i + 1]++] = e;
        }
        prepared = true;
    }
    int add(int idx, E elem){
        int eid = start.size();
        start.emplace_back(idx);
        elist.emplace_back(elem);
        return eid;
    }
    void build(){
        if (prepared) return ;
        int m = start.size();
        std::vector<E> nelist(m);
        std::vector<int> nstart(n + 2, 0);
        for (int i = 0; i < m; i++){
            nstart[start[i] + 2]++;
        }
        for (int i = 1; i < n; i++){
            nstart[i + 2] += nstart[i + 1];
        }
        for (int i = 0; i < m; i++){
            nelist[nstart[start[i] + 1]++] = elist[i];
        }
        swap(elist,nelist);
        swap(start,nstart);
        prepared = true;
    }
    const auto operator[](int idx) const {
        return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
    }
    auto operator[](int idx){
        return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
    }
    const auto operator()(int idx, int l, int r) const {
        return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
    }
    auto operator()(int idx, int l, int r){
        return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
    }
    size_t size() const {
        return n;
    }
    int n;
    std::vector<int> start;
    std::vector<E> elist;
    bool prepared = false;
};

} // namespace noya2::internal
#line 2 "/Users/noya2/Desktop/Noya2_library/graph/unweighted_type.hpp"

namespace noya2 {

struct unweighted {};

} // namespace noya2
#line 6 "/Users/noya2/Desktop/Noya2_library/graph/graph_query.hpp"

#line 12 "/Users/noya2/Desktop/Noya2_library/graph/graph_query.hpp"

namespace noya2 {

template<typename Cost>
struct graph {
    int n;
    internal::csr<std::pair<int,Cost>> g;
    Cost dist_inf = std::numeric_limits<Cost>::max() / 3;
    graph (int _n = 0) : n(_n), g(_n) {}
    graph (int _n, int _m) : n(_n), g(_n,_m) {}
    // 有向辺を追加 (無向辺ではないことに注意！)
    int add_edge(int u, int v, Cost cost = 1){
        int id = g.add(u, {v,cost});
        return id;
    }
    template<bool directed>
    static graph input(int _n, int _m, int indexed = 1){
        if constexpr (directed){
            graph g(_n, _m*2);
            for (int i = 0; i < _m; i++){
                int u, v; std::cin >> u >> v;
                u -= indexed, v -= indexed;
                Cost c; std::cin >> c;
                g.add_edge(u, v, c);
                g.add_edge(v, u, c);
            }
            g.build();
            return g;
        }
        else {
            graph g(_n, _m);
            for (int i = 0; i < _m; i++){
                int u, v; std::cin >> u >> v;
                u -= indexed, v -= indexed;
                Cost c; std::cin >> c;
                g.add_edge(u, v, c);
            }
            g.build();
            return g;
        }
    }
    void build(){
        g.build();
    }
    void set_inf(Cost new_inf){
        dist_inf = new_inf;
    }
    std::vector<Cost> dijkstra(int s){
        g.build();
        std::vector<Cost> dist(n,dist_inf);
        dist[s] = 0;
        using P = std::pair<Cost,int>;
        std::priority_queue<P,std::vector<P>,std::greater<P>> pque;
        pque.push(P(0,s));
        while (!pque.empty()){
            auto [d, v] = pque.top(); pque.pop();
            if (dist[v] < d) continue;
            for (auto [u, c] : g[v]){
                if (chmin(dist[u],d+c)){
                    pque.push(P(dist[u],u));
                }
            }
        }
        return dist;
    }
    std::vector<int> reconstruct(int s, int t, const std::vector<Cost> &dist){
        if (dist[t] == dist_inf) return {};
        g.build();
        std::vector<int> from(n,-1);
        std::queue<int> que;
        que.push(s);
        while (!que.empty()){
            int v = que.front(); que.pop();
            for (auto [u, c] : g[v]){
                if (from[u] == -1 && dist[u] == dist[v] + c){
                    from[u] = v;
                    que.push(u);
                }
            }
        }
        std::vector<int> ans = {t};
        while (t != s){
            t = from[t];
            ans.emplace_back(t);
        }
        std::reverse(ans.begin(),ans.end());
        return ans;
    }
    std::vector<Cost> bfs01(int s){
        g.build();
        std::vector<Cost> dist(n,dist_inf);
        dist[s] = 0;
        std::deque<int> que;
        que.push_back(s);
        while (!que.empty()){
            int v = que.front(); que.pop_front();
            for (auto [u, c] : g[v]){
                if (chmin(dist[u],dist[v]+c)){
                    if (c == 0) que.push_front(u);
                    else que.push_back(u);
                }
            }
        }
        return dist;
    }
    std::vector<Cost> bfs1(int s){
        g.build();
        std::vector<Cost> dist(n,dist_inf);
        dist[s] = 0;
        std::queue<int> que;
        que.push(s);
        while (!que.empty()){
            int v = que.front(); que.pop();
            for (auto [u, c] : g[v]){
                if (chmin(dist[u],dist[v]+c)){
                    que.push(u);
                }
            }
        }
        return dist;
    }
    std::vector<Cost> bellman_ford(int s, bool &ng_cycle){
        g.build();
        std::vector<Cost> dist(n,dist_inf);
        std::vector<int> ng;
        dist[s] = 0;
        int tm = 0;
        while (tm < n){
            bool finish = true;
            for (int v = 0; v < n; v++){
                if (dist[v] == dist_inf) continue;
                for (auto [u, c] : g[v]){
                    if (chmin(dist[u],dist[v]+c)){
                        finish = false;
                        if (tm == n-1) ng.emplace_back(u);
                    }
                }
            }
            if (finish) break;
            tm++;
        }
        ng_cycle = (tm == n);
        if (ng_cycle){
            for (auto v : ng) dist[v] = -dist_inf;
            tm = n;
            while (tm--){
                for (int v = 0; v < n; v++){
                    if (dist[v] != -dist_inf) continue;
                    for (auto [u, c] : g[v]){
                        dist[u] = -dist_inf;
                    }
                }
            }
        }
        return dist;
    }
    std::vector<std::vector<Cost>> warshall_floyd(){
        g.build();
        std::vector<std::vector<Cost>> dist(n,std::vector<Cost>(n,dist_inf));
        for (int v = 0; v < n; v++){
            dist[v][v] = 0;
            for (auto [u, c] : g[v]){
                chmin(dist[v][u],c);
            }
        }
        for (int k = 0; k < n; k++){
            for (int i = 0; i < n; i++){
                for (int j = 0; j < n; j++){
                    chmin(dist[i][j],dist[i][k]+dist[k][j]);
                }
            }
        }
        return dist;
    }
    const auto operator[](int idx) const { return g[idx]; }
    auto operator[](int idx) { return g[idx]; }
};


template<>
struct graph<unweighted> {
    int n;
    internal::csr<int> g;
    int dist_inf = std::numeric_limits<int>::max() / 2;
    graph (int _n = 0) : n(_n), g(_n) {}
    graph (int _n, int _m) : n(_n), g(_n,_m) {}
    // 有向辺を追加 (無向辺ではないことに注意！)
    int add_edge(int u, int v){
        int id = g.add(u, v);
        return id;
    }
    template<bool directed>
    static graph input(int _n, int _m, int indexed = 1){
        if constexpr (directed){
            graph g(_n, _m*2);
            for (int i = 0; i < _m; i++){
                int u, v; std::cin >> u >> v;
                u -= indexed, v -= indexed;
                g.add_edge(u, v);
                g.add_edge(v, u);
            }
            g.build();
            return g;
        }
        else {
            graph g(_n, _m);
            for (int i = 0; i < _m; i++){
                int u, v; std::cin >> u >> v;
                u -= indexed, v -= indexed;
                g.add_edge(u, v);
            }
            g.build();
            return g;
        }
    }
    void build(){
        g.build();
    }
    void set_inf(int new_inf){
        dist_inf = new_inf;
    }
    std::vector<int> reconstruct(int s, int t, const std::vector<int> &dist){
        if (dist[t] == dist_inf) return {};
        g.build();
        std::vector<int> from(n,-1);
        std::queue<int> que;
        que.push(s);
        while (!que.empty()){
            int v = que.front(); que.pop();
            for (auto u : g[v]){
                if (from[u] == -1 && dist[u] == dist[v] + 1){
                    from[u] = v;
                    que.push(u);
                }
            }
        }
        std::vector<int> ans = {t};
        while (t != s){
            t = from[t];
            ans.emplace_back(t);
        }
        std::reverse(ans.begin(),ans.end());
        return ans;
    }
    std::vector<int> bfs(int s){
        g.build();
        std::vector<int> dist(n,dist_inf);
        dist[s] = 0;
        std::queue<int> que;
        que.push(s);
        while (!que.empty()){
            int v = que.front(); que.pop();
            for (auto u : g[v]){
                if (chmin(dist[u],dist[v]+1)){
                    que.push(u);
                }
            }
        }
        return dist;
    }
    const auto operator[](int idx) const { return g[idx]; }
    auto operator[](int idx) { return g[idx]; }
};

template<>
struct graph<bool> {
    int n;
    internal::csr<std::pair<int,bool>> g;
    int dist_inf = std::numeric_limits<int>::max() / 2;
    graph (int _n = 0) : n(_n), g(_n) {}
    graph (int _n, int _m) : n(_n), g(_n,_m) {}
    // 有向辺を追加 (無向辺ではないことに注意！)
    int add_edge(int u, int v, bool cost){
        int id = g.add(u, {v, cost});
        return id;
    }
    void build(){
        g.build();
    }
    void set_inf(int new_inf){
        dist_inf = new_inf;
    }
    std::vector<int> reconstruct(int s, int t, const std::vector<int> &dist){
        if (dist[t] == dist_inf) return {};
        g.build();
        std::vector<int> from(n,-1);
        std::queue<int> que;
        que.push(s);
        while (!que.empty()){
            int v = que.front(); que.pop();
            for (auto [u, b] : g[v]){
                int c = (int)b;
                if (from[u] == -1 && dist[u] == dist[v] + c){
                    from[u] = v;
                    que.push(u);
                }
            }
        }
        std::vector<int> ans = {t};
        while (t != s){
            t = from[t];
            ans.emplace_back(t);
        }
        std::reverse(ans.begin(),ans.end());
        return ans;
    }
    std::vector<int> bfs01(int s){
        g.build();
        std::vector<int> dist(n,dist_inf);
        dist[s] = 0;
        std::deque<int> que;
        que.push_back(s);
        while (!que.empty()){
            int v = que.front(); que.pop_front();
            for (auto [u, b] : g[v]){
                int c = (int)b;
                if (chmin(dist[u],dist[v]+c)){
                    if (c == 0) que.push_front(u);
                    else que.push_back(u);
                }
            }
        }
        return dist;
    }
    const auto operator[](int idx) const { return g[idx]; }
    auto operator[](int idx) { return g[idx]; }
};

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/graph/scc.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/graph/scc.hpp"

namespace noya2{

template <class E> struct internal_csr {
    std::vector<int> start;
    std::vector<E> elist;
    explicit internal_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;
        }
    }
};

struct scc_graph {
  public:
    explicit 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 = internal_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;
    }
    
    int _n;
    struct edge {
        int to;
    };
    std::vector<std::pair<int, edge>> edges;
};

} // namespace noya2
#line 5 "c.cpp"

void solve(){
    int n; in(n);
    graph<unweighted> g(n);
    scc_graph sg(n);
    rep(i,n){
        int m; in(m);
        while (m--){
            int j; in(j); j--;
            g.add_edge(i,j);
            sg.add_edge(i,j);
        }
    }
    auto dist = g.bfs(0);
    rep(i,n){
        if (dist[i] == g.dist_inf){
            no();
            return ;
        }
    }
    auto scc = sg.scc();
    vector<int> col(n);
    int sz = scc.size();
    rep(i,sz){
        for (int v : scc[i]){
            col[v] = i;
        }
    }
    rep(i,sz-1){
        bool ok = false;
        for (int v : scc[i]){
            for (int u : g[v]){
                if (col[u] == i+1){
                    ok = true;
                }
            }
        }
        if (!ok){
            no();
            return ;
        }
    }
    yes();
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}
yukicoder

結果

ソースコード
