結果

問題 No.1545 [Cherry 2nd Tune N] Anthem
ユーザー 👑 hitonanodehitonanode
提出日時 2021-06-11 23:15:56
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 285 ms / 3,000 ms
コード長 12,404 bytes
コンパイル時間 2,258 ms
コンパイル使用メモリ 167,256 KB
実行使用メモリ 76,068 KB
最終ジャッジ日時 2024-05-08 19:38:15
合計ジャッジ時間 13,919 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
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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 2 ms
5,248 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 73 ms
30,792 KB
testcase_05 AC 285 ms
73,904 KB
testcase_06 AC 97 ms
28,160 KB
testcase_07 AC 83 ms
25,536 KB
testcase_08 AC 201 ms
49,972 KB
testcase_09 AC 63 ms
16,896 KB
testcase_10 AC 51 ms
12,032 KB
testcase_11 AC 145 ms
38,568 KB
testcase_12 AC 232 ms
61,568 KB
testcase_13 AC 67 ms
17,792 KB
testcase_14 AC 91 ms
32,764 KB
testcase_15 AC 17 ms
6,656 KB
testcase_16 AC 135 ms
44,928 KB
testcase_17 AC 30 ms
6,656 KB
testcase_18 AC 146 ms
18,048 KB
testcase_19 AC 112 ms
28,344 KB
testcase_20 AC 48 ms
16,384 KB
testcase_21 AC 165 ms
53,760 KB
testcase_22 AC 109 ms
29,184 KB
testcase_23 AC 98 ms
16,256 KB
testcase_24 AC 9 ms
6,944 KB
testcase_25 AC 12 ms
8,704 KB
testcase_26 AC 2 ms
5,376 KB
testcase_27 AC 8 ms
5,376 KB
testcase_28 AC 14 ms
10,496 KB
testcase_29 AC 12 ms
9,344 KB
testcase_30 AC 10 ms
7,168 KB
testcase_31 AC 14 ms
7,928 KB
testcase_32 AC 6 ms
5,504 KB
testcase_33 AC 16 ms
10,240 KB
testcase_34 AC 13 ms
8,576 KB
testcase_35 AC 38 ms
25,856 KB
testcase_36 AC 29 ms
19,712 KB
testcase_37 AC 4 ms
5,376 KB
testcase_38 AC 17 ms
10,368 KB
testcase_39 AC 5 ms
5,376 KB
testcase_40 AC 7 ms
6,144 KB
testcase_41 AC 3 ms
5,376 KB
testcase_42 AC 10 ms
7,296 KB
testcase_43 AC 13 ms
8,576 KB
testcase_44 AC 4 ms
5,376 KB
testcase_45 AC 5 ms
7,296 KB
testcase_46 AC 14 ms
8,448 KB
testcase_47 AC 26 ms
12,800 KB
testcase_48 AC 34 ms
20,856 KB
testcase_49 AC 42 ms
20,352 KB
testcase_50 AC 75 ms
33,096 KB
testcase_51 AC 5 ms
5,376 KB
testcase_52 AC 90 ms
44,012 KB
testcase_53 AC 35 ms
18,952 KB
testcase_54 AC 8 ms
5,684 KB
testcase_55 AC 84 ms
34,432 KB
testcase_56 AC 4 ms
5,376 KB
testcase_57 AC 65 ms
26,844 KB
testcase_58 AC 47 ms
22,016 KB
testcase_59 AC 8 ms
5,888 KB
testcase_60 AC 9 ms
7,168 KB
testcase_61 AC 19 ms
10,240 KB
testcase_62 AC 55 ms
22,400 KB
testcase_63 AC 26 ms
12,288 KB
testcase_64 AC 269 ms
67,944 KB
testcase_65 AC 8 ms
5,504 KB
testcase_66 AC 178 ms
76,068 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 # 

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), 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, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
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> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
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, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
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, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &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, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif

void Impossible() {
    puts("Impossible");
    exit(0);
}

template <typename T, T INF = std::numeric_limits<T>::max() / 2, int INVALID = -1> struct ShortestPath {
    int V, E;
    bool single_positive_weight;
    T wmin, wmax;
    std::vector<std::vector<std::pair<int, T>>> to;

    ShortestPath(int V = 0) : V(V), E(0), single_positive_weight(true), wmin(0), wmax(0), to(V) {}
    void add_edge(int s, int t, T w) {
        assert(0 <= s and s < V);
        assert(0 <= t and t < V);
        to[s].emplace_back(t, w);
        E++;
        if (w > 0 and wmax > 0 and wmax != w) single_positive_weight = false;
        wmin = std::min(wmin, w);
        wmax = std::max(wmax, w);
    }

    std::vector<T> dist;
    std::vector<int> prev;

    // Dijkstra algorithm
    // Complexity: O(E log E)
    void Dijkstra(int s) {
        assert(0 <= s and s < V);
        dist.assign(V, INF);
        dist[s] = 0;
        prev.assign(V, INVALID);
        using P = std::pair<T, int>;
        std::priority_queue<P, std::vector<P>, std::greater<P>> pq;
        pq.emplace(0, s);
        while (!pq.empty()) {
            T d;
            int v;
            std::tie(d, v) = pq.top();
            pq.pop();
            if (dist[v] < d) continue;
            for (auto nx : to[v]) {
                T dnx = d + nx.second;
                if (dist[nx.first] > dnx) {
                    dist[nx.first] = dnx, prev[nx.first] = v;
                    pq.emplace(dnx, nx.first);
                }
            }
        }
    }

    // Dijkstra algorithm, O(V^2 + E)
    void DijkstraVquad(int s) {
        assert(0 <= s and s < V);
        dist.assign(V, INF);
        dist[s] = 0;
        prev.assign(V, INVALID);
        std::vector<char> fixed(V, false);
        while (true) {
            int r = INVALID;
            T dr = INF;
            for (int i = 0; i < V; i++) {
                if (!fixed[i] and dist[i] < dr) r = i, dr = dist[i];
            }
            if (r == INVALID) break;
            fixed[r] = true;
            int nxt;
            T dx;
            for (auto p : to[r]) {
                std::tie(nxt, dx) = p;
                if (dist[nxt] > dist[r] + dx) dist[nxt] = dist[r] + dx, prev[nxt] = r;
            }
        }
    }

    // Bellman-Ford algorithm
    // Complexity: O(VE)
    bool BellmanFord(int s, int nb_loop) {
        assert(0 <= s and s < V);
        dist.assign(V, INF), prev.assign(V, INVALID);
        dist[s] = 0;
        for (int l = 0; l < nb_loop; l++) {
            bool upd = false;
            for (int v = 0; v < V; v++) {
                if (dist[v] == INF) continue;
                for (auto nx : to[v]) {
                    T dnx = dist[v] + nx.second;
                    if (dist[nx.first] > dnx) dist[nx.first] = dnx, prev[nx.first] = v, upd = true;
                }
            }
            if (!upd) return true;
        }
        return false;
    }

    // Bellman-ford algorithm using queue (deque)
    // Complexity: O(VE)
    // Requirement: no negative loop
    void SPFA(int s) {
        assert(0 <= s and s < V);
        dist.assign(V, INF);
        prev.assign(V, INVALID);
        std::deque<int> q;
        std::vector<char> in_queue(V);
        dist[s] = 0;
        q.push_back(s), in_queue[s] = 1;
        while (!q.empty()) {
            int now = q.front();
            q.pop_front(), in_queue[now] = 0;
            for (auto nx : to[now]) {
                T dnx = dist[now] + nx.second;
                int nxt = nx.first;
                if (dist[nxt] > dnx) {
                    dist[nxt] = dnx;
                    if (!in_queue[nxt]) {
                        if (q.size() and dnx < dist[q.front()]) { // Small label first optimization
                            q.push_front(nxt);
                        } else {
                            q.push_back(nxt);
                        }
                        prev[nxt] = now, in_queue[nxt] = 1;
                    }
                }
            }
        }
    }

    void ZeroOneBFS(int s) {
        assert(0 <= s and s < V);
        dist.assign(V, INF), prev.assign(V, INVALID);
        dist[s] = 0;
        std::deque<int> que;
        que.push_back(s);
        while (!que.empty()) {
            int v = que.front();
            que.pop_front();
            for (auto nx : to[v]) {
                T dnx = dist[v] + nx.second;
                if (dist[nx.first] > dnx) {
                    dist[nx.first] = dnx, prev[nx.first] = v;
                    if (nx.second) {
                        que.push_back(nx.first);
                    } else {
                        que.push_front(nx.first);
                    }
                }
            }
        }
    }

    void solve(int s) {
        if (wmin >= 0) {
            if (single_positive_weight) {
                ZeroOneBFS(s);
            } else {
                if ((long long)V * V < (E << 4)) {
                    DijkstraVquad(s);
                } else {
                    Dijkstra(s);
                }
            }
        } else {
            BellmanFord(s, V);
        }
    }

    // Warshall-Floyd algorithm
    // Complexity: O(E + V^3)
    std::vector<std::vector<T>> dist2d;
    void WarshallFloyd() {
        dist2d.assign(V, std::vector<T>(V, INF));
        for (int i = 0; i < V; i++) {
            dist2d[i][i] = 0;
            for (auto p : to[i]) dist2d[i][p.first] = std::min(dist2d[i][p.first], p.second);
        }
        for (int k = 0; k < V; k++) {
            for (int i = 0; i < V; i++) {
                if (dist2d[i][k] == INF) continue;
                for (int j = 0; j < V; j++) {
                    if (dist2d[k][j] == INF) continue;
                    dist2d[i][j] = std::min(dist2d[i][j], dist2d[i][k] + dist2d[k][j]);
                }
            }
        }
    }

    void dump_graphviz(std::string filename = "shortest_path") const {
        std::ofstream ss(filename + ".DOT");
        ss << "digraph{\n";
        for (int i = 0; i < V; i++) {
            for (const auto &e : to[i]) ss << i << "->" << e.first << "[label=" << e.second << "];\n";
        }
        ss << "}\n";
        ss.close();
        return;
    }
};


int main() {
    int N, S, T, K;
    cin >> N >> S >> T >> K;
    K--;
    vector<int> X(N);
    cin >> X;
    int M;
    cin >> M;
    vector<vector<pint>> to(N);
    REP(e, M) {
        int a, b, y;
        cin >> a >> b >> y;
        a--, b--;
        to[a].emplace_back(b, y);
    }

    ShortestPath<lint> graph(N * (K + 1));
    auto v = [&](int i, int t) { return t * N + i; };
    REP(i, N) {
        REP(k, K + 1) {
            for (auto [j, w] : to[i]) {
                graph.add_edge(v(i, k), v(j, min(k + 1, K)), w + X[i]);
            }
        }
    }
    int gs = v(S - 1, 0);
    int gt = v(T - 1, K);
    graph.solve(gs);
    auto retd = graph.dist[gt];
    if (retd > 1LL << 60) Impossible();
    cout << "Possible\n" << retd + X[T - 1] << '\n';
    vector<int> ret;
    ret.push_back(gt % N + 1);
    while (gt != gs) {
        gt = graph.prev[gt];
        ret.push_back(gt % N + 1);
    }
    reverse(ALL(ret));
    cout << ret.size() << '\n';
    for (auto x : ret) cout << x << ' ';
    cout << '\n';
}
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