#734694 (C++17) No.1069 電柱 / Pole (Hard)

• 問題: No.1069 電柱 / Pole (Hard)
• ユーザー: MitI_7
• 提出日時: 2022-01-28 16:47:29
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 308 ms / 2,000 ms
• コード長: 12,247 bytes
• コンパイル時間: 2,495 ms
• コンパイル使用メモリ: 166,984 KB
• 最終ジャッジ日時: 2025-01-27 15:53:23
• ジャッジサーバーID （参考情報）: judge4 / judge2

ファイルパターン	結果
sample	AC * 4
other	AC * 79

ソースコード

#include <iostream>
#include <array>
#include <vector>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <algorithm>
#include <cmath>
#include <string>
#include <climits>
#include <cassert>
#include <iomanip>
#include <bitset>
#include <queue>
#include <deque>
#include <stack>
#include <functional>
#include <fstream>
#include <random>
#include <functional>

#define LEN(x) (long long)(x.size())
#define FOR(i, a, n) for(int i=(a);i<(n); ++i)
#define FOE(i, a) for(auto i : a)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define SUM(x) std::accumulate(ALL(x), 0LL)
#define MIN(v) *std::min_element(v.begin(), v.end())
#define MAX(v) *std::max_element(v.begin(), v.end())
#define EXIST(v, x) (std::find(v.begin(), v.end(), x) != v.end())
#define BIT_COUNT32(bit) (__builtin_popcount(bit))
#define BIT_COUNT64(bit) (__builtin_popcountll(bit))

typedef long long LL;
template<typename T> std::vector<T> make_v(size_t a){return std::vector<T>(a);}
template<typename T,typename... Ts> auto make_v(size_t a, Ts... ts){ return std::vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));}    // C++14
template<typename T,typename V> typename std::enable_if<std::is_class<T>::value==0>::type fill_v(T &t,const V &v){t=v;}
template<typename T,typename V> typename std::enable_if<std::is_class<T>::value!=0>::type fill_v(T &t,const V &v){for(auto &e:t) fill_v(e,v);}
template<class T> inline T ceil(T a, T b) { return (a + b - 1) / b; }
void print() { std::cout << std::endl; }
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) { std::cout << head; if (sizeof...(tail) != 0) {std::cout << " ";} print(std::forward<Tail>(tail)...); }
template <class T> void print(std::vector<T> &v) {for (auto& a : v) { std::cout << a; if (&a != &v.back()) {std::cout << " ";} }std::cout << std::endl;}
template <class T> void print(std::vector<std::vector<T>> &vv) { for (auto& v : vv) { print(v); }}
void debug() { std::cerr << std::endl; }
template <class Head, class... Tail> void debug(Head&& head, Tail&&... tail) { std::cerr << head; if (sizeof...(tail) != 0) {std::cerr << " ";} print(std::forward<Tail>(tail)...); }
template <class T> void debug(std::vector<T> &v) {for (auto& a : v) { std::cerr << a; if (&a != &v.back()) {std::cerr << " ";} }std::cerr << std::endl;}
template <class T> void debug(std::vector<std::vector<T>> &vv) { for (auto& v : vv) { print(v); }}
inline bool inside(long long y, long long x, long long H, long long W) {return 0 <= y and y < H and 0 <= x and x < W; }
template<class T> inline double euclidean_distance(T y1, T x1, T y2, T x2) { return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); }
template<class T> inline T manhattan_distance(T y1, T x1, T y2, T x2) { return abs(x1 - x2) + abs(y1 - y2); }
template<typename T> T &chmin(T &a, const T &b) { return a = std::min(a, b); }
template<typename T> T &chmax(T &a, const T &b) { return a = std::max(a, b); }
bool is_bit_on(const unsigned long long bit, const unsigned int i) { return (bit >> i) & 1u; }
unsigned long long bit_set(const unsigned long long bit, const unsigned int i, const unsigned int b) {
    assert(b == 0 or b == 1);
    if (b == 0) { return bit & ~(1ull << i); }
    else        {return bit | (1ull << i); }
}

template<class T> inline std::vector<T> unique(std::vector<T> v) {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
    return v;
}

// 初項s交差d長さnの数列の和
long long sum_of_arithmetic_progression(long long s, long long d, long long n) {
    return n * (2 * s + (n - 1) * d) / 2;
}

// xが2の階乗かどうか判定
bool is_power_of_two(long long x) {
    return !(x & (x - 1));
}

long long gcd(long long a, long long b) {
    if (b == 0) { return a; }
    return gcd(b, a % b);
}

long long gcd(std::vector<long long> &v) {
    long long ans = v[0];
    for (int i = 1; i < (int) v.size(); ++i) {
        ans = gcd(ans, v[i]);
    }
    return ans;
}

long long lcm(long long a, long long b) {
    long long g = gcd(a, b);
    return a / g * b;
}

const int INF = 1u << 30u;  // 1,073,741,824
const long long LINF = 1ull << 60u;
const double EPS = 1e-9;
const long double PI = acos(-1.0);
const std::vector<int> dy2 = {0, 1}, dx2 = {1, 0};  // 右，下
const std::vector<int> dy4 = {0, 1, 0, -1}, dx4 = {1, 0, -1, 0};
const std::vector<int> dy6 = {0, -1, 0, 1, 1, 1}, dx6 = {1, 0, -1, 0, 1, -1};
const std::vector<int> dy8 = {0, -1, 0, 1, 1, -1, -1, 1}, dx8 = {1, 0, -1, 0, 1, 1, -1, -1};



template<typename T> class Edge {
public:
    const int u;
    const int v;
    const T distance;
    const int no;
    Edge(int u, int v, T distance, int no=-1) : u(u), v(v), distance(distance), no(no) {
    }
};

// Yen's algorithm
// 最短経路をK個見つける
// O(KN * SP)．SPは最短経路問題の計算量
template<typename T> class KShortestPath {
public:
    const int num_nodes;
    const int K;
private:
    std::vector<std::vector<int>> graph;
    std::vector<Edge<T>> edges;
    std::vector<T> distance;
    std::vector<std::vector<int>> A;            // A[k][i] = k 番目の最短経路の i 番目の edge
    std::set<std::pair<T, std::vector<int>>> B; // deviation path
    std::vector<int> removed_edge;              // removed_edge[i] = edge i が使えない time

public:
    KShortestPath(const int num_nodes, const int K) : num_nodes(num_nodes), K(K) {
        this->graph.resize(num_nodes);
    }

    void add_directed_edge(const int u, const int v, const T w) {
        const int no = this->edges.size();
        this->graph[u].emplace_back(no);
        this->edges.emplace_back(Edge(u, v, w, no));
    }

    void add_undirected_edge(const int u, const int v, const T w) {
        const int no = this->edges.size();
        this->graph[u].emplace_back(no);
        this->graph[v].emplace_back(no + 1);
        this->edges.emplace_back(Edge(u, v, w, no));
        this->edges.emplace_back(Edge(v, u, w, no));
    }

    Edge<T> get_edge(const int edge_no) const {
        return this->edges[edge_no];
    }

    // k番目の最短経路の距離を返す
    // 0-index
    T k_shortest_path_distance(const int k) const {
        return this->distance.at(k);
    }

    // k番目の最短経路の辺のindexを格納した配列を返す
    // 0-index
    std::vector<int> k_shortest_path(const int k) const {
        return this->A.at(k);
    }

    size_t num_shortest_path() const {
        return A.size();
    }

    void build(const int s, const int t) {
        assert(s < this->num_nodes);
        assert(t < this->num_nodes);
        assert(s != t);

        this->removed_edge.resize(this->edges.size(), -1);
        int time = 0;
        // 1つ目の最短経路を見つける
        {
            auto[dist, path] = this->dijkstra(s, t, 0, std::unordered_set<int>());
            if (path.empty()) {
                return;
            }
            this->A.emplace_back(path);
            this->distance.emplace_back(dist);
        }

        for (int _ = 1; _ < this->K; ++_) {
            const auto &last_path = this->A.back();
            std::vector<int> spur_root;
            T now_distance = 0;

            std::vector<int> candidate(A.size());
            std::iota(candidate.begin(), candidate.end(), 0);
            std::unordered_set<int> used_node;

            for (int i = 0; i < int(last_path.size()); ++i) {
                const int edge_idx = last_path[i];
                const auto &edge = this->edges[edge_idx];
                const int spur_node = edge.u;

                used_node.insert(spur_node);

                std::vector<int> accept;
                // 使えない辺を見つける
                for (const auto c : candidate) {
                    const auto &path_k = this->A[c];
                    if (int(path_k.size()) < i) {
                        continue;
                    }
                    this->removed_edge[this->edges[path_k[i]].no] = time;
                    // 次回にも使える最短経路
                    if (path_k[i] == last_path[i]) {
                        accept.emplace_back(c);
                    }
                }
                candidate = move(accept);

                auto [dist, suf_path] = this->dijkstra(spur_node, t, time, used_node);
                time++;

                // spur_node -> t へのパスがみつからなかった
                if (suf_path.empty()) {
                    spur_root.push_back(edge_idx);
                    now_distance += edge.distance;
                    continue;
                }

                // 候補の経路を作成
                std::vector<int> path = spur_root;
                path.insert(path.end(), suf_path.begin(), suf_path.end());
                this->B.insert({now_distance + dist, path});

                spur_root.push_back(edge_idx);
                now_distance += edge.distance;
            }

            // これ以上最短経路はない
            if (B.empty()) {
                break;
            }

            // 候補のうち最短の経路を確定にする
            this->A.emplace_back(this->B.begin()->second);
            this->distance.emplace_back(B.begin()->first);
            B.erase(B.begin());
        }
    }

private:
    // 負辺がないとき用
    std::pair<T, std::vector<int>> dijkstra(const int start, const int end, const int time, const std::unordered_set<int> &used_node) const {
        //[(最短距離, node番号)]のque(距離が近い順にとりだす)
        std::priority_queue<std::pair<T, int>, std::vector<std::pair<T, int>>, std::greater<std::pair<T, int>>> que;
        que.push({0, start});

        std::vector<std::pair<int, int>> prev(this->num_nodes);        // 経路復元用
        std::vector<T> distance(this->num_nodes, std::numeric_limits<T>::max());   // startからの距離
        distance[start] = 0;
        std::vector<bool> used(this->num_nodes);

        while (not que.empty()) {
            const auto [now_dist, u] = que.top();
            que.pop();

            if (used[u]) {
                continue;
            }
            used[u] = true;

            if (u == end) {
                break;
            }

            for (const auto edge_idx : this->graph[u]) {
                const auto &edge = this->edges[edge_idx];
                if (this->removed_edge[edge.no] == time) {
                    continue;
                }

                const auto v = edge.v;
                const auto new_dist = now_dist + edge.distance;

                if (used_node.find(v) != used_node.end()) {
                    continue;
                }

                if (new_dist < distance[v]) {
                    prev[v] = {u, edge_idx};
                    distance[v] = new_dist;
                    que.push({new_dist, v});
                }
            }
        }

        // t にたどり着けなかった
        if (not used[end]) {
            return {0, {}};
        }

        std::vector<int> path;
        int now = end;
        while (now != start) {
            path.emplace_back(prev[now].second);
            now = prev[now].first;
        }
        reverse(path.begin(), path.end());

        return {distance[end], path};
    }
};

using namespace std;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(0);

    int N, M, K, X, Y;
    cin >> N >> M >> K;
    cin >> X >> Y;
    X--; Y--;

    vector<int> P(N), Q(N);
    for (int i = 0; i < N; ++i) {
        cin >> P[i] >> Q[i];
    }

    KShortestPath<long double> ksp(N, K);
    for (int i = 0; i < M; ++i) {
        int a, b;
        cin >> a >> b;
        a--; b--;
        auto d = sqrt((P[a] - P[b]) * (P[a] - P[b]) + (Q[a] - Q[b]) * (Q[a] - Q[b]));
        ksp.add_undirected_edge(a, b, d);
    }
    ksp.build(X, Y);

    for (int i = 0; i < K; ++i) {
        if (i < int(ksp.num_shortest_path())) {
            print(ksp.k_shortest_path_distance(i));
//            FOE(r, ksp.k_shortest_path(i)) {
//                cout << ksp.get_edge(r).u << "->" << ksp.get_edge(r).v << ", ";
//            }
//            cout << endl;
        }
        else {
            print(-1);
        }
    }

    return 0;
}