結果

問題 No.114 遠い未来
ユーザー rin204
提出日時 2023-02-17 02:16:25
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,368 ms / 5,000 ms
コード長 9,766 bytes
コンパイル時間 2,990 ms
コンパイル使用メモリ 224,872 KB
最終ジャッジ日時 2025-02-10 16:05:11
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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 * 3
other AC * 25
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 # 

#line 1 "A.cpp"
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));

#ifndef RIN__LOCAL
#define endl "\n"
#endif
#define spa ' '
#define len(A) A.size()
#define all(A) begin(A), end(A)

#define fori1(a) for(ll _ = 0; _ < (a); _++)
#define fori2(i, a) for(ll i = 0; i < (a); i++)
#define fori3(i, a, b) for(ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for(ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)

template <typename T>
vector<tuple<ll, T>> ENUMERATE(vector<T> &A, ll s = 0){
    vector<tuple<ll, T>> ret(A.size());
    for(int i = 0; i < A.size(); i++) ret[i] = {i + s, A[i]};
    return ret;
}

vector<tuple<ll, char>> ENUMERATE(string &A, ll s = 0){
    vector<tuple<ll, char>> ret(A.size());
    for(int i = 0; i < A.size(); i++) ret[i] = {i + s, A[i]};
    return ret;
}

#define enum1(A) fori(A.size())
#define enum2(a, A) for(auto a:A)
#define enum3(i, a, A) for(auto&& [i, a]: ENUMERATE(A))
#define enum4(i, a, A, s) for(auto&& [i, a]: ENUMERATE(A, s))
#define enum(...) overload4(__VA_ARGS__, enum4, enum3, enum2, enum1)(__VA_ARGS__)

template <typename T, typename S>
vector<tuple<T, S>> ZIP(vector<T> &A, vector<S> &B){
    int n = min(A.size(), B.size());
    vector<tuple<T, S>> ret(n);
    for(int i = 0; i < n; i++) ret[i] = {A[i], B[i]};
    return ret;
}

template <typename T, typename S>
vector<tuple<ll, T, S>> ENUMZIP(vector<T> &A, vector<S> &B, ll s = 0){
    int n = min(A.size(), B.size());
    vector<tuple<ll, T, S>> ret(n);
    for(int i = 0; i < n; i++) ret[i] = {i + s, A[i], B[i]};
    return ret;
}

#define zip4(a, b, A, B) for(auto&& [a, b]: ZIP(A, B))
#define enumzip5(i, a, b, A, B) for(auto&& [i, a, b]: ENUMZIP(A, B))
#define enumzip6(i, a, b, A, B, s) for(auto&& [i, a, b]: ENUMZIP(A, B, s))
#define overload6(a, b, c, d, e, f, g, ...) g
#define zip(...) overload6(__VA_ARGS__, enumzip6, enumzip5, zip4, _, _, _)(__VA_ARGS__)

vector<char> stoc(string &S){
    int n = S.size();
    vector<char> ret(n);
    for(int i = 0; i < n; i++) ret[i] = S[i];
    return ret;
}

#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);

const ll MOD1 = 1000000007;
const ll MOD9 = 998244353;

template<class T> auto min(const T& a){
    return *min_element(all(a));
}
template<class T> auto max(const T& a){
    return *max_element(all(a));
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

void FLUSH(){cout << flush;}
void print(){cout << endl;}
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
    cout << head;
    if (sizeof...(Tail)) cout << spa;
    print(forward<Tail>(tail)...);
}
template<typename T>
void print(vector<T> &A){
    int n = A.size();
    for(int i = 0; i < n; i++){
        cout << A[i];
        if(i == n - 1) cout << endl;
        else cout << spa;
    }
}
template<typename T>
void print(vector<vector<T>> &A){
    for(auto &row: A) print(row);
}
template<typename T, typename S>
void print(pair<T, S> &A){
    cout << A.first << spa << A.second << endl;
}
template<typename T, typename S>
void print(vector<pair<T, S>> &A){
    for(auto &row: A) print(row);
}
template<typename T, typename S>
void prisep(vector<T> &A, S sep){
    int n = A.size();
    for(int i = 0; i < n; i++){
        cout << A[i];
        if(i == n - 1) cout << endl;
        else cout << sep;
    }
}
template<typename T, typename S>
void priend(T A, S end){
    cout << A << end;
}
template<typename T>
void priend(T A){
    priend(A, spa);
}
template<class... T>
void inp(T&... a){
    (cin >> ... >> a);
}
template<typename T>
void inp(vector<T> &A){
    for(auto &a:A) cin >> a;
}
template<typename T>
void inp(vector<vector<T>> &A){
    for(auto &row:A) inp(row);
}
template<typename T, typename S>
void inp(pair<T, S> &A){
    inp(A.first, A.second);
}
template<typename T, typename S>
void inp(vector<pair<T, S>> &A){
    for(auto &row: A) inp(row.first, row.second);
}

template<typename T>
T sum(vector<T> &A){
    T tot = 0;
    for(auto a:A) tot += a;
    return tot;
}

template<typename T>
pair<vector<T>, map<T, int>> compression(vector<T> X){
    sort(all(X));
    X.erase(unique(all(X)), X.end());
    map<T, int> mp;
    for(int i = 0; i < X.size(); i++) mp[X[i]] = i;
    return {X, mp};
}

#line 2 "Library/C++/data_structure/UnionFind.hpp"

struct UnionFind{
    int n;
    vector<int> par;
    int group;

    UnionFind(int n) : n(n){
        par.assign(n, -1);
        group = n;
    }

    int find(int x){
        if(par[x] < 0) return x;
        par[x] = find(par[x]);
        return par[x];
    }

    bool unite(int x, int y){
        x = find(x);
        y = find(y);
        if(x == y) return false;
        if(par[x] > par[y]) swap(x, y);
        group--;
        par[x] += par[y];
        par[y] = x;
        return true;
    }

    bool same(int x, int y){
        return find(x) == find(y);
    }

    int size(int x){
        return -par[find(x)];
    }

    vector<int> roots(){
        vector<int> ret;
        for(int i = 0; i < n; i++){
            if(i == find(i)) ret.push_back(i);
        }
        return ret;
    }

};
#line 3 "_tmp/SteinerTree.hpp"

template<typename T=long long, T inf=1LL << 60>
struct SteinerTree{
    struct Edge{
        int to;
        T cost;
    };
    int n;
    vector<vector<Edge>> G;

    SteinerTree(int n) : n(n){
        G.resize(n);
    }

    void add_edge(int u, int v, T cost){
        G[u].push_back({v, cost});
        G[v].push_back({u, cost});
    }

    T solve1(vector<int> &terminal){
        // O(n3^t + (n + m)2^t log(n))
        int t = terminal.size();
        if(t == 0) return T(0);
        vector<vector<T>> dp(1 << t, vector<T>(n, inf));
        for(int i = 0; i < t; i++) dp[1 << i][terminal[i]] = 0;
        for(int i = 1; i < (1 << t); i++){
            for(int j = 0; j < n; j++){
                for(int k = i; k > 0; k = (k - 1) & i){
                    dp[i][j] = min(dp[i][j], dp[k][j] + dp[i ^ k][j]);
                }
            }
            if(i == (1 << t) - 1) break;
            priority_queue<pair<T, int>, vector<pair<T, int>>, greater<pair<T, int>>> pq;
            for(int j = 0; j < n; j++){
                pq.push({dp[i][j], j});
            }
            while(!pq.empty()){
                T d = pq.top().first;
                int pos = pq.top().second;
                pq.pop();
                if(dp[i][pos] < d) continue;
                for(auto &e:G[pos]){
                    if(dp[i][e.to] > dp[i][pos] + e.cost){
                        dp[i][e.to] = dp[i][pos] + e.cost;
                        pq.push({dp[i][e.to], e.to});
                    }
                }
            }
        }
        return dp[(1 << t) - 1][terminal[0]];
    }

    T solve2(vector<int> &terminal){
        // O(2^(n-t)m)
        T res = inf;
        int t = terminal.size();
        int k = n - t;
        vector<bool> use(n, false);
        for(auto t:terminal) use[t] = true;
        vector<int> free;
        for(int i = 0; i < n; i++){
            if(!use[i]) free.push_back(i);
        }

        vector<tuple<T, int, int>> C;
        for(int i = 0; i < n; i++){
            for(auto &e:G[i]){
                if(e.to > i) C.push_back({e.cost, i, e.to});
            }
        }
        sort(C.begin(), C.end());

        for(int bit = 0; bit < (1 << k); bit++){
            int cnt = t - 1;;
            for(int i = 0; i < k; i++){
                if((bit >> i) & 1){
                    use[free[i]] = true;
                    cnt++;
                }
            }
            T cost = 0;
            UnionFind UF(n);
            for(auto &e:C){
                if(!use[get<1>(e)] || !use[get<2>(e)]) continue;
                if(UF.unite(get<1>(e), get<2>(e))){
                    cost += get<0>(e);
                    cnt--;
                    if(cnt == 0){
                        res = min(res, cost);
                        break;
                    }
                }
            }

            for(int i = 0; i < k; i++){
                if((bit >> i) & 1) use[free[i]] = false;
            }
        }

        return res;
    }

    T solve(vector<int> &terminal, int thres=15){
        if(terminal.size() <= thres){
            return solve1(terminal);
        }
        else{
            return solve2(terminal);
        }
    }
};
#line 188 "A.cpp"

void solve(){
    INT(n, m, t);
    SteinerTree<int, 1 << 29> G(n);
    fori(m){
        INT(a, b, c);
        G.add_edge(a - 1, b - 1, c);
    }
    VEC(int, terminal, t);
    fori(i, t) terminal[i]--;
    auto ans = G.solve(terminal, 14);
    print(ans);
}

int main(){
    cin.tie(0)->sync_with_stdio(0);
    cout << fixed << setprecision(12);
    int t;
    t = 1;
    // cin >> t;
    while(t--) solve();
    return 0;
}
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