結果

問題 No.114 遠い未来
コンテスト
ユーザー fumiphys
提出日時 2019-09-09 04:44:35
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3,201 ms / 5,000 ms
コード長 7,738 bytes
コンパイル時間 3,023 ms
コンパイル使用メモリ 217,520 KB
最終ジャッジ日時 2025-01-07 17:31:47
ジャッジサーバーID
（参考情報） 		judge4 / 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 * 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 # 

// includes
#include <bits/stdc++.h>
using namespace std;

// macros
#define pb emplace_back
#define mk make_pair
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define bit(n) (1LL<<(n))
// functions
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
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){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << p.first << " " << p.second; return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
//  types
using ll = long long int;
using P = pair<int, int>;
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1000000007;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};
// io
struct fast_io{
  fast_io(){ios_base::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20);}
} fast_io_;

template <typename T>
struct Graph {
  int n;
  vector<vector<T> > d;
  vector<vector<int> > path;
  Graph(int n): n(n) {
    d = vector<vector<T>>(n, vector<T>(n, numeric_limits<T>::max() / 10));
    path = vector<vector<int>>(n, vector<int>(n, -1));
    for(int i = 0; i < n; i++)d[i][i] = 0;
  }
  void warshall_floyd(){
    for(int k = 0; k < n; k++){
      for(int i = 0; i < n; i++){
        for(int j = 0; j < n; j++){
          if(d[i][j] > d[i][k] + d[k][j]){
            d[i][j] = d[i][k] + d[k][j];
            path[i][j] = k;
          }
        }
      }
    }
  }
  void adde(int at, int to, T cost){
    d[at][to] = cost;
  }
  vector<T>& operator[](size_t i){
    return d[i];
  }
};

using GraphI = Graph<int>;
using GraphL = Graph<ll>;


template <typename T>
struct SteinerTree{
  int n;
  vector<vector<T>> d;
  T inf = numeric_limits<T>::max() / 10;
  explicit SteinerTree(int n): n(n){
    d.resize(n, vector<T>(n, inf));
    for(int i = 0; i < n; i++)d[i][i] = 0;
  }
  void adde(int from, int to, T cost){
    d[from][to] = min(d[from][to], cost);
  }
  T steiner_tree(const vector<int> &v){
    if(v.size() == 1)return 0;
    // warshall floyd
    Graph<T> g(n);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < n; j++){
        if(i != j && d[i][j] != inf)g.adde(i, j, d[i][j]);
      }
    }
    g.warshall_floyd();

    int t = v.size();
    vector<vector<T>> opt(1 << t, vector<T>(n, inf));
    for(int i = 0; i < t; i++){
      for(int j = 0; j < n; j++){
        opt[1 << i][j] = g.d[v[i]][j];
      }
    }

    for(int s = 0; s < (1 << t); s++){
      if(!(s & (s - 1)))continue;
      for(int p = 0; p < n; p++){
        for(int u = s; ; u = (u - 1) & s){
          opt[s][p] = min(opt[s][p], opt[u][p] + opt[s - u][p]);
          if(u == 0)break;
        }
      }
      for(int p = 0; p < n; p++){
        for(int q = 0; q < n; q++){
          opt[s][p] = min(opt[s][p], opt[s][q] + g.d[p][q]);
        }
      }
    }
    T res = inf;
    for(int s = 0; s < (1 << t); s++){
      for(int p = 0; p < n; p++){
        res = min(res, opt[s][p] + opt[(1<<t)-1-s][p]);
      }
    }
    return res;
  }
};

typedef struct UnionFind_ {
	vector<int> par, rank_, siz;
  UnionFind_(){}
	explicit UnionFind_(int n): rank_(n, 0), siz(n, 1) {
    par.resize(n);
    for(int i = 0; i < n; i++)par[i] = i;
	}
	int find(int x) {
    if(par[x] == x)return x;
    else return par[x] = find(par[x]);
	}
	bool same(int x, int y) {
    if(find(x) == find(y))return true;
    else return false;
	}
	bool unite(int x, int y){
    int xp = find(x);
    int yp = find(y);
    if(xp == yp)return false;
    if(rank_[xp] > rank_[yp]){
      par[yp] = xp;
      siz[xp] += siz[yp];
    }
    else if(rank_[xp] < rank_[yp]){
      par[xp] = yp;
      siz[yp] += siz[xp];
    }
    else {
      par[yp] = xp;
      siz[xp] += siz[yp];
      rank_[xp]++;
    }
    return true;
	}
  int size(int i){
    return siz[find(i)];
  }
} UnionFind;

template <typename T>
struct edge{
  int from;
  int to;
  T cost;
};

template <typename T>
bool comp(const edge<T> &a, const edge<T> &b){
  return a.cost < b.cost;
}

template <typename T>
struct GraphK {
  int n;
  vector<edge<T>> es;
  GraphK(int n_){
    n = n_;
  }
  void adde(int from, int to, T cost){
    es.push_back((edge<T>){from, to, cost});
  }
  void build(){
    sort(es.begin(), es.end(), comp<T>);
  }
  T kruskal(ll mask){
    T res = 0;
    UnionFind uf(n);
    for(auto e: es){
      int from = e.from;
      int to = e.to;
      if(!(bit(from) & mask) || !(bit(to) & mask))continue;
      T cost = e.cost;
      if(uf.same(from, to))continue;
      res += cost;
      uf.unite(from, to);
    }
    int c = 0;
    while(!(bit(c) & mask))c++;
    if(uf.siz[uf.find(c)] != __builtin_popcountll(mask))return inf;
    return res;
  }
};

using GraphKI = GraphK<int>;


int eds[36][36];

int main(int argc, char const* argv[])
{
  int n, m, t;
  cin >> n >> m >> t;
  if(t <= 15){
    SteinerTree<int> st(n);
    rep(i, m){
      int a, b, c;
      cin >> a >> b >> c, a--, b--;
      st.adde(a, b, c);
      st.adde(b, a, c);
    }
    vector<int> v(t);
    cin >> v;
    rep(i, t)v[i]--;
    cout << st.steiner_tree(v) << endl;
  }else{
    GraphKI gk(n);
    rep(i, m){
      int a, b, c;
      cin >> a >> b >> c, a--, b--;
      gk.adde(a, b, c);
      gk.adde(b, a, c);
    }
    gk.build();
    vector<bool> use(n, false);
    rep(i, t){
      int u;
      cin >> u, u--;
      use[u] = true;
    }
    vector<int> ve;
    ll res = linf;
    rep(i, n)if(!use[i])ve.pb(i);
    //for(int i = 0; i < (1 << (n - t)); i++){
    rrep(i, (1 << (n - t))){
      ll mask = 0;
      rep(j, n)if(use[j])mask |= (1LL << j);
      rep(j, sz(ve)){
        if((i >> j) & 1)mask |= (1LL << ve[j]);
      }
      res = min(res, (ll)gk.kruskal(mask));
    }
    cout << res << endl;
  }
  return 0;
}
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