#998451 (C++17) No.114 遠い未来

提出ソース

結果

問題	No.114 遠い未来
ユーザー	wanui
提出日時	2024-07-30 01:03:03
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	TLE
実行時間	-
コード長	6,231 bytes
コンパイル時間	3,146 ms
コンパイル使用メモリ	228,308 KB
実行使用メモリ	8,064 KB
最終ジャッジ日時	2024-07-30 01:03:30
合計ジャッジ時間	26,418 ms
ジャッジサーバーID （参考情報）	judge5 / judge2

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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	49 ms 6,816 KB
testcase_01	AC	2,329 ms 6,940 KB
testcase_02	AC	391 ms 6,944 KB
testcase_03	AC	61 ms 6,940 KB
testcase_04	AC	2 ms 6,940 KB
testcase_05	AC	16 ms 6,940 KB
testcase_06	AC	866 ms 6,940 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	2 ms 6,940 KB
testcase_09	AC	40 ms 6,944 KB
testcase_10	AC	343 ms 6,944 KB
testcase_11	AC	2,816 ms 8,064 KB
testcase_12	AC	1,671 ms 6,940 KB
testcase_13	TLE	-
testcase_14	AC	852 ms 6,940 KB
testcase_15	AC	2,962 ms 6,940 KB
testcase_16	AC	406 ms 6,940 KB
testcase_17	AC	460 ms 6,940 KB
testcase_18	AC	2,090 ms 6,940 KB
testcase_19	AC	206 ms 6,944 KB
testcase_20	AC	253 ms 6,940 KB
testcase_21	AC	14 ms 6,940 KB
testcase_22	AC	16 ms 6,944 KB
testcase_23	AC	2 ms 6,940 KB
testcase_24	AC	4 ms 6,940 KB
testcase_25	AC	2 ms 6,940 KB
testcase_26	AC	2 ms 6,944 KB
testcase_27	AC	2 ms 6,944 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
// clang-format off
using namespace std; using ll=long long; using ull=unsigned long long; using pll=pair<ll,ll>; const ll INF=4e18;
void print0(){}; template<typename H,typename... T> void print0(H h,T... t){cout<<h;print0(t...);}
void print1(){print0("\n");}; template<typename H,typename... T>void print1(H h,T... t){print0(h);if(sizeof...(T)>0)print0(" ");print1(t...);}
#define debug1(a) { cerr<<#a<<":"<<a<<endl; }
#define debug2(a,b) { cerr<<#a<<":"<<a<<" "<<#b<<":"<<b<<endl; }
#define debug3(a,b,c) { cerr<<#a<<":"<<a<<" "<<#b<<":"<<b<<" "<<#c<<":"<<c<<endl; }
#define debug4(a,b,c,d) { cerr<<#a<<":"<<a<<" "<<#b<<":"<<b<<" "<<#c<<":"<<c<<" "<<#d<<":"<<d<<endl; }
// clang-format on

namespace SteinerTree {
ll solve(vector<vector<pll>>& graph, vector<bool>& is_city) {
    ll N = graph.size();
    ll K = 0;
    vector<ll> cityid(N, -1);
    for (ll u = 0; u < N; u++) {
        if (is_city[u]) {
            cityid[u] = K;
            K++;
        }
    }

    ll ans = INF;
    {
        vector<vector<ll>> dp(N, vector<ll>(1 << K, INF));
        for (ll u = 0; u < N; u++) {
            if (cityid[u] >= 0) {
                ll city = cityid[u];
                dp[u][1 << city] = 0;
            }
            dp[u][0] = 0;
        }

        for (ll s = 1; s < (1 << K); s++) {
            for (ll u = 0; u < N; u++) {
                for (ll j = s;; j = (j - 1) & s) {
                    ll k = s ^ j;  // 残り
                    if (k > 0 && j > 0) {
                        dp[u][s] = min(dp[u][s], dp[u][j] + dp[u][k]);
                    }
                    if (!j) break;
                }
            }
            priority_queue<pll, vector<pll>, greater<pll>> pq;
            for (ll u = 0; u < N; u++) {
                ll city = cityid[u];
                if (dp[u][s] == INF) continue;
                pq.push({dp[u][s], u});
            }
            vector<bool> done(N);
            while (pq.size()) {
                ll cost, u;
                tie(cost, u) = pq.top();
                pq.pop();
                if (done[u]) continue;
                done[u] = true;
                dp[u][s] = min(dp[u][s], cost);
                if (cityid[u] >= 0) {
                    ll t = (1 << cityid[u]) | s;
                    dp[u][t] = min(dp[u][t], cost);
                }
                for (auto e : graph[u]) {
                    pq.push({e.second + cost, e.first});
                }
            }
        }
        for (ll u = 0; u < N; u++) {
            ans = min(ans, dp[u][(1 << K) - 1]);
        }
    }
    return ans;
}

};  // namespace SteinerTree

namespace LargeSolver {
class unionfind {
   public:
    vector<ll> partition;
    vector<ll> rank;
    vector<ll> siz;
    ll n;
    unionfind(ll n_) {
        partition.resize(n_);
        rank.resize(n_);
        siz.resize(n_);
        for (ll x = 0; x < n_; x++) {
            partition[x] = x;
            rank[x] = 0;
            siz[x] = 1;
        }
        n = n_;
    }
    ll find(ll x) {
        if (partition[x] == x) {
            return x;
        } else {
            partition[x] = find(partition[x]);
            return partition[x];
        }
    }
    void unite(ll x, ll y) {
        x = find(x);
        y = find(y);
        if (x == y) {
            return;
        }
        ll sx = siz[x];
        ll sy = siz[y];
        if (rank[x] < rank[y]) {
            partition[x] = y;
        } else {
            partition[y] = x;
            if (rank[x] == rank[y]) {
                rank[x]++;
            }
        }
        siz[find(x)] = sx + sy;
    }
    bool same(ll x, ll y) {
        return find(x) == find(y);
    }
    ll clstsize(ll x) {
        return siz[find(x)];
    }
    vector<pair<ll, vector<ll>>> get_clusters() {
        vector<vector<ll>> con(n);
        for (ll i = 0; i < n; i++) {
            con[find(i)].push_back(i);
        }

        vector<pair<ll, vector<ll>>> result;
        for (ll i = 0; i < n; i++) {
            if (con[i].size() > 0) {
                vector<ll> members = con[i];
                result.push_back({i, members});
            }
        }
        return result;
    }
};

ll solve(vector<vector<pll>>& graph, vector<bool>& is_city) {
    ll N = graph.size();
    vector<ll> villages;
    for (ll u = 0; u < N; u++) {
        if (!is_city[u]) villages.push_back(u);
    }
    vector<ll> edgs;
    for (ll u = 0; u < N; u++) {
        for (auto e : graph[u]) {
            ll v = e.first;
            ll c = e.second;
            if (u > v) continue;
            edgs.push_back(c * 1000000 + u * 1000 + v);
        }
    }
    sort(edgs.begin(), edgs.end());

    ll ans = INF;
    ll m = villages.size();
    for (ll i = 0; i < (1 << m); i++) {
        ll first_city = N;
        ll usenum = 0;
        vector<bool> use(N);
        for (ll u = 0; u < N; u++) {
            if (is_city[u]) {
                first_city = min(first_city, u);
                use[u] = true;
                usenum++;
            }
        }
        for (ll j = 0; j < m; j++) {
            if ((i >> j) & 1) {
                use[villages[j]] = true;
                usenum++;
            }
        }

        ll now = 0;
        auto uf = unionfind(N);
        for (auto e : edgs) {
            ll c = e / 1000000;
            ll u = (e % 1000000) / 1000;
            ll v = e % 1000;
            if (!use[u] || !use[v]) continue;
            if (!uf.same(u, v)) {
                uf.unite(u, v);
                now += c;
            }
        }
        if (uf.clstsize(first_city) == usenum) {
            ans = min(ans, now);
        }
    }
    return ans;
}

};  // namespace LargeSolver

int main() {
    ll N, M, T;
    cin >> N >> M >> T;
    vector<vector<pll>> graph(N);
    for (ll i = 0; i < M; i++) {
        ll u, v, c;
        cin >> u >> v >> c;
        u--;
        v--;
        graph[u].push_back({v, c});
        graph[v].push_back({u, c});
    }
    vector<bool> is_city(N);
    for (ll i = 0; i < T; i++) {
        ll u;
        cin >> u;
        u--;
        is_city[u] = true;
    }
    if (T <= 14) {
        print1(SteinerTree::solve(graph, is_city));
    } else {
        print1(LargeSolver::solve(graph, is_city));
    }
}

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結果

テストケース

ソースコード