Submission #561873

#	Time	Username	Problem	Language	Result	Execution time	Memory
561873		Cyanmond	Toll (APIO13_toll)	C++17	100 / 100	2381 ms	11544 KiB

toll

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#include <bits/stdc++.h>
 
using namespace std;
using i64 = int64_t;
 
constexpr int inf = 1 << 30;
 
#define REP(i, n) for (int i = 0; i < (n); ++i)
 
template <typename T> void chmax(T &a, const T b) {
    if (a < b) a = b;
}
 
template <typename T> void chmin(T &a, const T b) {
    if (a > b) a = b;
}
 
struct UnionFind {
    int n;
    vector<int> data;
    UnionFind(const int n_) : n(n_), data(n, -1) {}
    int find(int v) {
        if (data[v] < 0)
            return v;
        else
            return data[v] = find(data[v]);
    }
    int is_same(int a, int b) { return find(a) == find(b); }
    int size(int v) { return -data[find(v)]; }
    void unite(int a, int b) {
        a = find(a);
        b = find(b);
        if (a == b) return;
        if (size(a) < size(b)) swap(a, b);
        data[a] += data[b];
        data[b] = a;
    }
};
 
struct UF2 {
    array<char, 21> data;
    UF2() { fill(data.begin(), data.end(), -1); }
    char find(char v) {
        if (data[v] < 0)
            return v;
        else
            return data[v] = find(data[v]);
    }
    int is_same(char a, char b) { return find(a) == find(b); }
    int size(int v) { return -data[find(v)]; }
    void unite(char a, char b) {
        a = find(a);
        b = find(b);
        if (a == b) return;
        if (data[a] > data[b]) swap(a, b);
        data[a] += data[b];
        data[b] = a;
    }
};
 
struct Edge {
    int cost;
    int a;
    int b;
};
 
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
 
    int N, M, K;
    cin >> N >> M >> K;
    vector<Edge> E(M);
    REP(i, M) {
        cin >> E[i].a >> E[i].b >> E[i].cost;
        --E[i].a, --E[i].b;
    }
    vector<pair<int, int>> A(K);
    for (auto &[x, y] : A) {
        cin >> x >> y;
        --x, --y;
    }
    vector<i64> P(N);
    for (auto &e : P) cin >> e;
    sort(E.begin(), E.end(), [](Edge &a, Edge &b) { return a.cost < b.cost; });
 
    {
        UnionFind uft(N);
        int L = 1;
        REP(i, K) {
            if (uft.is_same(A[i].first, A[i].second)) --L;
            ++L;
            uft.unite(A[i].first, A[i].second);
        }
        vector<vector<int>> graph(N);
        for (const auto &[cost, a, b] : E) {
            if (uft.is_same(a, b)) continue;
            uft.unite(a, b);
            graph[a].push_back(b);
            graph[b].push_back(a);
        }
 
        vector<char> used(N);
        vector<vector<int>> groups(L);
        int cnt = 0;
        REP(i, N) {
            if (used[i]) continue;
            auto dfs = [&](auto &&self, const int v) -> void {
                used[v] = true;
                groups[cnt].push_back(v);
                for (const int t : graph[v]) {
                    if (used[t]) continue;
                    self(self, t);
                }
            };
            dfs(dfs, i);
            ++cnt;
        }
        vector<int> att(N);
        REP(i, L) {
            const auto &g = groups[i];
            for (const int e : g) att[e] = i;
        }
        vector<i64> NP(L);
        REP(i, N) NP[att[i]] += P[i];
        P = move(NP);
        for (auto &[x, y] : A) {
            x = att[x];
            y = att[y];
        }
        REP(i, M) {
            E[i].a = att[E[i].a];
            E[i].b = att[E[i].b];
        }
 
        vector<Edge> E2;
        uft = UnionFind(L);
        for (const auto &[cost, a, b] : E) {
            if (a == b) continue;
            if (uft.is_same(a, b)) continue;
            uft.unite(a, b);
            E2.push_back({cost, a, b});
        }
        E = move(E2);
        N = L;
        M = (int)size(E);
    }
 
    i64 ans = 0;
    UF2 uft;
    vector<pair<char, char>> tree[21];
    array<int, 21> nec;
    REP(bit, 1 << K) {
        REP(i, N) tree[i].clear();
        fill(uft.data.begin(), uft.data.end(), -1);
        fill(nec.begin(), nec.end(), inf);
        bool possible = true;
        int cnt = 0;
        REP(i, K) {
            if (bit & (1 << i)) {
                ++cnt;
                if (uft.is_same(A[i].first, A[i].second)) {
                    possible = false;
                    break;
                }
                uft.unite(A[i].first, A[i].second);
                tree[A[i].first].emplace_back(A[i].second, i);
                tree[A[i].second].emplace_back(A[i].first, i);
            }
        }
        if (not possible) continue;
        REP(i, M) {
            if (cnt == N - 1 or uft.is_same(E[i].a, E[i].b)) {
                auto dfs = [&](auto &&self, const int v, const int p) -> bool {
                    for (auto &[t, c] : tree[v]) {
                        if (t == p) continue;
                        if (t == E[i].b) {
                            chmin(nec[c], E[i].cost);
                            return true;
                        }
                        if (self(self, t, v)) {
                            chmin(nec[c], E[i].cost);
                            return true;
                        }
                    }
                    return false;
                };
                dfs(dfs, E[i].a, -1);
            } else {
                ++cnt;
                uft.unite(E[i].a, E[i].b);
                tree[E[i].a].emplace_back(E[i].b, -1);
                tree[E[i].b].emplace_back(E[i].a, -1);
            }
        }
 
        i64 res = 0;
        auto dfs = [&](auto &&self, const int v, const int p) -> i64 {
            i64 sum = 0;
            for (const auto &[t, c] : tree[v]) {
                if (t == p) continue;
                const i64 e = self(self, t, v);
                if (c != -1) res += nec[c] * e;
                sum += e;
            }
            return sum + P[v];
        };
        dfs(dfs, 0, -1);
        chmax(ans, res);
    }
 
    cout << ans << '\n';
}

• Subtask 1: 16 / 16
• Subtask 2: 18 / 18
• Subtask 3: 22 / 22
• Subtask 4: 22 / 22
• Subtask 5: 22 / 22