Submission #1221404

#	Time	Username	Problem	Language	Result	Execution time	Memory
1221404		Zero_OP	Toll (APIO13_toll)	C++20	100 / 100	844 ms	19924 KiB

toll

#include <bits/stdc++.h>

using namespace std;

//loops (warning : long long)
#define FOR(i, l, r) for(int i = (l); i < (r); ++i)
#define ROF(i, r, l) for(int i = (r - 1); i >= l; --i)
#define rep(i, l, r) for(int i = (l); i < (r); ++i)

//pairs, tuples
#define mp make_pair
#define mt make_tuple
#define ff first
#define ss second

//vectors
#define all(v) begin(v), end(v)
#define rall(v) rbegin(v), rend(v)
#define pb push_back
#define eb emplace_back
#define sum_of(v) accumulate(all(v), 0ll)
#define sz(v) (int)v.size()
#define compact(v) v.erase(unique(all(v)), end(v))

//binary search
#define lwb lower_bound
#define upb upper_bound

//other stuffs
#define dbg(x) "[" #x " = " << (x) << "]"
#define file(task) if(fopen(task".inp", "r")){ freopen(task".inp", "r", stdin); freopen(task".out", "w", stdout); }

template<typename T>
bool minimize(T& a, const T& b){
    if(a > b) return a = b, true;
    return false;
}

template<typename T>
bool maximize(T& a, const T& b){
    if(a < b) return a = b, true;
    return false;
}

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using db = double;
using pi = pair<int, int>;
using pl = pair<ll, ll>;

using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vpi = vector<pi>;
using vpl = vector<pl>;

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());

const int MAX = 3e5 + 5;

struct edge{
    int u, v, w;
    edge(int u, int v, int w) : u(u), v(v), w(w) {}
    edge() : u(0), v(0), w(0) {}

    bool operator < (const edge& o) const {
        return w < o.w;
    }
} e[MAX], add[20], mst[MAX];

struct DSU{
    vi lab; int components;
    DSU(int n) : lab(n, -1), components(n) {}

    int root(int u){
        return lab[u] < 0 ? u : (lab[u] = root(lab[u]));
    }

    bool join(int u, int v){
        u = root(u);
        v = root(v);
        if(u == v) return false;
        if(lab[u] > lab[v]) swap(u, v);
        --components;
        lab[u] += lab[v]; lab[v] = u;
        return true;
    }

    void reset(){
        fill(all(lab), -1);
        components = sz(lab);
    }
};  

int N, M, K, p[MAX], c[MAX];

int avail[30], par[30], depth[30];
ll sum_p[30], sum[30];
bool type[MAX];
vi adj[MAX];

void dfs_cc(int u, int color){
    c[u] = color;
    for(auto v : adj[u]) if(c[v] == -1){
        // cout << "mst : " << u+1 << ' ' << v+1 << '\n';
        dfs_cc(v, color);
    }
}

void dfs_tree(int u, int p){
    // cout << "visit : " << u << '\n';
    sum[u] = sum_p[u];
    for(auto v : adj[u]) if(v != p){
        // cout << dbg(u) << dbg(v) << '\n';
        depth[v] = depth[u] + 1;
        par[v] = u;
        dfs_tree(v, u);
        sum[u] += sum[v];
    }
}

void update(int u, int v, int w){
    // cout << "update : " << u << ' ' << v << ' ' << w << '\n';
    if(depth[u] < depth[v]) swap(u, v);
    while(depth[u] > depth[v]){
        minimize(avail[u], w);
        u = par[u];
    }
    
    while(u != v){
        minimize(avail[u], w); u = par[u];
        minimize(avail[v], w); v = par[v];
    }
}

void testcase(int ntestcase){
    cin >> N >> M >> K;
    rep(i, 0, M){
        int u, v, w;
        cin >> u >> v >> w;
        --u, --v;
        e[i] = edge(u, v, w);
    }

    rep(i, 0, K){
        int u, v;
        cin >> u >> v;
        --u, --v;
        add[i] = edge(u, v, 0);
    }

    rep(i, 0, N) cin >> p[i];

    sort(e, e + M);
    DSU dsu(N);

    rep(i, 0, K){
        dsu.join(add[i].u, add[i].v);
    }

    rep(i, 0, M){
        type[i] = dsu.join(e[i].u, e[i].v);
        if(type[i]){
            adj[e[i].u].pb(e[i].v);
            adj[e[i].v].pb(e[i].u);
        }
    }

    dsu.reset();
    rep(i, 0, M){
        if(type[i] == 1) dsu.join(e[i].u, e[i].v);
    }

    vector<edge> extra;
    rep(i, 0, M){
        if(type[i] == 0){
            if(dsu.join(e[i].u, e[i].v)){
                extra.eb(e[i]);
            }
        }
    }

    memset(c, -1, sizeof(c));
    int cnt = 0;
    rep(i, 0, N){
        if(c[i] == -1){
            dfs_cc(i, cnt++);
        }

        sum_p[c[i]] += p[i];
    }

    // rep(i, 0, cnt) cout << sum_p[i] << ' '; cout << '\n';

    rep(i, 0, sz(extra)) extra[i].u = c[extra[i].u], extra[i].v = c[extra[i].v];
    rep(i, 0, K) add[i].u = c[add[i].u], add[i].v = c[add[i].v];
    
    // for(auto [u, v, w] : extra) cout << "extra : " << u << ' ' << v << ' ' << w << '\n';

    ll ans = 0;
    DSU compressed_dsu(cnt);
    rep(mask, 1, (1 << K)){
        compressed_dsu.reset();
        rep(i, 0, cnt) avail[i] = 1e9, adj[i].clear();
        bool ok = true;
        rep(i, 0, K) if(mask >> i & 1){
            if(!compressed_dsu.join(add[i].u, add[i].v)){
                ok = false;
                break;
            }
            adj[add[i].u].pb(add[i].v);
            adj[add[i].v].pb(add[i].u);
        }

        if(!ok) continue;

        rep(i, 0, sz(extra)){
            type[i] = (compressed_dsu.join(extra[i].u, extra[i].v));
            if(type[i]){
                adj[extra[i].u].pb(extra[i].v);
                adj[extra[i].v].pb(extra[i].u);
            }
        }

        // assert(compressed_dsu.components == 1);

        dfs_tree(0, -1);
        rep(i, 0, sz(extra)){
            update(extra[i].u, extra[i].v, extra[i].w);
        }

        ll cur = 0;
        rep(i, 0, K) if(mask >> i & 1){
            int lower = (depth[add[i].u] < depth[add[i].v] ? add[i].v : add[i].u);
            cur += 1LL * sum[lower] * avail[lower];
            // cout << dbg(sum[lower]) << dbg(avail[lower]) << '\n';
        }  

        // cout << bitset<3>(mask) << " : " << cur << '\n';
        maximize(ans, cur);
        // cout << "____________________\n";
    }
    cout << ans << '\n';
}

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

#ifdef LOCAL
    freopen("task.inp", "r", stdin);
    freopen("task.out", "w", stdout);
#endif // LOCAL

    int T = 1;
//    cin >> T;
    FOR(i, 0, T) testcase(i);

    return 0;
}

/*

9 14 5
1 6 9
5 3 20
5 6 18
7 3 9
2 6 18
9 1 20
4 1 20
5 1 14
8 1 7
3 2 8
2 8 19
2 7 12
5 1 18
5 9 8
5 7
5 3
9 1
9 3
2 9
10 18 12 15 2 8 5 9 17 
1386


*/

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