Submission #1221176

#	Time	Username	Problem	Language	Result	Execution time	Memory
1221176		Zero_OP	통행료 (APIO13_toll)	C++20	56 / 100	2589 ms	20432 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, used;
    DSU(int n) : lab(n, -1), used() {}

    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);
        if(lab[u] == -1) used.pb(u);
        if(lab[v] == -1) used.pb(v);
        lab[u] += lab[v]; lab[v] = u;
        return true;
    }

    void reset(){
        for(auto u : used) lab[u] = -1;
        used.clear();
    }
};  

int N, M, K, depth[MAX], par[MAX], p[MAX], sum[MAX], avail[MAX];
vi adjTree[MAX];

void dfs_tree(int u, int pre){
    sum[u] = p[u];
    for(auto v : adjTree[u]) if(v != pre){
        // cout << "edge : " << u << ' ' << 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){
    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);
        minimize(avail[v], w);
        u = par[u]; 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];

    /*
    
    all M edges have distinct weights => only 1 MST
    Observation 1: 
    - Let W = sum of weight in the base MST, W' = sum of weight in the new MST 
    (including some additional edges, and these edges do not create any cycles)
    - In the optimal weight assignment : W = W'
    Proof : 
    - If W > W' => exist a additional edge where any resultant graph's MST(s) never have that edge
    - If W < W' => exist a way to increase a weight assignment of a additional edge 
    until no other edge can overtake the edge in the MST 
    => W = W'


    */

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

    int cnt = 0;
    rep(i, 0, M){
        if(dsu.join(e[i].u, e[i].v)){
            int u = e[i].u, v = e[i].v, w = e[i].w;
            mst[cnt++] = e[i];
        }
    }
    assert(cnt == N-1);
    ll ans = 0;

    for(int mask = 1; mask < (1 << K); ++mask){
        dsu.reset();
        rep(i, 0, N) {
            adjTree[i].clear();
            avail[i] = 1e9;
        }
        bool ok = true;
        rep(i, 0, K){
            if((mask >> i & 1) && !dsu.join(add[i].u, add[i].v)){
                ok = false;
                break;
            }

            if(mask >> i & 1){
                adjTree[add[i].u].pb(add[i].v);
                adjTree[add[i].v].pb(add[i].u);
            }
        }

        if(!ok) continue;
        vb in_mst(N-1);
        rep(i, 0, N-1){
            in_mst[i] = dsu.join(mst[i].u, mst[i].v);
            if(in_mst[i]){
                adjTree[mst[i].u].pb(mst[i].v);
                adjTree[mst[i].v].pb(mst[i].u);
            }
        }

        dfs_tree(0, -1);

        rep(i, 0, N-1){
            if(!in_mst[i]){
                update(mst[i].u, mst[i].v, mst[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);
                // cout << dbg(lower) << avail[lower] << ' ' << sum[lower] << '\n';
                cur += 1LL * sum[lower] * avail[lower]; 
            }
        }
        maximize(ans, cur);
        // cout << dbg(cur) << '\n';
        // cout << "_______________\n";
    }
    cout << ans << '\n';
}

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

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

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

    return 0;
}

• Subtask 1: 16 / 16
• Subtask 2: 18 / 18
• Subtask 3: 22 / 22
• Subtask 4: 0 / 22
• Subtask 5: 0 / 22