Submission #1194076

#	Time	Username	Problem	Language	Result	Execution time	Memory
1194076		_callmelucian	Toll (APIO13_toll)	C++17	56 / 100	165 ms	12428 KiB

toll

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

using ll = long long;
using ld = long double;
using pl = pair<ll,ll>;
using pii = pair<int,int>;
using tpl = tuple<int,int,int>;

#define all(a) a.begin(), a.end()
#define filter(a) a.erase(unique(all(a)), a.end())

struct DSU {
    vector<int> lab, weight;
    DSU (int sz) : lab(sz + 1, -1), weight(sz + 1) {}

    int get (int u) {
        if (lab[u] < 0) return u;
        return lab[u] = get(lab[u]);
    }

    int getWeight (int u) { return weight[get(u)]; }
    void asgn (int u, int cur) { weight[get(u)] = cur; }

    bool unite (int a, int b) {
        a = get(a), b = get(b);
        if (a == b) return 0;
        if (-lab[a] < -lab[b]) swap(a, b);
        lab[a] += lab[b], weight[a] += weight[b];
        return lab[b] = a, 1;
    }
};

const int mn = 1e5 + 5;
ll cmpr[mn], cmp[mn], edw[mn], sumWeight[mn];
ll dp[mn], par[mn], depth[mn];
vector<pii> adj[mn];

void dfs (int u, int p, int d) {
    dp[u] = sumWeight[u], par[u] = p, depth[u] = d;
    for (auto [v, w] : adj[u]) {
        if (v == p) continue;
        dfs(v, u, d + 1);
        edw[v] = w, dp[u] += dp[v];
    }
}

void process (int u, int v, ll cur) {
    while (u != v) {
        if (depth[u] == depth[v]) {
            edw[u] = min(edw[u], cur), u = par[u];
            edw[v] = min(edw[v], cur), v = par[v];
        }
        else if (depth[u] > depth[v]) edw[u] = min(edw[u], cur), u = par[u];
        else if (depth[v] > depth[u]) edw[v] = min(edw[v], cur), v = par[v];
    }
}

int main()
{
//    freopen("TOLL.inp", "r", stdin);
//    freopen("TOLL.out", "w", stdout);

    ios::sync_with_stdio(0);
    cin.tie(0);

    /// read input
    int n, m, k; cin >> n >> m >> k;
    vector<tpl> edge(m), unused;
    vector<pii> newEdge(k), used;
    DSU init(n), dsu(n);

    for (int i = 0; i < m; i++) {
        int a, b, c; cin >> a >> b >> c;
        edge[i] = make_tuple(c, a, b);
    }
    for (int i = 0; i < k; i++) {
        int a, b; cin >> a >> b;
        newEdge[i] = make_pair(a, b);
        init.unite(a, b);
    }
    sort(all(edge));

    for (int i = 1; i <= n; i++) {
        int w; cin >> w;
        dsu.asgn(i, w);
    }

    /// classify edges
    for (auto [c, a, b] : edge) {
        if (init.unite(a, b)) used.emplace_back(a, b);
        else unused.emplace_back(c, a, b);
    }
    init = DSU(n), edge.clear();
    for (auto [a, b] : used)
        init.unite(a, b), dsu.unite(a, b);
    for (auto [c, a, b] : unused)
        if (init.unite(a, b)) edge.emplace_back(c, a, b);

    /// re-index connected components
    int counter = 0;
    for (int i = 1; i <= n; i++)
        if (i == dsu.get(i))
            cmpr[i] = ++counter, sumWeight[counter] = dsu.getWeight(i);
    for (int i = 1; i <= n; i++)
        cmp[i] = cmpr[dsu.get(i)];

    /// try all subsets of new edges
    ll ans = 0;
    for (int mask = 0; mask < (1 << k); mask++) {
        // process chosen edges
        dsu = DSU(counter);
        bool flag = 1;
        for (int i = 0; i < k; i++) {
            if (mask & (1 << i)) continue;
            int a, b; tie(a, b) = newEdge[i];
            a = cmp[a], b = cmp[b];
            if (dsu.unite(a, b)) {
                adj[a].emplace_back(b, INT_MAX);
                adj[b].emplace_back(a, INT_MAX);
            }
            else {
                flag = 0;
                break;
            }
        }

        if (flag) {
            // form 1 component
            for (auto [c, a, b] : edge) {
                int u = cmp[a], v = cmp[b];
                if (dsu.unite(u, v)) {
                    adj[u].emplace_back(v, 0);
                    adj[v].emplace_back(u, 0);
                }
            }

            // dfs & set edge weight
            dfs(cmp[1], 0, 0);
            for (auto [c, a, b] : edge)
                process(cmp[a], cmp[b], c);

            ll curCost = 0;
            for (int i = 1; i <= counter; i++)
                curCost += 1LL * edw[i] * dp[i];
            ans = max(ans, curCost);
        }

        // clear data
        for (int i = 1; i <= counter; i++) adj[i].clear();
    }
    cout << ans;

    return 0;
}

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