Submission #247663

#	Time	Username	Problem	Language	Result	Execution time	Memory
247663		keko37	Toll (APIO13_toll)	C++14	100 / 100	1785 ms	24240 KiB

toll

#include<bits/stdc++.h>

using namespace std;

typedef long long llint;
typedef pair <int, int> pi;

const int MAXN = 300005;

llint n, m, k, cnt, sol;
int a[MAXN], b[MAXN], c[MAXN], na[MAXN], nb[MAXN], in[MAXN], par[MAXN], p[MAXN], dub[MAXN], mn[MAXN], ok[MAXN];
llint cost[MAXN], comp[MAXN], val[MAXN], siz[MAXN];
vector <int> e, rip, v[MAXN];

int nadi (int x) {
    if (x == par[x]) return x;
    return par[x] = nadi(par[x]);
}

bool spoji (int x, int y) {
    x = nadi(x); y = nadi(y);
    par[x] = y;
    return x != y;
}

bool cmp (int e1, int e2) {
    return c[e1] < c[e2];
}

void oboji (int x) {
    if (comp[x] != 0) return;
    comp[x] = cnt;
    val[cnt] += cost[x];
    for (auto sus : v[x]) {
        oboji(sus);
    }
}

void build_graph () {
    sort(in, in + m, cmp);
    for (int i = 1; i <= n; i++) par[i] = i;
    for (int i = 0; i < m; i++) {
        if (spoji(a[in[i]], b[in[i]])) e.push_back(in[i]);
    }

    for (int i = 1; i <= n; i++) par[i] = i;
    for (int i = 0; i < k; i++) spoji(na[i], nb[i]);
    for (auto i : e) {
        if (spoji(a[i], b[i])) {
            v[a[i]].push_back(b[i]);
            v[b[i]].push_back(a[i]);
        } else {
            rip.push_back(i);
        }
    }
    for (int i = 1; i <= n; i++) {
        if (comp[i] == 0) {
            cnt++;
            oboji(i);
        }
    }

    e = rip;
    for (auto i : e) a[i] = comp[a[i]], b[i] = comp[b[i]];
    for (int i = 0; i < k; i++) na[i] = comp[na[i]], nb[i] = comp[nb[i]];
}

void dfs (int x, int rod) {
    dub[x] = 1 + dub[rod];
    p[x] = rod;
    siz[x] = val[x];
    for (auto sus : v[x]) {
        if (sus == rod) continue;
        dfs(sus, x);
        siz[x] += siz[sus];
    }
}

void lca (int a, int b, int c) {
    if (dub[a] < dub[b]) swap(a, b);
    while (dub[a] > dub[b]) {
        mn[a] = min(mn[a], c);
        a = p[a];
    }
    while (a != b) {
        mn[a] = min(mn[a], c); a = p[a];
        mn[b] = min(mn[b], c); b = p[b];
    }
}

void solve (int mask) {
    for (int i = 1; i <= cnt; i++) {
        par[i] = i;
        mn[i] = 1e9;
        v[i].clear();
    }
    for (int i = 0; i < k; i++) {
        if ((mask & (1 << i)) && spoji(na[i], nb[i])) {
            v[na[i]].push_back(nb[i]);
            v[nb[i]].push_back(na[i]);
            ok[i] = 1;
        } else {
            ok[i] = 0;
        }
    }
    rip.clear();
    for (auto i : e) {
        if (spoji(a[i], b[i])) {
            v[a[i]].push_back(b[i]);
            v[b[i]].push_back(a[i]);
        } else {
            rip.push_back(i);
        }
    }
    dfs(1, 0);
    for (auto i : rip) lca(a[i], b[i], c[i]);
    llint sum = 0;
    for (int i = 0; i < k; i++) {
        if (!ok[i]) continue;
        if (dub[na[i]] < dub[nb[i]]) swap(na[i], nb[i]);
        sum += siz[na[i]] * mn[na[i]];
    }
    sol = max(sol, sum);
}

int main () {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cin >> n >> m >> k;
    for (int i = 0; i < m; i++) {
        cin >> a[i] >> b[i] >> c[i];
        in[i] = i;
    }
    for (int i = 0; i < k; i++) {
        cin >> na[i] >> nb[i];
    }
    for (int i = 1; i <= n; i++) cin >> cost[i];
    build_graph();
    for (int mask = 0; mask < (1 << k); mask++) solve(mask);
    cout << sol;
    return 0;
}

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