Submission #1158305

#	Time	Username	Problem	Language	Result	Execution time	Memory
1158305		Sang	Toll (APIO13_toll)	C++20	100 / 100	1051 ms	12712 KiB

toll

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

#define int long long
#define FOR(i, a, b) for (int i = (a), _b = (b); i <= _b; i++)
#define FORD(i, a, b) for (int i = (a), _b = (b); i >= _b; i--)
#define fi first
#define se second
#define pb push_back
#define ALL(a) (a).begin(), (a).end()
#define task "kbsiudthw"

typedef vector<int> vi;
typedef pair<int, int> ii;
typedef pair<int, ii> pii;

const int N = 1e5 + 5;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 2277;

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

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

    bool join(int u, int v){
        if ((u = Find(u)) == (v = Find(v))) return 0;
        if (lab[u] < lab[v]) swap(u, v);
        lab[u] += lab[v];
        lab[v] = u;
        return 1;
    }
};
int n, m, k, id[N], mx[N], s[N], total[25], h[25], c[N], P[25];
vector<int> G[25];

void dfs(int u, int par){
    s[u] = total[u];
    for (int v : G[u]){
        if (v == par) continue;
        h[v] = h[u] + 1;
        P[v] = u;
        dfs(v, u);
        s[u] += s[v];
    }
}

void up(int u, int v, int w){
    if (h[u] < h[v]) swap(u, v);
    while (h[u] > h[v]){
        mx[u] = min(mx[u], w);
        u = P[u];
    }
    while (u != v){
        mx[u] = min(mx[u], w);
        mx[v] = min(mx[v], w);
        u = P[u];
        v = P[v];
    }
}

signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    if (fopen(task".inp", "r")){
        freopen(task".inp", "r", stdin);
        freopen(task".out", "w", stdout);
    }
    cin >> n >> m >> k;
    vector<pii> edges;
    vector<ii> eg;
    FOR (i, 1, m){
        int u, v, w; cin >> u >> v >> w;
        edges.pb({w, {u, v}});
    }
    sort(ALL(edges));
    FOR (i, 1, k){
        int u, v; cin >> u >> v;
        eg.pb({u, v});
    }
    FOR (i, 1, n) cin >> c[i];
    DSU dsu(n+5);
    for (ii &x : eg) dsu.join(x.fi, x.se);
    vector<bool> marked(m, 0);
    FOR (i, 0, m - 1){
        if (dsu.join(edges[i].se.fi, edges[i].se.se)){
            marked[i] = 1;
        }
    }
    dsu = DSU(n+5);
    FOR (i, 0, m - 1) if (marked[i]) dsu.join(edges[i].se.fi, edges[i].se.se);
    FOR (i, 1, n){
        int x = dsu.Find(i);
        if (id[x] == 0) id[x] = ++id[0];
        id[i] = id[x];
        total[id[i]] += c[i];
    }
    dsu = DSU(id[0]+1);
    vector<pii> mst;
    for (pii &x : edges){
        x.se.fi = id[x.se.fi];
        x.se.se = id[x.se.se];
        if (dsu.join(x.se.fi, x.se.se)){
            mst.pb(x);
        }
    }
    for (ii &x : eg){
        x.se = id[x.se];
        x.fi = id[x.fi];
    }
    assert(id[1] == 1);
    assert((int)mst.size() == id[0] - 1);
    int ans = 0;
    for (int mask = 0; mask < (1<<k); mask++){
        FOR (i, 1, id[0]){
            mx[i] = INF;
            h[i] = 0;
            G[i].clear();
        }
        bool ok = 1;
        dsu = DSU(id[0]+1);
        FOR (i, 0, k - 1){
            if ((mask>>i)&1){
                if (!dsu.join(eg[i].fi, eg[i].se)) ok = 0;
                G[eg[i].fi].pb(eg[i].se);
                G[eg[i].se].pb(eg[i].fi);
            }
        }
        if (!ok) continue;
        marked.assign(mst.size(), false);
        FOR (i, 0, (int)mst.size() - 1){
            if (dsu.join(mst[i].se.fi, mst[i].se.se)){
                marked[i] = 1;
                G[mst[i].se.fi].pb(mst[i].se.se);
                G[mst[i].se.se].pb(mst[i].se.fi);
            }
        }
        dfs(1, 0);
        FOR (i, 0, (int)mst.size() - 1){
            if (marked[i]) continue;
            up(mst[i].se.fi, mst[i].se.se, mst[i].fi);
        }
        int res = 0;
        FOR (i, 0, k - 1){
            if ((mask>>i)&1){
                int u = eg[i].fi, v = eg[i].se;
                if (u == P[v]) swap(u, v);
                assert(mx[u] != INF);
                res += s[u] * mx[u];
            }
        }
        ans = max(ans, res);
    }
    cout << ans;

    return 0;
}

Compilation message (stderr)

toll.cpp: In function 'int main()':
toll.cpp:69:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   69 |         freopen(task".inp", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
toll.cpp:70:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   70 |         freopen(task".out", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

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