Submission #978582

#	Time	Username	Problem	Language	Result	Execution time	Memory
978582		steveonalex	Toll (APIO13_toll)	C++17	16 / 100	2591 ms	8884 KiB

toll

#include <bits/stdc++.h>
 
using namespace std;
 
typedef long long ll;
typedef unsigned long long ull;
 
#define ALL(v) (v).begin(), (v).end()
#define MASK(i) (1LL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
 
// mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng(1);
ll rngesus(ll l, ll r){return ((ull) rng()) % (r - l + 1) + l;}
 
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
 
ll LASTBIT(ll mask){return mask & (-mask);}
ll pop_cnt(ll mask){return __builtin_popcountll(mask);}
ll ctz(ll mask){return __builtin_ctzll(mask);}
ll clz(ll mask){return __builtin_clzll(mask);}
ll logOf(ll mask){return 63 - clz(mask);}
 
template <class T1, class T2>
    bool minimize(T1 &a, T2 b){
        if (a > b){a = b; return true;}
        return false;
    }
template <class T1, class T2>
    bool maximize(T1 &a, T2 b){
        if (a < b){a = b; return true;}
        return false;
    }
template <class T>
    void printArr(T a, string separator = " ", string finish = "\n", ostream& out = cout){
        for(auto i: a) out << i << separator;
        out << finish;
    }
template <class T>
    void remove_dup(vector<T> &a){
        sort(ALL(a));
        a.resize(unique(ALL(a)) - a.begin());
    }
 
#define int long long
struct DSU{
    int n;
    vector<int> parent, sz, mi;
 
    DSU(int _n){
        n = _n;
        parent.resize(n+1); sz.resize(n+1, 1);
        for(int i = 1; i<=n; ++i) parent[i] = i;
        mi = parent;
    }
 
    int find_set(int u){return (u == parent[u]) ? u : (parent[u] = find_set(parent[u]));}
    bool same_set(int u, int v){return find_set(u) == find_set(v);}
    bool join_set(int u, int v){
        u = find_set(u), v = find_set(v);
        if (u != v){
            if (sz[u] < sz[v]) {swap(u, v); mi[u] = v;}
            parent[v] = u;
            sz[u] += sz[v];
            return true;
        }
        return false;
    }

    int get_parent(int u){return mi[find_set(u)];}
};
 
const int N = 1e5 + 69;
const int INF = 1e9 + 69;
 
int n, m, k;
vector<array<int, 3>> path, useful;
vector<pair<int, int>> money;
vector<pair<int, int>> graph[N];
ll goon[N];
 
namespace Nig{
    vector<pair<int, int>> graph[N];
    ll chode[N], toll[N];
    int parent[N], h[N];
    void reset(){
        for(int i = 1; i<=n; ++i){
            graph[i].clear();
        }
    }
 
    void dfs(int u, int p){
        chode[u] = goon[u];
        for(pair<int, int> v: graph[u]) if (v.first != p){
            h[v.first] = h[u] + 1;
            parent[v.first] = u;
            if (v.second == 1) toll[v.first] = INF;
            else toll[v.first] = 0;

            dfs(v.first, u);
            chode[u] += chode[v.first];
        }
    }
 
    void go(int root, DSU &mst){
        vector<array<int, 3>> outlier;
        for(array<int, 3> i: useful){
            int u = i[0], v = i[1];
            if (mst.join_set(u, v)){
                graph[u].push_back({v, 0});
                graph[v].push_back({u, 0});
            }
            else outlier.push_back(i);
        }
        dfs(root, root);

        DSU nigga(n);
        for(array<int, 3> i: outlier){
            int u = i[0], v = i[1], w = i[2];;
            u = nigga.get_parent(u), v = nigga.get_parent(v);
            while(u != v){
                if (h[u] > h[v]){
                    minimize(toll[u], w);
                    nigga.join_set(parent[u], u);
                }
                else{
                    minimize(toll[v], w);
                    nigga.join_set(parent[v], v);
                }
                u = nigga.get_parent(u), v = nigga.get_parent(v);
            }
        }
    }
}
 
signed main(void){
    ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);

    clock_t start = clock();
 
    #define int long long
    cin >> n >> m >> k;
    path.resize(m);
    for(int i = 0; i<m; ++i){
        for(int j = 0;j < 3; ++j) cin >> path[i][j];
    }
    sort(ALL(path), [] (array<int, 3> x, array<int, 3> y){return x[2] < y[2];});
 
    DSU mst(n);
    for(int i = 0; i<m; ++i){
        int u = path[i][0], v = path[i][1], w = path[i][2];
        if (mst.join_set(u, v)){
            useful.push_back(path[i]);
            graph[u].push_back({v, w});
            graph[v].push_back({u, w});
        }
    }
    money.resize(k);
    for(int i = 0; i<k; ++i) cin >> money[i].first >> money[i].second;
 
    for(int i = 1; i<=n; ++i) cin >> goon[i];
 
    mst = DSU(n);
    vector<array<int, 3>> annoying, chill;
    for(pair<int, int> i: money) mst.join_set(i.first, i.second);
    for(array<int, 3> i: useful){
        if (mst.join_set(i[0], i[1])) {
            chill.push_back(i);
        }
        else annoying.push_back(i);
    }
 
    mst = DSU(n);
    for(array<int, 3> i: chill) {
        mst.join_set(i[0], i[1]);
    }
    vector<int> S;
    S.push_back(0);
    for(int i= 1; i<=n; ++i) if (i == mst.find_set(i)) S.push_back(i);
 
    for(pair<int, int> &i: money){
        i.first = lower_bound(ALL(S), mst.find_set(i.first)) - S.begin();
        i.second = lower_bound(ALL(S), mst.find_set(i.second)) - S.begin();
    }
    for(array<int, 3> &i: annoying){
        i[0] = lower_bound(ALL(S), mst.find_set(i[0])) - S.begin();
        i[1] = lower_bound(ALL(S), mst.find_set(i[1])) - S.begin();
    }
    useful = annoying;
 
    vector<ll> sum(S.size());
    for(int i= 1; i<=n; ++i){
        int idx = lower_bound(ALL(S), mst.find_set(i)) - S.begin();
        sum[idx] += goon[i];
    }
 
    memset(goon, 0, sizeof goon);
    for(int i= 1; i<S.size(); ++i) goon[i] = sum[i];
 
    n = S.size() - 1;
 
    // cout << n << "\n";
    // for(int i = 1; i<=n; ++i) cout << goon[i] << " "; cout << "\n\n";
    // for(pair<int, int> i: money) cout << i.first << " " << i.second << "\n";
    // for(array<int, 3> i: useful) printArr(i);
 
    int root = lower_bound(ALL(S), mst.find_set(1)) - S.begin();
 
    ll ans = 0;
    for(int mask = 1; mask < MASK(k); ++mask){
        DSU mst(n);
        bool check = true;
        for(int i = 0; i<k; ++i) if (GETBIT(mask, i)){
            check = check && mst.join_set(money[i].first, money[i].second);
        }
        if (check == false) continue;
 
        Nig::reset();
 
        // cerr << string(50, '-') << endl;
 
        for(int i= 0; i<k; ++i) if (GETBIT(mask, i)) {
            int u = money[i].first, v = money[i].second;
            Nig::graph[u].push_back({v, 1});
            Nig::graph[v].push_back({u, 1});
        }
 
        Nig::go(root, mst);
 
        ll cur = 0;
        for(int i = 1; i<=n; ++i) if (i != root){
            cur += Nig::toll[i] * Nig::chode[i];
        }
        maximize(ans, cur);
    }
    cout << ans << "\n";

    cerr << "Time elapsed: " << clock() - start << "ms\n";
 
    return 0;
}

Compilation message (stderr)

toll.cpp: In function 'int main()':
toll.cpp:199:20: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  199 |     for(int i= 1; i<S.size(); ++i) goon[i] = sum[i];
      |                   ~^~~~~~~~~

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