Submission #489848

#	Time	Username	Problem	Language	Result	Execution time	Memory
489848		JerryLiu06	Toll (APIO13_toll)	C++17	100 / 100	1618 ms	13396 KiB

toll

// https://oj.uz/problem/view/APIO13_toll
 
#include <bits/stdc++.h>
 
using namespace std;
 
using ll = long long;
using ld = long double;
using db = double;
using str = string;
 
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
 
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
 
#define FASTIO ios_base::sync_with_stdio(false); cin.tie(0);
 
#define mp make_pair
#define f first
#define s second
 
#define sz(x) (int)(x).size()
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert 
#define ft front()
#define bk back()
#define pb push_back
#define pf push_front
 
#define lb lower_bound
#define ub upper_bound
 
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b) - 1; i >= (a); i--)
#define R0F(i, a) ROF(i, 0, a)
#define EACH(a, x) for (auto& a : x)
 
ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); }
ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); }
 
template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
 
template<class T> void remDup(vector<T>& v) { sor(v); v.erase(unique(all(v)), v.end()); }
 
const int MOD = 1e9 + 7;
const int MX = 1e5 + 10;
const ll INF = 1e18;
 
int N, M, K, comp[MX]; vector<array<int, 3>> ed, add; vpi nxt;
 
ll compSz[22]; ll ans = 0, res = 0;
 
vpi adj[22]; int dep[22]; pi par[22];
 
template<int SZ> struct DSU {
    int par[SZ], sz[SZ];
 
    void init() { 
        F0R(i, SZ) {
            par[i] = i;
            sz[i] = 1;
        }
    }
    int find(int A) {
        return A == par[A] ? A : (par[A] = find(par[A]));
    }
    bool onion(int A, int B) {
        A = find(A);
        B = find(B);
 
        if (A == B) {
            return false;
        }
        if (sz[A] < sz[B]) {
            swap(A, B);
        }
        par[B] = A;
        sz[A] += sz[B];
 
        return true;
    }
};
 
void DFS1(int X) {
    EACH(Y, adj[X]) if (Y.f != par[X].f) {  
        dep[Y.f] = dep[X] + 1;
        par[Y.f] = {X, Y.s};
        
        DFS1(Y.f);
    }
}
void markEdges(array<int, 3> E) {
    int A = E[1], B = E[2];
 
    while (A != B) {
        if (dep[A] < dep[B]) swap(A, B);
 
        ckmin(par[A].s, E[0]);
        A = par[A].f;
    }
}
void DFS2(int X, ll cost) {
    res += compSz[X] * cost;
 
    EACH(Y, adj[X]) if (Y.f != par[X].f) {
        DFS2(Y.f, cost + par[Y.f].s);
    }
}
 
void solve(int msk) {
    DSU<22> D; D.init();
 
    FOR(i, 1, K + 2) {
        adj[i].clear();
    }
    F0R(i, K) {
        if (msk & (1 << i)) {
            if (!D.onion(nxt[i].f, nxt[i].s)) {
                return ;
            } 
            adj[nxt[i].f].pb({nxt[i].s, MOD});
            adj[nxt[i].s].pb({nxt[i].f, MOD});
        }
    }
    vector<array<int, 3>> bad;
 
    EACH(E, add) {
        if (!D.onion(E[1], E[2])) {
            bad.pb(E);
        }
        else {
            adj[E[1]].pb({E[2], 0});
            adj[E[2]].pb({E[1], 0});
        }
    }
    DFS1(1);
    
    EACH(E, bad) {
        markEdges(E);
    }
    res = 0;
 
    DFS2(1, 0);
    
    ckmax(ans, res);
}
 
int main() {
    FASTIO;
 
    cin >> N >> M >> K; 
 
    F0R(i, M) {
        int A, B, C;
        cin >> A >> B >> C;
 
        ed.pb({C, A, B});
    }
    sor(ed);
 
    DSU<MX> D1, D2; // original, new
    
    D1.init(), D2.init();
 
    F0R(i, K) {
        int A, B; cin >> A >> B;
 
        nxt.pb({A, B});
        D2.onion(A, B);
    }
    EACH(E, ed) {
        // Guaranteed to be in MST
        if (D2.onion(E[1], E[2])) {
            D1.onion(E[1], E[2]);
        }
        // May create cycle with new edges
    }
    map<int, int> MP; int numComp = 0;

    FOR(i, 1, N + 1) {
        int P; cin >> P;
 
        int curPar = D1.find(i);
        
        if (!MP.count(curPar)) {
            MP[curPar] = ++numComp;
        }
        comp[i] = MP[curPar];
        compSz[comp[i]] += P; 
    }
    EACH(E, ed) {
        if (D1.onion(E[1], E[2])) {
            add.pb(E);
        }
    }
    EACH(E, nxt) {
        E.f = comp[E.f];
        E.s = comp[E.s];
    }
    EACH(E, add) {
        E[1] = comp[E[1]];
        E[2] = comp[E[2]];
    }
    F0R(msk, (1 << K)) {
        solve(msk);
    }
    cout << ans;
}

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