Submission #1185483

#	Time	Username	Problem	Language	Result	Execution time	Memory
1185483		thieunguyenhuy	Toll (APIO13_toll)	C++20	100 / 100	983 ms	8992 KiB

toll

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

#define POPCOUNT(n) (__builtin_popcountll((n)))
#define CLZ(n) (__builtin_clzll((n)))
#define CTZ(n) (__builtin_ctzll((n)))
#define LOG(n) (63 - __builtin_clzll((n)))
#define BIT(n, i) (((n) >> (i)) & 1ll)
#define MASK(i) (1ll << (i))
#define FLIP(n, i) ((n) ^ (1ll << (i)))
#define ON(n, i) ((n) | MASK(i))
#define OFF(n, i) ((n) & ~MASK(i))

#define Int __int128
#define fi first
#define se second

typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef pair<long long, int> pli;
typedef pair<int, long long> pil;
typedef vector<pair<int, int>> vii;
typedef vector<pair<long long, long long>> vll;
typedef vector<pair<long long, int>> vli;
typedef vector<pair<int, long long>> vil;

template <class T1, class T2> bool maximize(T1 &x, T2 y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}
template <class T1, class T2> bool minimize(T1 &x, T2 y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}

template <class T> void remove_duplicate(vector<T> &ve) {
    sort (ve.begin(), ve.end());
    ve.resize(unique(ve.begin(), ve.end()) - ve.begin());
}

mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
template <class T1, class T2> T1 random(T1 l, T2 r) {
    return uniform_int_distribution<T1>(l, r)(rng);
}
template <class T> T random(T r) {
    return rng() % r;
}

const int N = 1e5 + 5, M = 3e5 + 20 + 5;
const int MOD = 1e9 + 7;
const int inf = 1e9;
const long long INF = 1e18;

int n, m, k;
int f[N], p[N], dep[N], weight[M];
ll sz[N];
pii par[N];
vii adj[N];
bitset<M> inMST1, used;

struct Edge {
	int u, v, w, id;

	Edge(int _u = 0, int _v = 0, int _w = 0, int _id = 0) {
		u = _u, v = _v, w = _w, id = _id;
	}

	bool operator < (const Edge &other) {
		return w < other.w;
	}
} edges[M];

struct DSU {
	vector<int> lab;

	DSU() {}

	void resize(int n) {
		lab.assign(n + 1, -1);
	}

	int find_set(int p) {
		return lab[p] < 0 ? p : lab[p] = find_set(lab[p]);
	}

	bool same_set(int u, int v) {
		return find_set(u) == find_set(v);
	}

	bool join(int u, int v) {
		u = find_set(u), v = find_set(v);
		if (u != v) {
			if (lab[u] > lab[v]) swap(u, v);
			lab[u] += lab[v], lab[v] = u;
			return true;
		}
		return false;
	}
} dsu;

void dfs(int u, int fa) {
	for (auto [v, id] : adj[u]) if (v != fa) {
		dep[v] = dep[u] + 1, par[v] = make_pair(u, id);
		dfs(v, u); sz[u] += sz[v];
	}
}

signed main() {
    ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);

    cin >> n >> m >> k;

    for (int i = 0; i < m; ++i) {
    	int u, v, w; cin >> u >> v >> w;
    	edges[i] = Edge(u, v, w, i);
    }

    for (int i = 0; i < k; ++i) {
    	int u, v; cin >> u >> v;
    	edges[m + i] = Edge(u, v, 0, m + i);
    }

    for (int i = 1; i <= n; ++i) cin >> p[i];

    dsu.resize(n);
    for (int i = 0; i < k; ++i) {
    	auto [u, v, w, id] = edges[m + i];
    	dsu.join(u, v);
    }

    sort (edges, edges + m);
    for (int i = 0; i < m; ++i) {
    	auto [u, v, w, id] = edges[i];
    	if (dsu.join(u, v)) inMST1[id] = true;
    }

    dsu.resize(n);
    for (int i = 0; i < m; ++i) {
    	auto [u, v, w, id] = edges[i];
    	if (inMST1[id]) dsu.join(u, v); 
    }

    vil components;
    for (int i = 1; i <= n; ++i) {
    	f[i] = dsu.find_set(i), sz[f[i]] += p[i];
    	if (f[i] == i) components.emplace_back(i, 0);
    }

    for (auto &it : components) it.se = sz[it.fi];

    dsu.resize(n); vector<Edge> extra;
	for (int i = 0; i < m; ++i) {
		auto [u, v, w, id] = edges[i];
		if (dsu.join(u, v)) {
			if (!inMST1[id]) extra.emplace_back(edges[i]);
		}
	}

	for (auto &[u, v, w, id] : extra) u = f[u], v = f[v];
	for (int i = 0; i < k; ++i) {
		auto &[u, v, w, id] = edges[m + i];
		u = f[u], v = f[v];
	}

	// for (auto &[u, v, w, id] : extra)
	// 	cerr << u << ' ' << v << ' ' << w << ' ' << id << '\n';

	ll ans = 0;
	for (int mask = 1; mask < MASK(k); ++mask) {
		for (auto &it : components) {
			adj[it.fi].clear(), dsu.lab[it.fi] = -1;
			sz[it.fi] = it.se;
		}

		for (int i = 0; i < k; ++i) if (BIT(mask, i)) {
			auto [u, v, w, id] = edges[m + i];
			if (dsu.join(u, v)) {
				weight[id] = inf;
				adj[u].emplace_back(v, id);
				adj[v].emplace_back(u, id);
			}
			else weight[id] = -1;
		}

		for (auto [u, v, w, id] : extra) {
			used[id] = dsu.join(u, v);
			if (used[id]) {
				adj[u].emplace_back(v, id);
				adj[v].emplace_back(u, id);
			}
		}

		dfs(f[1], -1);
	
		for (auto [u, v, w, id] : extra) if (!used[id]) {
			// cerr << "w = " << w << '\n';
			while (u != v) {
				if (dep[u] < dep[v]) swap(u, v);
				minimize(weight[par[u].se], w);
				u = par[u].fi;
			}
		}

		ll res = 0;
		for (int i = 0; i < k; ++i) if (BIT(mask, i)) {
			auto [u, v, w, id] = edges[m + i];
			if (weight[id] == -1) continue;
			if (dep[u] > dep[v]) swap(u, v);
			res += 1ll * weight[id] * sz[v];
		}

		maximize(ans, res);
	}

	cout << ans;
    return 0;
}

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