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답안 #621114

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
621114 2022-08-03T12:25:54 Z Bungmint 통행료 (APIO13_toll) C++17
100 / 100
 2211 ms 13464 KB 
// Copyright © 2022 Youngmin Park. All rights reserved.
//#pragma GCC optimize("O3")
//#pragma GCC target("avx2")
#include <bits/stdc++.h>
using namespace std;

#pragma region TEMPLATE

using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;
using vpi = vector<pii>;
using pll = pair<ll, ll>;
using vl = vector<ll>;
using vpl = vector<pll>;
using ld = long double;
template <typename T, size_t SZ>
using ar = array<T, SZ>;
template <typename T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define all(v) (v).begin(), (v).end()
#define pb push_back
#define sz(x) (int)(x).size()
#define fi first
#define se second
#define lb lower_bound
#define ub upper_bound

constexpr int INF = 1e9;
constexpr ll LINF = 1e18;
const ld PI = acos((ld)-1.0);
constexpr int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T>
constexpr bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; }
template <typename T>
constexpr bool ckmax(T &a, const T &b) { return b > a ? a = b, 1 : 0; }
ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); } // divide a by b rounded down

#ifdef LOCAL
#include "miscellaneous/debug.h"
#else
#define dbg(...) 42
#endif

inline namespace RecursiveLambda {
	template <typename Fun>
	struct y_combinator_result {
		Fun fun_;
		template <typename T>
		explicit constexpr y_combinator_result(T &&fun) : fun_(forward<T>(fun)) {}
		template <typename... Args>
		constexpr decltype(auto) operator()(Args &&...args) const {
			return fun_(ref(*this), forward<Args>(args)...);
		}
	};
	template <typename Fun>
	decltype(auto) y_combinator(Fun &&fun) {
		return y_combinator_result<decay_t<Fun>>(forward<Fun>(fun));
	}
};

#pragma endregion TEMPLATE

/*
 * Description: Disjoint Set Union with both path compression and size heuristic
 * Source: USACO Guide/Benq
 * Verification:
 * Time complexity: amortized O(\alpha(n)) updates/queries
 */

struct DSU {
	vi e;
	DSU(int N) { e = vi(N, -1); }
	int get(int x) { return e[x] < 0 ? x : e[x] = get(e[x]); }
	bool same_set(int a, int b) { return get(a) == get(b); }
	int size(int x) { return -e[get(x)]; }
	bool unite(int x, int y) {
		x = get(x), y = get(y);
		if (x == y) return false;
		if (e[x] > e[y]) swap(x, y);
		e[x] += e[y]; e[y] = x;
		return true;
	}
};

struct Edge {
	int u{}, v{}, c{};
	bool operator<(const Edge& o) const {
		return c < o.c;
	}
};

ll sum[25];
int cc{}, root{};

void solve() {
	int n, m, k; cin >> n >> m >> k;
	vi p(n);
	vector<Edge> all_edges(m), mr(k), tree_edges, extra;
	DSU dsu(n), tree(n), comp(n);
	for (int i = 0; i < m; i++) {
		auto &[u, v, c] = all_edges[i];
		cin >> u >> v >> c; u--, v--;
	}
	for (int i = 0; i < k; i++) {
		auto &[u, v, c] = mr[i];
		cin >> u >> v; u--, v--;
		dsu.unite(u, v);
	}
	for (int i = 0; i < n; i++) cin >> p[i];
	sort(all(all_edges));
	for (auto &e : all_edges) {
		if (tree.unite(e.u, e.v)) tree_edges.pb(e);
	}
	for (auto &e : tree_edges) {
		if (!dsu.unite(e.u, e.v)) extra.pb(e);
		else comp.unite(e.u, e.v);
	}
	vi id(n);
	vector<bool> vis(n);
	for (int i = 0; i < n; i++) {
		int r = comp.get(i);
		if (!vis[r]) {
			vis[r] = 1;
			id[r] = cc++;
		}
		sum[id[r]] += p[i];
		if (i == 0) root = id[r];
	}
	for (auto &e : mr) {
		e.u = comp.get(e.u);
		e.v = comp.get(e.v);
		e.u = id[e.u];
		e.v = id[e.v];
	}
	for (auto &e : extra) {
		e.u = comp.get(e.u);
		e.v = comp.get(e.v);
		e.u = id[e.u];
		e.v = id[e.v];
	}
	ll ans{};
	vector<vpi> adj(cc);
	vi depth(cc), we(cc), par(cc);
	vl peeps(cc);
	for (int mask = 0; mask < (1 << k); mask++) {
		for (int i = 0; i < cc; i++) adj[i].clear(), depth[i] = peeps[i] = 0, we[i] = INF;
		DSU small(cc);
		ll cur{};
		bool ok = 1;
		for (int i = 0; i < k; i++) {
			if (mask>>i & 1) {
				ok &= small.unite(mr[i].u, mr[i].v);
				adj[mr[i].u].pb({mr[i].v, 1});
				adj[mr[i].v].pb({mr[i].u, 1});
			}
		}
		if (!ok) continue;
		auto dfs = y_combinator([&](auto self, int u = root, int pu = -1) -> void {
			peeps[u] = sum[u];
			for (auto &[v, idid] : adj[u]) {
				if (v == pu) continue;
				depth[v] = depth[u] + 1;
				par[v] = u;
				self(v, u);
				if (idid) cur += peeps[v]*we[v];
				peeps[u] += peeps[v];
			}
		});
		auto dfs_min = [&](int u, int v, int c) -> void {
			if (depth[u] < depth[v]) swap(u, v);
			while (depth[u] != depth[v]) {
				if (we[u] > c) we[u] = c;
				u = par[u];
			}
			while (u != v) {
				if (we[u] > c) we[u] = c;
				if (we[v] > c) we[v] = c;
				u = par[u]; v = par[v];
			}
		};
		vector<Edge> todo;
		for (auto &[u, v, c] : extra) {
			if (!small.unite(u, v)) {
				todo.pb({u, v, c});
				// dfs_min(u, v, c);
			}else{
				adj[u].pb({v, 0});
				adj[v].pb({u, 0});
			}
		}
		dfs();
		for (auto &[u, v, c] : todo) {
			dfs_min(u, v, c);
		}
		cur = 0;
		dfs();
		ckmax(ans, cur);
	}
	cout << ans << '\n';
}

int main() {
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(cin.failbit);
	int testcase = 1;
	// cin >> testcase;
	while (testcase--) {
		solve();
	}
#ifdef LOCAL
	cerr << "Time elapsed: " << 1.0 * (double)clock() / CLOCKS_PER_SEC << " s.\n";
#endif
}

Compilation message

toll.cpp:7: warning: ignoring '#pragma region TEMPLATE' [-Wunknown-pragmas]
    7 | #pragma region TEMPLATE
      | 
toll.cpp:65: warning: ignoring '#pragma endregion TEMPLATE' [-Wunknown-pragmas]
   65 | #pragma endregion TEMPLATE
      |

Subtask #1
16.0 / 16.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 320 KB Output is correct

Subtask #2
18.0 / 18.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 320 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 2 ms 328 KB Output is correct

Subtask #3
22.0 / 22.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 320 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 2 ms 328 KB Output is correct
5 Correct 3 ms 468 KB Output is correct
6 Correct 3 ms 468 KB Output is correct

Subtask #4
22.0 / 22.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 320 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 2 ms 328 KB Output is correct
5 Correct 3 ms 468 KB Output is correct
6 Correct 3 ms 468 KB Output is correct
7 Correct 162 ms 13464 KB Output is correct
8 Correct 180 ms 13448 KB Output is correct
9 Correct 161 ms 13448 KB Output is correct

Subtask #5
22.0 / 22.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 320 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 2 ms 328 KB Output is correct
5 Correct 3 ms 468 KB Output is correct
6 Correct 3 ms 468 KB Output is correct
7 Correct 162 ms 13464 KB Output is correct
8 Correct 180 ms 13448 KB Output is correct
9 Correct 161 ms 13448 KB Output is correct
10 Correct 1735 ms 13452 KB Output is correct
11 Correct 2211 ms 13448 KB Output is correct
12 Correct 2207 ms 13456 KB Output is correct