Submission #401823

#	Time	Username	Problem	Language	Result	Execution time	Memory
401823		Jorge213	Toll (APIO13_toll)	C++17	100 / 100	1724 ms	11940 KiB

toll

#include <bits/stdc++.h>
using namespace std;
using pii = pair<int, int>;
const int N = 1e5 + 10;
const int K = 25;
int a[N], comp[N];
long long p[K];

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

struct DSU {
	int dsu[N];

	void clear(int n) {
		for (int i = 0; i <= n; i++) dsu[i] = i;
	}

	int root(int idx) {
		while (idx != dsu[idx]) {
			dsu[idx] = dsu[dsu[idx]];
			idx = dsu[idx];
		}
		return idx;
	}

	bool join(int a, int b) {
		if (root(a) == root(b))
			return false;
		dsu[root(a)] = root(b);
		return true;
	}
};

struct Tree {
	vector<pii> adjList[K];
	int we[K], d[K], par[K];
	long long cnt[N];

	void clear(int n) {
		for (int i = 1; i <= n; i++) {
			adjList[i].clear();
			cnt[i] = p[i];
		}
	}

	void addEdge(int u, int v, int w) {
		adjList[u].push_back({v, w});
		adjList[v].push_back({u, w});
	}

	void dfs(int v, int p) {
		par[v] = p;
		d[v] = d[p] + 1;
		for (auto [u, w] : adjList[v]) {
			if (u == p) continue;
			dfs(u, v);
			we[u] = w;
			cnt[v] += cnt[u];
		}
	}
};

DSU dsu, ndsu;
Tree g;

int main() {
	int n, m, k;
	scanf("%d %d %d", &n, &m, &k);

	vector<Edge> edges, nedges;

	int ai, bi, ci;
	for (int i = 0; i < m; i++) {
		scanf("%d %d %d", &ai, &bi, &ci);
		edges.push_back({ai, bi, ci});
	}

	sort(edges.begin(), edges.end());

	int xi, yi;
	for (int i = 0; i < k; i++) {
		scanf("%d %d", &xi, &yi);
		nedges.push_back({xi, yi, 0});
	}

	for (int i = 1; i <= n; i++) {
		scanf("%d", a + i);
	}

	int edgs = 0;

	dsu.clear(n);
	ndsu.clear(n);
	for (auto [u, v, w] : nedges) {
		if (ndsu.join(u, v))
			edgs++;
	}
	for (auto [u, v, w] : edges) {
		if (ndsu.join(u, v)) {
			dsu.join(u, v);
			edgs++;
			if (edgs == n - 1) break;
		}
	}

	int sz = 0;
	for (int i = 1; i <= n; i++) {
		int v = dsu.root(i);
		if (!comp[v]) {
			comp[v] = ++sz;
		}
		comp[i] = comp[v];
	}

	for (int i = 1; i <= n; i++) {
		p[comp[i]] += (long long) a[i];
	}

	for (auto &[u, v, w] : nedges) {
		u = comp[u], v = comp[v];
	}

	dsu.clear(sz);
	vector<Edge> mn;
	edgs = 0;

	for (auto [u, v, w] : edges) {
		if (dsu.join(comp[u], comp[v])) {
			mn.push_back({comp[u], comp[v], w});
			edgs++;
			if (edgs == sz - 1) break;
		}
	}

	long long ans = 0;
	for (int bm = 1; bm < (1 << k); bm++) {
		dsu.clear(sz);
		g.clear(sz);

		for (int i = 0; i < k; i++) {
			if (!(bm & (1 << i))) continue;
			auto [u, v, w] = nedges[i];
			if (dsu.join(u, v)) {
				g.addEdge(u, v, INT_MAX);
			}
		}

		vector<Edge> unused;
		for (auto [u, v, w] : mn) {
			if (dsu.join(u, v)) {
				g.addEdge(u, v, 0);
			}
			else {
				unused.push_back({u, v, w});
			}
		}

		g.dfs(1, -1);
		for (auto [u, v, w] : unused) {
			if (g.d[u] < g.d[v])
				swap(u, v);

			while (g.d[u] > g.d[v]) {
				g.we[u] = min(g.we[u], w);
				u = g.par[u];
			}
		
			while (u != v) {
				g.we[u] = min(g.we[u], w);
				g.we[v] = min(g.we[v], w);
				u = g.par[u], v = g.par[v];
			}
		}

		long long can = 0;
		for (int v = 1; v <= sz; v++) {
			can += 1LL * g.we[v] * g.cnt[v];
		}

		ans = max(ans, can);
	}

	printf("%lld\n", ans);

	return 0;
}

Compilation message (stderr)

toll.cpp: In function 'int main()':
toll.cpp:73:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   73 |  scanf("%d %d %d", &n, &m, &k);
      |  ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
toll.cpp:79:8: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   79 |   scanf("%d %d %d", &ai, &bi, &ci);
      |   ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~
toll.cpp:87:8: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   87 |   scanf("%d %d", &xi, &yi);
      |   ~~~~~^~~~~~~~~~~~~~~~~~~
toll.cpp:92:8: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   92 |   scanf("%d", a + i);
      |   ~~~~~^~~~~~~~~~~~~
toll.cpp:58:13: warning: array subscript -1 is below array bounds of 'int [25]' [-Warray-bounds]
   58 |   d[v] = d[p] + 1;
      |          ~~~^
toll.cpp:41:13: note: while referencing 'Tree::d'
   41 |  int we[K], d[K], par[K];
      |             ^
toll.cpp:69:6: note: defined here 'g'
   69 | Tree g;
      |      ^

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