Submission #767134

#	Time	Username	Problem	Language	Result	Execution time	Memory
767134		radoslav11	Highway Tolls (IOI18_highway)	C++17	90 / 100	219 ms	13824 KiB

highway

#include <bits/stdc++.h>
#include "highway.h"

using namespace std;

tuple<vector<int>, vector<int>, vector<int>> bfs(
	int N, int M, vector<vector<pair<int, int>>> &adj, vector<int> srcs
) {
	vector<int> dist(N, -1);
	queue<int> q;

	for(int u: srcs) {
		dist[u] = 0;
		q.push(u);
	}

	vector<int> tree_edges;
	vector<int> cross_edges_mask(M, true);

	while(!q.empty()) {
		int u = q.front();
		q.pop();

		for(auto [v, i]: adj[u]) {
			if(dist[v] == -1) {
				dist[v] = dist[u] + 1;
				cross_edges_mask[i] = false;
				tree_edges.push_back(i);
				q.push(v);
			}
		}
	}

	vector<int> cross_edges;
	for(int i = 0; i < M; i++) {
		if(cross_edges_mask[i]) {
			cross_edges.push_back(i);
		}
	}

	return {dist, tree_edges, cross_edges};
}

int find_first(
	vector<int> edges, vector<int> order, int l, int r, int m, int64_t dist_cmp,
	function<bool(int, int)> cmp
) {
	int found = -1, start = l;
	while(l <= r) {
		int mid = (l + r) >> 1;
		vector<int> mask(m, 1);

		for(int i = start; i <= mid; i++) {
			if(edges[order[i]] != -1) {
				mask[edges[order[i]]] = 0;
			}
		}

		int64_t val = ask(mask);
		if(cmp(val, dist_cmp)) {
			r = mid - 1;
			if(val == dist_cmp) {
				found = order[mid];
			}
		} else {
			l = mid + 1;
		}
	}

	return found;
}

int find_first2(
	vector<int> edges, vector<int> order, int l, int r, int m, int64_t dist_cmp,
	function<bool(int, int)> cmp
) {
	int found = -1, start = l;
	while(l <= r) {
		int mid = (l + r) >> 1;
		vector<int> mask(m, 0);

		for(int i = start; i < mid; i++) {
			if(edges[order[i]] != -1) {
				mask[edges[order[i]]] = 1;
			}
		}

		int64_t val = ask(mask);
		if(cmp(val, dist_cmp)) {
			r = mid - 1;
			found = mid - 1;
		} else {
			l = mid + 1;
		}
	}

	return found;
}


void find_pair(int N, std::vector<int> U, std::vector<int> V, int A, int B) {
	vector<vector<pair<int, int>>> adj;
	adj.assign(N, {});

	for(int i = 0; i < (int)U.size(); i++) {
		adj[U[i]].push_back({V[i], i});
		adj[V[i]].push_back({U[i], i});
	}

	vector<int> dist, tree_edges, cross_edges;
	tie(dist, tree_edges, cross_edges) = bfs(N, U.size(), adj, {0});

	// 1 query
	int64_t dist_heavy = ask(vector<int>(U.size(), 1));	
	int64_t dist_light = dist_heavy / B * A;

	// ceil(log2(M - N)) queries. Worst case 16 queries

	vector<int> order(cross_edges.size());
	iota(order.begin(), order.end(), 0);
	int found = find_first2(
		cross_edges, order, 0, (int)cross_edges.size(), U.size(),
		dist_light,
		[](int64_t val, int64_t dist) { return val != dist; }
	);

	if(found != -1) {
		// reroot needed to guarantee that shortest path is on bfs tree
		int cross_edge = cross_edges[found];
		cerr << U[cross_edge] << " " << V[cross_edge] << endl;
		tie(dist, tree_edges, cross_edges) =
			bfs(N, U.size(), adj, {U[cross_edge], V[cross_edge]});

		tree_edges.push_back(cross_edge);
	}

	vector<int> main_edge(N, -1);
	for(auto i: tree_edges) {
		int u = U[i], v = V[i];
		if(dist[u] > dist[v]) {
			swap(u, v);
		}
		main_edge[v] = i;
	}

	int root = -1;
	for(int i = 0; i < N; i++) {
		if(main_edge[i] == -1) {
			root = i;
		}
	}

	vector<int> order_s(N);
	iota(order_s.begin(), order_s.end(), 0);
	sort(order_s.begin(), order_s.end(), [&](int i, int j) {
		return dist[i] < dist[j];
	});

	int s = find_first(
		main_edge, order_s, 0, (int)order_s.size() - 1, U.size(), dist_light,
		[](int64_t val, int64_t dist) { return val == dist; }
	);

	if(s == -1) {
		s = root;
	}
	tie(dist, tree_edges, cross_edges) = bfs(N, U.size(), adj, {s});

	vector<int> order_t(N);
	iota(order_t.begin(), order_t.end(), 0);
	sort(order_t.begin(), order_t.end(), [&](int u, int v) {
		return dist[u] < dist[v];
	});

	main_edge.assign(N, -1);
	for(auto i: tree_edges) {
		int u = U[i], v = V[i];
		if(dist[u] > dist[v]) {
			swap(u, v);
		}
		main_edge[v] = i;
	}

	int t = find_first(
		main_edge, order_t, 0, (int)order_t.size() - 1, U.size(), dist_light,
		[](int64_t val, int64_t dist) { return val == dist; }
	);

	answer(s, t);
}

• Subtask 1: 5 / 5
• Subtask 2: 7 / 7
• Subtask 3: 6 / 6
• Subtask 4: 33 / 33
• Subtask 5: 18 / 18
• Subtask 6: 21 / 31