Submission #766635

#	Time	Username	Problem	Language	Result	Execution time	Memory
766635		radoslav11	Highway Tolls (IOI18_highway)	C++17	51 / 100	147 ms	11128 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_heavy
) {
    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;
            }
        }

        if(ask(mask) < dist_heavy) {
            r = mid - 1;
            found = order[mid];
        } 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));

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

    vector<int> order(cross_edges.size());
    iota(order.begin(), order.end(), 0);
    int found = find_first(
        cross_edges, order, 0, (int)cross_edges.size() - 1, U.size(),
        dist_heavy
    );

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

        tree_edges.push_back(found);
    }

    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_heavy
	);

	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_heavy
    );
	
	answer(s, t);
}

• Subtask 1: 5 / 5
• Subtask 2: 7 / 7
• Subtask 3: 6 / 6
• Subtask 4: 33 / 33
• Subtask 5: 0 / 18
• Subtask 6: 0 / 31