Submission #483045

#	Time	Username	Problem	Language	Result	Execution time	Memory
483045		blue	Roller Coaster Railroad (IOI16_railroad)	C++17	100 / 100	730 ms	74744 KiB

railroad

#include "railroad.h"
#include <vector>
#include <set>
#include <map>
#include <algorithm>
#include <iostream>
using namespace std;

const int INF = 1'000'000'001;

int N;

set<int> pos;
map<int, int> norm;
vector<int> act;

int K;




struct ds
{
    int Z;
    vector<int> parent;
    vector<int> subtree;
    vector<int> mx;
    vector<int> mn;

    ds()
    {
        ;
    }

    ds(int Z_)
    {
        Z = Z_;
        parent = vector<int>(Z);
        subtree = vector<int>(Z, 1);
        mx = vector<int>(Z);
        mn = vector<int>(Z);
        for(int i = 0; i < Z; i++) parent[i] = mx[i] = mn[i] = i;
    }

    int root(int u)
    {
        if(parent[u] == u) return u;
        parent[u] = root(parent[u]);
        return parent[u];
    }

    bool connected(int u, int v)
    {
        return root(u) == root(v);
    }

    void join(int u, int v)
    {
        u = root(u);
        v = root(v);

        if(u == v) return;

        if(subtree[u] < subtree[v]) swap(u, v);

        parent[v] = u;
        subtree[u] += subtree[v];
        mx[u] = max(mx[u], mx[v]);
        mn[u] = min(mn[u], mn[v]);
    }
};


long long plan_roller_coaster(vector<int> s, vector<int> t)
{
    s.push_back(INF);
    t.push_back(1);

    N = int(s.size());

    for(int i = 0; i < N; i++)
    {
        pos.insert(s[i]);
        pos.insert(t[i]);
    }

    int ct = -1;

    for(int p: pos)
    {
        ct++;
        norm[p] = ct;
        act.push_back(p);
    }

    K = 1+ct;

    ds DSU(K);

    for(int i = 0; i < N; i++)
    {
        s[i] = norm[s[i]];
        t[i] = norm[t[i]];

        // DSU.join(s[i], t[i]);
    }

    // for(int i = 0; i < K; i++) cerr << i << ' ' << act[i] << '\n';

    vector<int> indegree(K, 0), outdegree(K, 0);
    for(int i = 0; i < N; i++)
    {
        outdegree[s[i]]++;
        indegree[t[i]]++;
    }

    set<int> positive, negative;
    for(int i = 0; i < K; i++)
    {
        if(outdegree[i] > indegree[i])
            positive.insert(i);
        else if(outdegree[i] < indegree[i])
            negative.insert(i);
    }

    // cerr << "positive: ";
    // for(int p: positive) cerr << p << ' ';
    // cerr << '\n';
    //
    // cerr << "negative: ";
    // for(int n: negative) cerr << n << ' ';
    // cerr << '\n';

    long long ans = 0;
    while(!positive.empty())
    {
        int p = *positive.begin();
        int n = *negative.begin();

        // cerr << p << ' ' << n << '\n';

        int a = min(p, n);
        int b = max(p, n);
        while(1)
        {
            a = DSU.root(a);
            if(DSU.mx[a] >= b) break;
            DSU.join(a, DSU.mx[a]+1);
        }
        // DSU.join(p, n);
        if(n > p) ans += act[n] - act[p];
        outdegree[n]++;
        indegree[p]++;

        // cerr << "extra edge " << n << ' ' << p << '\n';
        // cerr << "ans = " << ans << '\n';

        if(outdegree[n] - indegree[n] == 0) negative.erase(n);
        if(indegree[p] - outdegree[p] == 0) positive.erase(p);
    }

    for(int i = 0; i < N; i++) DSU.join(s[i], t[i]);

    // cerr << "DSU: ";
    // for(int i = 0; i < K; i++) cerr << i << ' ' << DSU.root(i) << '\n';

    vector< pair<int, int> > H;
    for(int i = 0; i+1 < K; i++) H.push_back(make_pair(i, i+1));

    sort(H.begin(), H.end(), [] (pair<int, int> g, pair<int, int> h)
    {
        return act[g.second] - act[g.first] < act[h.second] - act[h.first];
    });

    for(pair<int, int> h: H)
    {
        if(!DSU.connected(h.first, h.second))
        {
            ans += act[h.second] - act[h.first];
            DSU.join(h.first, h.second);
        }
    }

    // ans += INF;

    return ans;
}

• Subtask 1: 11 / 11
• Subtask 2: 23 / 23
• Subtask 3: 30 / 30
• Subtask 4: 36 / 36