Submission #1082206

#	Time	Username	Problem	Language	Result	Execution time	Memory
1082206		Boas	Longest Trip (IOI23_longesttrip)	C++17	15 / 100	1014 ms	5936 KiB

longesttrip

#include "longesttrip.h"

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;

template <typename T1, typename T2>
using indexed_map = tree<T1, T2, less<T1>, rb_tree_tag, tree_order_statistics_node_update>;
template <typename T>
using indexed_set = indexed_map<T, null_type>;

#define loop(x, i) for (int i = 0; i < (x); i++)
#define loop1(x, i) for (int i = 1; i <= (x); i++)
#define rev(x, i) for (int i = (int)(x) - 1; i >= 0; i--)
#define itloop(x) for (auto it = begin(x); x != end(x); it++)
#define itrev(x) for (auto it = rbegin(x); x != rend(x); it++)
#define INF32 ((int32_t)(2e9 + 1))
#define ALL(x) begin(x), end(x)
#define RALL(x) rbegin(x), rend(x)
#define removeIn(x, l) l.erase(find(ALL(l), x))
#define pb push_back
#define sz(x) (int)(x).size()
#define F first
#define S second
#define var const auto &
#define foreach(l) for (var e : l)

typedef int8_t i8;
typedef int16_t i16;
typedef int32_t i32;
typedef int64_t i64;
typedef pair<int, int> ii;
typedef tuple<int, int, int> iii;
typedef tuple<int, int, int, int> iiii;
typedef vector<int> vi;
typedef vector<i32> vi32;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vi32> vvi32;
typedef vector<ii> vii;
typedef vector<iii> viii;
typedef vector<vii> vvii;
typedef vector<viii> vviii;
typedef set<int> si;
typedef set<ii> sii;
typedef set<iii> siii;
typedef vector<si> vsi;
typedef vector<sii> vsii;
typedef vector<vsi> vvsi;
typedef vector<string> vstr;
typedef vector<vector<string>> vvstr;
typedef vector<bool> vb;
typedef vector<vb> vvb;

vi longest_trip(int N, int D)
{
    if (D >= 2)
    {
        vi res(N);
        iota(ALL(res), 0);
        if (D == 3)
        {
            return res;
        }
        si resterend;
        loop1(N - 1, i) resterend.insert(res[i]);
        loop1(N - 1, i)
        {
            auto it = resterend.begin();
            if (are_connected({res[i - 1]}, {*it}))
            {
                res[i] = *it;
                resterend.erase(it);
            }
            else
            {
                if (resterend.size() == 1)
                {
                    res.insert(res.begin(), *it);
                    res.pop_back();
                    return res;
                }
                res[i] = *next(it);
                resterend.erase(next(it));
            }
        }
        return res;
    }
    else
    {
        vsi adj(N);
        for (int i = 0; i < N; i++)
        {
            for (int j = i + 1; j < N; j++)
            {
                if (are_connected({i}, {j}))
                {
                    // cerr << i << ' ' << j << endl;
                    adj[i].insert(j);
                    adj[j].insert(i);
                }
            }
        }
        if (N <= 10)
        {
            vi best;
            for (int mask = 1; mask < (1 << N); mask++)
            {
                vi all;
                loop(N, i) if ((1 << i) & mask) all.pb(i);
                do
                {
                    if (sz(all) <= sz(best))
                        break;
                    bool val = 1;
                    loop(sz(all) - 1, i) if (!adj[all[i]].count(all[i + 1]))
                    {
                        val = 0;
                    }
                    if (val)
                        best = all;
                } while (next_permutation(ALL(all)));
            }
            if (sz(best) != N)
            {
                vb comp(N);
                for (int i : best)
                {
                    for (int j : best)
                    {
                        if (i != j && !adj[i].count(j))
                            throw;
                    }
                    comp[i] = 1;
                }
                vi others;
                loop(N, i) if (!comp[i]) others.pb(i);
                for (int i : others)
                {
                    for (int j : others)
                    {
                        if (i != j && !adj[i].count(j))
                            throw;
                    }
                }
            }
            return best;
        }
        si clique1, clique2;
        auto checkCliques = [&]()
        {
            for (int i : clique1)
            {
                for (int j : clique1)
                {
                    assert(i == j || adj[i].count(j));
                }
            }
            for (int i : clique2)
            {
                for (int j : clique2)
                {
                    assert(i == j || adj[i].count(j));
                }
            }
        };
        loop(2, iter) loop(N, i)
        {
            for (int j = i + 1; j < N; j++)
            {
                if (adj[i].count(j))
                    continue;
                if (clique1.empty())
                {
                    clique1.insert(i);
                    clique2.insert(j);
                }
                else
                {
                    bool iVal2 = 1, iVal1 = 1, jVal2 = 1, jVal1 = 1;
                    for (int k : clique1)
                    {
                        if (k != i && !adj[i].count(k))
                        {
                            iVal1 = 0;
                        }
                        if (k != j && !adj[j].count(k))
                        {
                            jVal1 = 0;
                        }
                    }
                    for (int k : clique2)
                    {
                        if (i != k && !adj[i].count(k))
                        {
                            iVal2 = 0;
                        }
                        if (j != k && !adj[j].count(k))
                        {
                            jVal2 = 0;
                        }
                    }
                    if (iVal1 && jVal2 && !iVal2 && !jVal1)
                    {
                        clique1.insert(i);
                        clique2.insert(j);
                    }
                    if (iVal2 && jVal1 && !iVal1 && !jVal2)
                    {
                        clique2.insert(i);
                        clique1.insert(j);
                    }
                }
            }
        }
        checkCliques();
        loop(N, i)
        {
            if (clique1.count(i) || clique2.count(i))
                continue;
            bool iVal2 = 1, iVal1 = 1;
            for (int k : clique1)
            {
                if (!adj[i].count(k))
                {
                    iVal1 = 0;
                }
            }
            for (int k : clique2)
            {
                if (!adj[i].count(k))
                {
                    iVal2 = 0;
                }
            }
            if (iVal1)
            {
                clique1.insert(i);
            }
            else if (iVal2)
            {
                clique2.insert(i);
            }
        }
        ii bridge = {-1, -1};
        for (int i : clique1)
        {
            for (int j : adj[i])
            {
                if (clique2.count(j))
                {
                    bridge = {i, j};
                    break;
                }
            }
        }
        assert(sz(clique1) + sz(clique2) == N);
        checkCliques();
        vi res;
        if (bridge.F == -1)
        {
            if (sz(clique1) < sz(clique2))
            {
                swap(clique1, clique2);
            }
            for (int i : clique1)
                res.pb(i);
            // loop(sz(res) - 1, i) assert(adj[res[i]].count(res[i + 1]));
            return res;
        }
        for (int i : clique1)
        {
            if (i != bridge.F)
                res.pb(i);
        }
        res.pb(bridge.F);
        res.pb(bridge.S);
        for (int i : clique2)
        {
            if (i != bridge.S)
                res.pb(i);
        }
        assert(sz(res) == N);
        // loop(sz(res) - 1, i) assert(adj[res[i]].count(res[i + 1]));
        return res;
    }
    throw;
    return {};
}

• Subtask 0: 0 / 0
• Subtask 1: 5 / 5
• Subtask 2: 10 / 10
• Subtask 3: 0 / 25
• Subtask 4: 0 / 60