Submission #1067651

#	Time	Username	Problem	Language	Result	Execution time	Memory
1067651		golf	Longest Trip (IOI23_longesttrip)	C++17	85 / 100	16 ms	1368 KiB

longesttrip

#include "longesttrip.h"
#include <bits/stdc++.h>
using namespace std;

vector<int> solve_d3(int N, int D)
{
    vector<int> res(N);
    iota(res.begin(), res.end(), 0);
    return res;
}

vector<int> solve_d2(int N, int D)
{
    queue<int> stops;
    for (int i = 1; i < N; i++)
        stops.push(i);

    deque<int> trip = {0};
    while (stops.size() > 1)
    {
        int next = stops.front();
        stops.pop();
        int last = trip.back();

        if (are_connected({next}, {last}))
        {
            trip.push_back(next);
        }
        else
        {
            trip.push_back(stops.front());
            stops.pop();
            trip.push_back(next);
        }
    }

    if (stops.size() == 1)
    {
        int next = stops.front();
        int last = trip.back();
        if (are_connected({next}, {last}))
        {
            trip.push_back(next);
        }
        else
        {
            trip.push_front(stops.front());
            stops.pop();
        }
    }

    vector<int> res;
    for (int x : trip)
        res.push_back(x);
    return res;
}

int pop(queue<int> &q)
{
    int x = q.front();
    q.pop();
    return x;
}

const bool maybe = true;

map<pair<set<int>, set<int>>, bool> cache;
bool are_conn(vector<int> a, vector<int> b) {
    // if (a.size() != 1 || b.size() != 1) return are_connected(a, b);

    // int x = a[0], y = b[0];
    // if (x < y) swap(x, y);
    // if (cache.count({x, y})) return cache[{x, y}];

    // cache[{x, y}] = are_connected(a, b);
    // return cache[{x, y}];
    set<int> A, B;
    for (int x : a) A.insert(x);
    for (int x : b) B.insert(x);

    if (cache.count({A, B})) return cache[{A, B}];
    if (cache.count({B, A})) return cache[{B, A}];

    bool res = are_connected(a, b);
    cache[{A, B}] = res;
    cache[{B, A}] = res;
    return res;
}

vector<int> longest_trip(int N, int D)
{
    if (D == 3)
        return solve_d3(N, D);
    if (D == 2)
        return solve_d2(N, D);

    cache.clear();

    srand(time(0));
    vector<int> rand_nodes(N);
    iota(rand_nodes.begin(), rand_nodes.end(), 0);
    random_shuffle(rand_nodes.begin(), rand_nodes.end());

    queue<int> nodes;
    for (int x : rand_nodes)
        nodes.push(x);

    vector<int> a, b;
    a.push_back(pop(nodes));

    bool ends_connected = maybe;
    // false = a and b are not connected
    // true  = a and b are maybe connected
    while (!nodes.empty())
    {
        if (b.empty())
        {
            int n = pop(nodes);
            b.push_back(n);
            ends_connected = maybe;
            // if (are_conn({a.back()}, {n}))
            // {
            //     a.push_back(n);
            // }
            // else
            // {
            //     // missed optimization
            //     // we could cache that a and b are not connected
            //     b.push_back(n);
            //     ends_connected = false;
            // }
            // continue;
        }

        // both a and b are non-empty
        int n = pop(nodes);

        if (are_conn({a.back()}, {n}))
        {
            a.push_back(n);
            ends_connected = maybe;
        }
        else if (are_conn({b.back()}, {n}))
        {
            b.push_back(n);
            ends_connected = false;
        }
        else
        {
            // ends of a and b are definitely connected
            while (!b.empty())
            {
                a.push_back(b.back());
                b.pop_back();
            }

            assert(b.empty());
            b.push_back(n);
        }
    }

    if (b.empty())
    {
        return a;
    }

    if (ends_connected == maybe && are_conn({a.back()}, {b.back()}))
    {
        while (!b.empty())
        {
            a.push_back(b.back());
            b.pop_back();
        }

        return a;
    }

    if (!are_conn(a, b))
    {
        if (a.size() > b.size())
        {
            return a;
        }
        else
        {
            return b;
        }
    }

    if (a.size() < b.size())
        swap(a, b);

    assert(a.size() >= b.size());

    bool a_circle = are_conn({a.front()}, {a.back()});

    if (!a_circle)
    {
        for (int x : a)
            b.push_back(x);
        return b;
    }

    // a is a circle

    bool b_circle = b.size() == 1 || are_conn({b.front()}, {b.back()});

    if (!b_circle) {
        for (int x : b) a.push_back(x);
        return a;
    }

    // both a and b are circles
    // deque<int> A, B;
    // for (int x : a) A.push_back(x);
    // for (int x : b) B.push_back(x);

    // while (true) {
    //     int e = A.front(); A.pop_front();
    //     A.push_back(e);
    //     if (are_conn({e}, b)) break;
    // }

    // while (true) {
    //     int e = B.back(); B.pop_back();
    //     B.push_front(e);
    //     if (are_conn({A.back()}, {e})) break;
    // }

    // vector<int> res;
    // for (int x : A) res.push_back(x);
    // for (int x : B) res.push_back(x);
    // return res;

    // both a and b are circles
    // there is atleast one edge between a and b

    int a_connect;
    vector<int> x, y, A;

    for (int i: a) A.push_back(i);

    while (A.size() > 1) {
        x.clear();
        y.clear();
        for (int i = 0; i < A.size(); i++) {
            if (i % 2 == 0) x.push_back(A[i]);
            else y.push_back(A[i]);
        }

        if (are_conn(x, b)) { // the connection is in x
            A = x;
        } else {
            A = y;
        }
    }

    assert(A.size() == 1);
    a_connect = A[0];

    x.clear();
    y.clear();
    vector<int> B;
    int b_connect;

    for (int i: b) B.push_back(i);
    while (B.size() > 1) {
        x.clear();
        y.clear();
        for (int i = 0; i < B.size(); i++) {
            if (i % 2 == 0) x.push_back(B[i]);
            else y.push_back(B[i]);
        }

        if (are_conn({a_connect}, x)) { // the connection is in x
            B = x;
        } else {
            B = y;
        }
    }

    assert(B.size() == 1);
    b_connect = B[0];


    deque<int> A_d, B_d;
    for (int x : a) A_d.push_back(x);
    for (int x : b) B_d.push_back(x);

    while (true) {
        A_d.push_back(A_d.front());
        A_d.pop_front();
        if (A_d.back() == a_connect) break;
    }

    while (true) {
        B_d.push_front(B_d.back());
        B_d.pop_back();
        if (B_d.front() == b_connect) break;
    }

    vector<int> res;
    for (int x: A_d) res.push_back(x);
    for (int x: B_d) res.push_back(x);
    return res;
}

Compilation message (stderr)

longesttrip.cpp: In function 'std::vector<int> longest_trip(int, int)':
longesttrip.cpp:246:27: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  246 |         for (int i = 0; i < A.size(); i++) {
      |                         ~~^~~~~~~~~~
longesttrip.cpp:270:27: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  270 |         for (int i = 0; i < B.size(); i++) {
      |                         ~~^~~~~~~~~~

• Subtask 0: 0 / 0
• Subtask 1: 5 / 5
• Subtask 2: 10 / 10
• Subtask 3: 25 / 25
• Subtask 4: 45 / 60