#955782 (C++17) No.5020 Averaging

• 問題: No.5020 Averaging
• ユーザー: tabae326
• 提出日時: 2024-02-25 17:26:31
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 903 ms / 1,000 ms
• コード長: 8,716 bytes
• コンパイル時間: 4,557 ms
• コンパイル使用メモリ: 273,352 KB
• 実行使用メモリ: 6,676 KB
• スコア: 63,329,566
• 最終ジャッジ日時: 2024-02-25 17:27:24
• 合計ジャッジ時間: 52,335 ms
• ジャッジサーバーID （参考情報）: judge13 / judge11

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	902 ms; 6,676 KB
testcase_01	AC	902 ms; 6,676 KB
testcase_02	AC	902 ms; 6,676 KB
testcase_03	AC	902 ms; 6,676 KB
testcase_04	AC	902 ms; 6,676 KB
testcase_05	AC	902 ms; 6,676 KB
testcase_06	AC	902 ms; 6,676 KB
testcase_07	AC	902 ms; 6,676 KB
testcase_08	AC	902 ms; 6,676 KB
testcase_09	AC	902 ms; 6,676 KB
testcase_10	AC	901 ms; 6,676 KB
testcase_11	AC	902 ms; 6,676 KB
testcase_12	AC	902 ms; 6,676 KB
testcase_13	AC	902 ms; 6,676 KB
testcase_14	AC	902 ms; 6,676 KB
testcase_15	AC	902 ms; 6,676 KB
testcase_16	AC	902 ms; 6,676 KB
testcase_17	AC	902 ms; 6,676 KB
testcase_18	AC	902 ms; 6,676 KB
testcase_19	AC	902 ms; 6,676 KB
testcase_20	AC	902 ms; 6,676 KB
testcase_21	AC	902 ms; 6,676 KB
testcase_22	AC	902 ms; 6,676 KB
testcase_23	AC	902 ms; 6,676 KB
testcase_24	AC	901 ms; 6,676 KB
testcase_25	AC	903 ms; 6,676 KB
testcase_26	AC	903 ms; 6,676 KB
testcase_27	AC	902 ms; 6,676 KB
testcase_28	AC	902 ms; 6,676 KB
testcase_29	AC	902 ms; 6,676 KB
testcase_30	AC	903 ms; 6,676 KB
testcase_31	AC	902 ms; 6,676 KB
testcase_32	AC	902 ms; 6,676 KB
testcase_33	AC	902 ms; 6,676 KB
testcase_34	AC	902 ms; 6,676 KB
testcase_35	AC	902 ms; 6,676 KB
testcase_36	AC	902 ms; 6,676 KB
testcase_37	AC	902 ms; 6,676 KB
testcase_38	AC	902 ms; 6,676 KB
testcase_39	AC	902 ms; 6,676 KB
testcase_40	AC	901 ms; 6,676 KB
testcase_41	AC	902 ms; 6,676 KB
testcase_42	AC	901 ms; 6,676 KB
testcase_43	AC	902 ms; 6,676 KB
testcase_44	AC	902 ms; 6,676 KB
testcase_45	AC	902 ms; 6,676 KB
testcase_46	AC	902 ms; 6,676 KB
testcase_47	AC	902 ms; 6,676 KB
testcase_48	AC	902 ms; 6,676 KB
testcase_49	AC	902 ms; 6,676 KB

ソースコード

#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
using ll = long long;
using pl = std::pair<long long, long long>;
//using mint = atcoder::modint1000000007;
using mint = atcoder::modint998244353;
#define rep(i, srt, end) for (long long i = (srt); i < (long long)(end); i++)
#define all(v) (v).begin(), (v).end()
#define dump(var)  do{ if(debug::enable) { std::cerr << #var << " : "; debug::print(var); } } while(0);
constexpr int di[4] = {1, -1, 0, 0};
constexpr int dj[4] = {0, 0, 1, -1};
constexpr long long inf = 1LL<<60;
template<typename T> inline void chmax(T &a, T b) { a = std::max(a, b); };
template<typename T> inline void chmin(T &a, T b) { a = std::min(a, b); };
template<typename T> void vprint(const std::vector<T>& v) { for(int i = 0; i < v.size(); i++) { std::cout << v[i] << (i == v.size()-1 ? "\n" : " "); } }
template<typename T> void vprintln(const std::vector<T>& v) { for(int i = 0; i < v.size(); i++) { std::cout << v[i] << "\n"; } }
template<int M> void vprint(const std::vector<atcoder::static_modint<M>>& v) { for(int i = 0; i < v.size(); i++) { std::cout << v[i].val() << (i == v.size()-1 ? "\n" : " "); } }
template<int M> void vprintln(const std::vector<atcoder::static_modint<M>>& v) { for(int i = 0; i < v.size(); i++) { std::cout << v[i].val() << "\n"; } }
namespace debug {    
    #if defined(ONLINE_JUDGE)
    const bool enable = false;
    #else
    const bool enable = true;
    #endif
    template<typename T> void push(const T& e) { std::cerr << e; }
    template<int M> void push(const atcoder::static_modint<M>& e) { std::cerr << e.val(); }
    template<typename T1, typename T2> void push(const std::pair<T1, T2>& e) { std::cerr << "("; push(e.first); std::cerr << ","; push(e.second); std::cerr << ")"; }   
    template<typename T1, typename T2, typename T3> void push(const std::tuple<T1, T2, T3>& e) { std::cerr << "("; push(get<0>(e)); std::cerr << ","; push(get<1>(e)); std::cerr << ","; push(get<2>(e)); std::cerr << ")"; }   
    template<typename T> void print(const T& e) { push(e); std::cerr << "\n"; }
    template<typename T> void print(const std::vector<T>& v) { for(int i = 0; i < v.size(); i++) { push(v[i]); std::cerr << " "; } std::cerr << "\n"; }
    template<typename T> void print(const std::vector<std::vector<T>>& v) { std::cerr << "\n"; for(int i = 0; i < v.size(); i++) { std::cerr << i << ": "; print(v[i]); } }
};

struct RandGenerator {
    random_device seed_gen;
    mt19937 engine;
    mt19937_64 engine64;
    static const int pshift = 1000000000;
    RandGenerator() : engine(seed_gen()), engine64(seed_gen()) {}
    /*mod以下の乱数を返す（32bit）*/
    int rand(int mod) {
        return engine() % mod;
    }
    /*mod以下の乱数を返す（64bit）*/
    long long randll(long long mod) {
        return engine64() % mod;
    } 
    /*確率pでTrueを返す*/
    bool pjudge(double p) {
        int p_int;
        if(p > 1) p_int = pshift;
        else p_int = p * pshift;
        return rand(pshift) < p_int;
    }
} ryuka;

#include <sys/time.h>
struct timer {
    double global_start;
    double gettime() {
        struct timeval tv;
        gettimeofday(&tv, NULL);
        return tv.tv_sec + tv.tv_usec * 1e-6;
    }
    void init() {
        global_start = gettime();
    }
    double elapsed() {
        return gettime() - global_start;
    }
} toki;

constexpr ll TARGET = 500000000000000000;

ll N;
vector<pl> V;


struct State {
    vector<long long> idx;
    long long end_pos;
    long long score;
    State() : score(-inf) {};
    long long calc_score();
    long long calc_score(ll);
    static State initState();
    static State generateState(const State& input_state);
};

template<class STATE>
struct IterationControl {
    int iteration_counter;
    int swap_counter;
    double average_time;
    double start_time;
    IterationControl() : iteration_counter(0), swap_counter(0) {}
    STATE climb(double time_limit, STATE initial_state);
    STATE anneal(double time_limit, double temp_start, double temp_end, STATE initial_state);
};

// 前から順に足していって、もっとも誤差が小さくなるタイミングを返す
pl calc_max_diff(const vector<ll>& idx) {
    const ll size = idx.size();
    ll sum_front = V[idx[0]].first;
    ll sum_back = V[idx[0]].second;
    ll min_diff = inf, min_i = 0;
    rep(i, 1, size) {
        sum_front = (sum_front + V[idx[i]].first) / 2;
        sum_back = (sum_back + V[idx[i]].second) / 2;
        ll diff = max(abs(TARGET - sum_front), abs(TARGET - sum_back));
        if(diff < min_diff) {
            min_diff = diff;
            min_i = i;
        }
    }
    return {min_diff, min_i};
}

// 順々に足す
vector<pl> add_ordinally(const vector<ll>& idx) {
    vector<pl> ans;
    rep(i, 1, idx.size()) ans.push_back({0, idx[i]});
    return ans;
}

void print_ans(const vector<pl>& ans) {
    cout << ans.size() << endl;
    for(auto [u, v]: ans) {
        cout << u+1 << " " << v+1 << endl;
    }
}

long long State::calc_score() {
    ll a = V[idx[0]].first, b = V[idx[0]].second;
    rep(i, 1, end_pos) {
        a = (a + V[idx[i]].first) / 2;
        b = (b + V[idx[i]].second) / 2;
    }
    ll diff = max(abs(a - TARGET), abs(b - TARGET));
    this->score = 2000000 - 100000 * log10(diff+1);
    return this->score;
}


long long State::calc_score(ll diff) {
    this->score = 2000000 - 100000 * log10(diff+1);
    return this->score;
}

State State::initState() {
    State res;
    res.idx.resize(N);
    iota(all(res.idx), 0);
    shuffle(res.idx.begin()+1, res.idx.end(), ryuka.engine);
    auto [_, pos] = calc_max_diff(res.idx); 
    res.end_pos = pos + 1;
    res.calc_score();
    return res;
}

State State::generateState(const State& input_state) {
    State res = input_state;
    {
        ll i = ryuka.rand(N-1) + 1;
        ll j = ryuka.rand(N-1) + 1;
        swap(res.idx[i], res.idx[j]);
    } 
    auto [diff, pos] = calc_max_diff(res.idx); 
    res.end_pos = pos + 1;
    assert(res.idx[0] == 0);
    res.calc_score(diff);
    return res;
}

template<class STATE>
STATE IterationControl<STATE>::climb(double time_limit, STATE initial_state) {
    start_time = toki.gettime();
    average_time = 0;
    STATE best_state = initial_state;
    double time_stamp = start_time;
    cerr << "[INFO] - IterationControl::climb - Starts climbing...\n";
    while(time_stamp - start_time + average_time < time_limit) {
        STATE current_state = STATE::generateState(best_state);
        if(current_state.score > best_state.score) {
            swap(best_state, current_state);
            swap_counter++;
        }
        iteration_counter++;
        time_stamp = toki.gettime();
        average_time = (time_stamp - start_time) / iteration_counter;
    }
    cerr << "[INFO] - IterationControl::climb - Iterated " << iteration_counter << " times and swapped " << swap_counter << " times.\n";
    return best_state;
}

template<class STATE>
STATE IterationControl<STATE>::anneal(double time_limit, double temp_start, double temp_end, STATE initial_state) {
    start_time = toki.gettime();
    average_time = 0;
    STATE best_state = initial_state;
    double elapsed_time = 0;
    cerr << "[INFO] - IterationControl::anneal - Starts annealing...\n";
    while(elapsed_time + average_time < time_limit) {
        double normalized_time = elapsed_time / time_limit;
        double temp_current = pow(temp_start, 1.0 - normalized_time) * pow(temp_end, normalized_time);
        STATE current_state = STATE::generateState(best_state);
        long long delta = current_state.score - best_state.score;
        if(delta > 0 || ryuka.pjudge(exp(1.0 * delta / temp_current)) ) {
            swap(best_state, current_state);
            swap_counter++;
        }
        iteration_counter++;
        elapsed_time = toki.gettime() - start_time;
        average_time = elapsed_time / iteration_counter;
    }
    cerr << "[INFO] - IterationControl::anneal - Iterated " << iteration_counter << " times and swapped " << swap_counter << " times.\n";
    return best_state;
}

void solve() {
    // 入力を受け取る。
    cin >> N;
    V.resize(N);
    for(auto& [a, b]: V) cin >> a >> b;
    // 実際に使うインデックスを決定する。
    IterationControl<State> sera;
    State stat = sera.anneal(0.9, 100000, 100, State::initState());
    dump(stat.score);
    vector<ll> idx_to_use = vector<ll>(stat.idx.begin(), stat.idx.begin()+stat.end_pos);
    dump(idx_to_use);
    // 出力
    vector<pl> ans = add_ordinally(idx_to_use);
    print_ans(ans);
}

int main() {
    toki.init();
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    solve();
    return 0;
}