結果

問題 No.5020 Averaging
ユーザー tabae326tabae326
提出日時 2024-02-25 15:09:24
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 703 ms / 1,000 ms
コード長 11,674 bytes
コンパイル時間 5,013 ms
コンパイル使用メモリ 276,448 KB
実行使用メモリ 6,676 KB
スコア 61,717,742
最終ジャッジ日時 2024-02-25 15:10:07
合計ジャッジ時間 42,447 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge15
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 702 ms
6,676 KB
testcase_01 AC 702 ms
6,676 KB
testcase_02 AC 702 ms
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testcase_03 AC 702 ms
6,676 KB
testcase_04 AC 701 ms
6,676 KB
testcase_05 AC 702 ms
6,676 KB
testcase_06 AC 702 ms
6,676 KB
testcase_07 AC 702 ms
6,676 KB
testcase_08 AC 702 ms
6,676 KB
testcase_09 AC 702 ms
6,676 KB
testcase_10 AC 701 ms
6,676 KB
testcase_11 AC 702 ms
6,676 KB
testcase_12 AC 702 ms
6,676 KB
testcase_13 AC 702 ms
6,676 KB
testcase_14 AC 702 ms
6,676 KB
testcase_15 AC 702 ms
6,676 KB
testcase_16 AC 703 ms
6,676 KB
testcase_17 AC 702 ms
6,676 KB
testcase_18 AC 702 ms
6,676 KB
testcase_19 AC 702 ms
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testcase_20 AC 702 ms
6,676 KB
testcase_21 AC 702 ms
6,676 KB
testcase_22 AC 702 ms
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testcase_23 AC 702 ms
6,676 KB
testcase_24 AC 701 ms
6,676 KB
testcase_25 AC 702 ms
6,676 KB
testcase_26 AC 703 ms
6,676 KB
testcase_27 AC 703 ms
6,676 KB
testcase_28 AC 702 ms
6,676 KB
testcase_29 AC 702 ms
6,676 KB
testcase_30 AC 702 ms
6,676 KB
testcase_31 AC 702 ms
6,676 KB
testcase_32 AC 702 ms
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testcase_33 AC 702 ms
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testcase_34 AC 702 ms
6,676 KB
testcase_35 AC 702 ms
6,676 KB
testcase_36 AC 702 ms
6,676 KB
testcase_37 AC 702 ms
6,676 KB
testcase_38 AC 703 ms
6,676 KB
testcase_39 AC 701 ms
6,676 KB
testcase_40 AC 703 ms
6,676 KB
testcase_41 AC 702 ms
6,676 KB
testcase_42 AC 702 ms
6,676 KB
testcase_43 AC 702 ms
6,676 KB
testcase_44 AC 702 ms
6,676 KB
testcase_45 AC 703 ms
6,676 KB
testcase_46 AC 702 ms
6,676 KB
testcase_47 AC 702 ms
6,676 KB
testcase_48 AC 702 ms
6,676 KB
testcase_49 AC 702 ms
6,676 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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();
    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);
};


// 2べき判定
bool is_2beki(ll val) {
    ll cnt = 0;
    while(val) {
        cnt += val % 2;
        val /= 2;
    }
    return cnt == 1;
}

// 与えられた集合に対して、全パターンを試し、
// 最もTARGETに近くなるパターンと、その誤差を返す。
pair<ll, vector<ll>> search_lowest_diff_pattern(const vector<ll>& idx) {
    const ll size = idx.size();
    ll best_diff = inf;
    ll best_mask = -1;
    rep(mask, 0, 1<<size) {
        // 0が含まれていなければスキップ
        if(!(mask & 1)) continue;
        unsigned long long sum_front = 0;
        unsigned long long sum_back = 0;
        rep(i, 1, size) {
            if(mask & (1<<i)) {
                sum_front = (sum_front + V[idx[i]].first) / 2;
                sum_back = (sum_back + V[idx[i]].second) / 2;
            }
        }
        ll max_ave = max(sum_front / size, sum_back / size);
        if(abs(TARGET - max_ave) < best_diff) {
            best_diff = abs(TARGET - max_ave);
            best_mask = mask;
        }
    }
    assert(best_mask != -1);
    vector<ll> res;
    rep(i, 0, size) if(best_mask & (1<<i)) res.push_back(i);
    return {best_diff, res};
}

// 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};
}

// ビット全探索ができるサイズ N=10くらいまで、ピックアップして、
// 平均値をなるべく5*10^17に近づけようとしてみる
// N=10の場合、unsiged long longならばオーバーフローしない。    
vector<ll> decide_indicies_to_use(const double time_limit = 0.6) {
    const double start_time = toki.gettime();
    ll best_diff = inf;
    vector<ll> best_idx_to_use;
    vector<ll> idx(N);
    iota(all(idx), 0);
    ll counter = 0;
    while(toki.gettime() - start_time < time_limit) {
        counter++;
        shuffle(all(idx), ryuka.engine);
        rep(i, 0, idx.size()) {
            if(idx[i] == 0 && i != 0) {
                swap(idx[i], idx[0]);
                break;
            }
        }
        auto [diff, pos] = calc_max_diff(idx);
        if(diff < best_diff) {
            best_diff = diff;
            best_idx_to_use = vector<ll>(idx.begin(), idx.begin()+pos+1);
        }
    }
    dump(counter);
    dump(toki.gettime() - start_time);
    assert(!best_idx_to_use.empty());
    assert(best_idx_to_use[0] == 0);
    return best_idx_to_use;
}

// 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;
}

// トーナメント方式でたす
vector<pl> add_uniformly(const vector<ll>& idx) {
    assert(idx[0] == 0);
    assert(is_2beki(idx.size()));
    vector<pl> debug_v = V;
    vector<pl> ans;
    for(ll b = 0; (1<<b) < idx.size(); b++) {
        for(ll i = 0; i < idx.size(); i += (1<<b) * 2) {
            ll u = idx[i];
            ll v = idx[i + (1<<b)];
            ans.push_back({u, v});
            ll ave_front = (debug_v[u].first + debug_v[v].first) / 2;
            ll ave_back = (debug_v[u].second + debug_v[v].second) / 2;
            debug_v[u] = debug_v[v] = {ave_front, ave_back};
        }
    }
    dump(debug_v);
    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;
}

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;
    if(i > j) swap(i, j);
    if(i == j) j++;
    shuffle(res.idx.begin() + i, res.idx.begin() + j, ryuka.engine);
    auto [_, pos] = calc_max_diff(res.idx); 
    res.end_pos = pos + 1;
    assert(res.idx[0] == 0);
    res.calc_score();
    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。
    // vector<ll> idx_to_use = decide_indicies_to_use();
    IterationControl<State> sera;
    State stat = sera.anneal(0.7, 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);
    // 平均をとるように加算していく
    vector<pl> ans = add_ordinally(idx_to_use);
    // 出力
    print_ans(ans);
}

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