#957205 (C++17) No.5020 Averaging

• 問題: No.5020 Averaging
• ユーザー: Jiro_tech15
• 提出日時: 2024-03-02 17:58:43
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 3 ms / 1,000 ms
• コード長: 9,917 bytes
• コンパイル時間: 2,573 ms
• コンパイル使用メモリ: 156,972 KB
• 実行使用メモリ: 6,676 KB
• スコア: 58,977,770
• 最終ジャッジ日時: 2024-03-02 17:58:48
• 合計ジャッジ時間: 5,037 ms
• ジャッジサーバーID （参考情報）: judge12 / judge15

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,676 KB
testcase_01	AC	2 ms; 6,676 KB
testcase_02	AC	3 ms; 6,676 KB
testcase_03	AC	3 ms; 6,676 KB
testcase_04	AC	3 ms; 6,676 KB
testcase_05	AC	2 ms; 6,676 KB
testcase_06	AC	3 ms; 6,676 KB
testcase_07	AC	3 ms; 6,676 KB
testcase_08	AC	3 ms; 6,676 KB
testcase_09	AC	3 ms; 6,676 KB
testcase_10	AC	3 ms; 6,676 KB
testcase_11	AC	3 ms; 6,676 KB
testcase_12	AC	3 ms; 6,676 KB
testcase_13	AC	3 ms; 6,676 KB
testcase_14	AC	2 ms; 6,676 KB
testcase_15	AC	3 ms; 6,676 KB
testcase_16	AC	2 ms; 6,676 KB
testcase_17	AC	3 ms; 6,676 KB
testcase_18	AC	2 ms; 6,676 KB
testcase_19	AC	2 ms; 6,676 KB
testcase_20	AC	3 ms; 6,676 KB
testcase_21	AC	2 ms; 6,676 KB
testcase_22	AC	3 ms; 6,676 KB
testcase_23	AC	2 ms; 6,676 KB
testcase_24	AC	3 ms; 6,676 KB
testcase_25	AC	2 ms; 6,676 KB
testcase_26	AC	3 ms; 6,676 KB
testcase_27	AC	2 ms; 6,676 KB
testcase_28	AC	3 ms; 6,676 KB
testcase_29	AC	3 ms; 6,676 KB
testcase_30	AC	3 ms; 6,676 KB
testcase_31	AC	2 ms; 6,676 KB
testcase_32	AC	2 ms; 6,676 KB
testcase_33	AC	3 ms; 6,676 KB
testcase_34	AC	3 ms; 6,676 KB
testcase_35	AC	2 ms; 6,676 KB
testcase_36	AC	3 ms; 6,676 KB
testcase_37	AC	3 ms; 6,676 KB
testcase_38	AC	3 ms; 6,676 KB
testcase_39	AC	2 ms; 6,676 KB
testcase_40	AC	3 ms; 6,676 KB
testcase_41	AC	2 ms; 6,676 KB
testcase_42	AC	3 ms; 6,676 KB
testcase_43	AC	3 ms; 6,676 KB
testcase_44	AC	3 ms; 6,676 KB
testcase_45	AC	2 ms; 6,676 KB
testcase_46	AC	2 ms; 6,676 KB
testcase_47	AC	2 ms; 6,676 KB
testcase_48	AC	3 ms; 6,676 KB
testcase_49	AC	3 ms; 6,676 KB

ソースコード

namespace atcoder {}

#ifdef LOCAL
#define dbg(x) cerr << __LINE__ << " : " << #x << " = " << (x) << endl;
#else
#define NDEBUG
#define dbg(x) true;
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif

#ifdef GTEST
#include <gtest/gtest.h>
#endif

#include <math.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#ifdef PERF
#include <gperftools/profiler.h>
#endif

using namespace std;
using namespace atcoder;
#define fast_io                     \
  ios_base::sync_with_stdio(false); \
  cin.tie(0);                       \
  cout.tie(0);
#define ll long long int
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define reps(i, n) for (int i = 1; i <= (int)(n); i++)
#define REP(i, n) for (int i = n - 1; i >= 0; i--)
#define REPS(i, n) for (int i = n; i > 0; i--)
#define MOD (long long int)(1e9 + 7)
#define INF (int)(1e9)
#define LINF (long long int)(1e18)
#define chmax(a, b) a = (((a) < (b)) ? (b) : (a))
#define chmin(a, b) a = (((a) > (b)) ? (b) : (a))
#define ALL(v) v.begin(), v.end()
typedef pair<int, int> Pii;
typedef pair<ll, ll> Pll;
constexpr double PI = acos(-1);

#ifdef NDEBUG
#define CHECK(v1, op, v2)
#else
#define CHECK(v1, op, v2)                            \
  if (!((v1)op(v2))) {                               \
    cerr << "ERROR:" << (v1) << " " << (v2) << endl; \
    assert((v1)op(v2));                              \
  }
#endif

long double nCr(const int n, const int r) {
  long double ret = 1;
  rep(t, r) {
    ret *= (n - t);
    ret /= (r - t);
  }
  return ret;
}

template <typename T>
string to_string(const vector<T>& vec) {
  string ret = "";
  rep(i, vec.size()) {
    ret += vec[i].to_string();
    if (i + 1 != vec.size()) {
      ret += ",";
    }
  }
  return ret;
}

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& vec) {
  os << to_string(vec);
  return os;
}

uint32_t xorshift() {
  static uint32_t x = 12345789;
  static uint32_t y = 362436069;
  static uint32_t z = 521288629;
  static uint32_t w = 88675123;
  uint32_t t;
  t = x ^ (x << 11);
  x = y;
  y = z;
  z = w;
  w ^= t ^ (t >> 8) ^ (w >> 19);

  return w;
}

int rand(const uint32_t l, const uint32_t r) {
  return xorshift() % (r - l) + l;
}

uint32_t rand_other_than(const uint32_t l, const uint32_t r,
                         const uint32_t other) {
  const uint32_t num = rand(l, r - 1);
  return num + (num >= other);
}

template <typename T>
const T& rand_vec(const vector<T>& vec) {
  assert(vec.size() > 0);
  return vec[rand(0, vec.size())];
}

template <typename T>
void shuffle(vector<T>& vec) {
  rep(l, (int)vec.size() - 1) {
    const int idx = rand(l, vec.size());
    swap(vec[idx], vec[l]);
  }
}


class Timer {
  chrono::system_clock::time_point _start, _end;
  ll _sum = 0, _count = 0;

 public:
  void start() { _start = chrono::system_clock::now(); }

  void stop() { _end = chrono::system_clock::now(); }

  void add() {
    const chrono::system_clock::time_point now = chrono::system_clock::now();
    _sum += static_cast<double>(
        chrono::duration_cast<chrono::nanoseconds>(now - _start).count());
    _count++;
  }

  ll sum() const { return _sum / 1000; }

  int count() const { return _count; }

  string average() const {
    if (_count == 0) {
      return "NaN";
    }
    return to_string(_sum / 1000 / _count);
  }

  void reset() {
    _start = chrono::system_clock::now();
    _sum = 0;
    _count = 0;
  }

  inline int ms() const {
    const chrono::system_clock::time_point now = chrono::system_clock::now();
    return static_cast<double>(
        chrono::duration_cast<chrono::microseconds>(now - _start).count() /
        1000);
  }

  inline int ns() const {
    const chrono::system_clock::time_point now = chrono::system_clock::now();
    return static_cast<double>(
        chrono::duration_cast<chrono::microseconds>(now - _start).count());
  }
};

#ifdef LOCAL
struct Timers : unordered_map<string, Timer> {
  friend ostream& operator<<(ostream& os, const Timers& timers) {
    for (const auto& pa : timers) {
      os << pa.first << " time: " << pa.second.sum() / 1000
         << " count: " << pa.second.count() << endl;
    }
    return os;
  }
};
#else
struct Timers {
  struct Dummy {
    void start() const {}
    void add() const {}
  };
  Dummy dummy;
  const Dummy& operator[](const std::string& str) { return dummy; }
  friend ostream& operator<<(ostream& os, const Timers& timers) { return os; }
};
#endif

Timers global_timers;





/* start */

Timer global_timer;
int N;

struct Card{
  ll a,b;

  static Card Mean(const Card& X, const Card& Y){
    const ll a = (X.a+Y.a)/2;
    const ll b = (X.b+Y.b)/2;
    return {a,b};
  }
  ll Cost() const{
    return max(abs(a), abs(b));
  }
  int OmoteUra()const{
    return  (a > 0 ? 2 : 0) + (b > 0 ? 1 : 0);
  }
};
vector<Card> inputCards;
constexpr ll base = 5 * (ll)(1e17);
const int Q = 50;
vector<pair<int,int>> globalAns;

void Do(vector<pair<int,int>>& ans, vector<Card>& cards, const int i, const int j){
  assert((int)ans.size() < Q);
  assert(i!=j);
  const auto card = Card::Mean(cards[i], cards[j]);
  cards[i] = card;
  cards[j] = card;
  ans.push_back({i,j});
}

void PrintAns(const vector<pair<int,int>>& vec){
  cout << vec.size()<<endl;
  for(const auto [i,j] : vec){
    cout << i+1<<" "<<j+1<<endl;
  }
}

struct Output {
  static void StaticInit(istream& is) { global_timer.start();
  cin>>N;
  inputCards.resize(N);
  rep(i,N){
    ll a,b;
    cin>>a>>b;
    a -= base;
    b -= base;
    inputCards[i].a = a;
    inputCards[i].b = b;
  }
   }
  friend ostream& operator<<(ostream& os, const Output& output) { return os; }
};



/* start */

vector<double> PARAMS = {1.0, 0.1};




/* start */

class Solver {
 public:
  Solver() {}
  void Solve() {
    // (表,裏)x(+,-)の組数を等しくしたい
    vector<pair<int,int>> ansCommands;
    rep(_t, 6){
        // (表が+? 2 :0) + (裏が+? 1: 0)
        vector<int> counts(4);
        int minEval = INF;
        pair<int,int> bestCommand = {-1,-1};
        rep(i, N){
            const auto& card = inputCards[i];
            const int val = card.OmoteUra();
            counts[val]++;
        }
        const auto func = [](const vector<int>& counts){
            int minCount = INF;
            int maxCount = 0;
            rep(i, 4){
                chmin(minCount, counts[i]);
                chmax(maxCount, counts[i]);
            }
            return maxCount - minCount;
        };
        minEval = func(counts);
        rep(i, N){
            rep(j, N){
                auto newCounts = counts;
                const auto& card0 = inputCards[i];
                const auto& card1 = inputCards[j];
                const auto newCard = Card::Mean(card0, card1);
                newCounts[card0.OmoteUra()]--;
                newCounts[card1.OmoteUra()]--;
                newCounts[newCard.OmoteUra()] += 2;
                const auto eval = func(newCounts);
                if(eval < minEval){
                    bestCommand = {i, j};
                }
            }
        }
        if(bestCommand.first == -1) continue;
        ansCommands.push_back(bestCommand);
        const auto newCard = Card::Mean(inputCards[bestCommand.first], inputCards[bestCommand.second]);
        inputCards[bestCommand.first] = newCard;
        inputCards[bestCommand.second] = newCard;
    }

    ll totalMinCost = LINF;
    size_t bestSize = 0;
    ll totalBestScore = 0;

    // 1/2, 1/4, 1/8, ...
    // 乱択貪欲
    long double sumA = 0;
    long double sumB = 0;
    vector<int> remainIds(N);
    vector<int> ansIds;
    std::iota(ALL(remainIds), 0);
    long double weight = 1.0;
    while(remainIds.size()){
        if((int)remainIds.size() != 1){
            weight *= 0.5;
        }
        ll minCost = LINF;
        ll bestSumA = 0;
        ll bestSumB = 0;
        int best_i = -1;
        rep(i, remainIds.size()){
            const auto id = remainIds[i];
            if(id == 0 && (int)remainIds.size() >= 2) continue;
            const auto& card = inputCards[id];
            const auto nextSumA = sumA + card.a * weight;
            const auto nextSumB = sumB + card.b * weight;
            const ll cost = max(abs(nextSumA), abs(nextSumB));
            if(cost < minCost){
                minCost = cost;
                bestSumA = nextSumA;
                bestSumB = nextSumB;
                best_i = i;
            }
        }
        assert(best_i >= 0);
        ansIds.push_back(remainIds[best_i]);
        swap(remainIds[best_i], remainIds.back());
        remainIds.pop_back();
        sumA = bestSumA;
        sumB = bestSumB;
        cerr << sumA<<" "<<sumB << endl;
        if(minCost < totalMinCost){
            totalMinCost = minCost;
            bestSize = ansIds.size();
            totalBestScore = (ll)(2000000 - 100000 * log(max(abs(sumA), abs(sumB)) + 1) / log(10));
        }
    }
    cerr << sumA <<" "<<sumB<<endl;
    ansIds.resize(bestSize);
    if(ansIds.back() != 0){
        ansIds.push_back(0);
    }
    REP(i, (int)ansIds.size()-1){
        const auto id0 = ansIds[i];
        ansCommands.push_back({id0, 0});
    }
    cerr << "score: " << totalBestScore<<endl;

    PrintAns(ansCommands);
    return; }

 private:
};

int main(int argc, char* argv[]) {
  fast_io;

  if (argc >= 2) {
    int idx = 0;
    for (int i = 1; i < argc; ++i) {
      PARAMS[idx++] = std::stod(argv[i]);
    }
  }

  Timer timer;
  timer.start();
  Output::StaticInit(cin);
  Solver solver;
  solver.Solve();
  return 0;
}