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#include <vector>
#include <iostream>
#include <numeric>
#include <random>

template<class T>
std::vector<std::vector<int>> non_dominated_sort(const std::vector<std::vector<T>>& p, int cnt) {
  const int N = p.size();
  const int M = p.empty() ? 0 : p.front().size();
  std::vector<int> n(N);
  std::vector<std::vector<int>> S(N);
  std::vector<std::vector<int>> F(1);
  for(int i = 0; i < N; i++) {
    for(int j = i + 1; j < N; j++) {
      int ic = 0;
      int id = 0;
      int jc = 0;
      int jd = 0;
      for(int k = 0; k < M; k++) {
        T x = p[i][k];
        T y = p[j][k];
        if(x <= y){
          ic++;
          if(x < y) {
            id++;
          }
        }
        if(x >= y){
          jc++;
          if(x > y) {
            jd++;
          }
        }
      }
      if(ic == M && id > 0) {
        S[i].push_back(j);
        n[j]++;
      }
      if(jc == M && jd > 0) {
        S[j].push_back(i);
        n[i]++;
      }
    }
    if(n[i] == 0) {
      cnt--;
      F[0].push_back(i);
    }
  }
  while(F.back().size() > 0 && cnt > 0) {
    std::vector<int> Q;
    for(auto i: F.back()) {
      for(auto j: S[i]) {
        n[j]--;
        if(n[j] == 0) {
          Q.push_back(j);
          cnt--;
        }
      }
    }
    F.push_back(std::move(Q));
  }
  return F;
}

template<class T>
std::vector<T> crowding_distances(const std::vector<std::vector<T>>& p, const T INF) {
  const int N = p.size();
  const int M = p.empty() ? 0 : p.front().size();
  std::vector<T> dist(p.size());
  std::vector<int> idx(N);
  std::iota(idx.begin(), idx.end(), 0);
  for(int m = 0; m < M; m++) {
    std::sort(idx.begin(), idx.end(), [&](int i, int j) { return p[i][m] < p[j][m]; });
    dist[idx.front()] = INF;
    dist[idx.back()] = INF;
    T fmin = p[idx.front()][m];
    T fmax = p[idx.back()][m];
    for(int k = 1; k + 1 < idx.size(); k++) {
      dist[idx[k]] += (p[idx[k + 1]][m] - p[idx[k - 1]][m]) / (fmax - fmin);
    }
  }
  for(int i = 0; i < dist.size(); i++) {
    if(dist[i] >= INF) dist[i] = INF;
  }
  return dist;
}

struct Individual {
  std::vector<int> x;

  Individual crossover(const Individual& p, std::mt19937& mt) const {
    static std::bernoulli_distribution dist(0.5);
    std::vector<int> next(x.size());
    for(int i = 0; i < x.size(); i++) {
      next[i] = dist(mt) ? x[i] : p.x[i];
    }
    return Individual { next };
  }

  void mutation(std::mt19937& mt) {
    static std::bernoulli_distribution dist(0.002);
    for(int i = 0; i < x.size(); i++) {
      if(dist(mt)) {
        x[i] ^= 1;
      }
    }
  }
};

struct Subject {
  std::vector<double> v;
  std::vector<double> w;
  double c;
  double sum_v;

  void build() {
    sum_v = std::accumulate(v.begin(), v.end(), 0.0);
  }

  double score(const Individual& ind) const {
    return sum_v - std::inner_product(v.begin(), v.end(), ind.x.begin(), 0.0);
  }
};

using Score = std::vector<double>;

struct MultiKnapsack {
  std::vector<Subject> subs;
  std::vector<int> fix_order;
  int N;

  void build() {
    N = subs.front().v.size();
    std::vector<double> q(subs.front().v.size(), 0);
    for(int i = 0; i < subs.size(); i++) {
      for(int j = 0; j < subs[i].v.size(); j++) {
        q[j] = std::max(q[j], subs[i].v[j] / subs[i].w[j]);
      }
    }
    fix_order.resize(q.size());
    std::iota(fix_order.begin(), fix_order.end(), 0);
    std::sort(fix_order.begin(), fix_order.end(), [&](int i, int j) { return q[i] < q[j]; });
  }

  void fix_to_feasible(Individual& ind) const {
    std::vector<double> weight(subs.size());
    std::vector<int> bad_idx;
    for(int i = 0; i < subs.size(); i++) {
      weight[i] = std::inner_product(subs[i].w.begin(), subs[i].w.end(), ind.x.begin(), 0.0);
      if(subs[i].c < weight[i]) {
        bad_idx.push_back(i);
      }
    }
    for(auto j: fix_order) {
      if(bad_idx.size() == 0) break;
      if(ind.x[j] == 0) continue;
      int k = 0;
      ind.x[j] = 0;
      while(k < bad_idx.size()) {
        int i = bad_idx[k];
        weight[i] -= subs[i].w[j];
        if(subs[i].c < weight[i]) {
          k++;
          continue;
        }
        else {
          if(k + 1 < bad_idx.size()) {
            std::swap(bad_idx[k], bad_idx.back());
          }
          bad_idx.pop_back();
        }
      }
    }
  }

  Score score(const Individual& ind) const {
    Score scores(subs.size());
    for(int i = 0; i < subs.size(); i++) {
      scores[i] = subs[i].score(ind);
    }
    return scores;
  }
};

void solve(const MultiKnapsack& knap) {
  constexpr int Cnt = 200;
  constexpr int Save = 100;
  constexpr int Gen = 20000;
  constexpr int Tounament = 2;

  std::mt19937 mt(786);

  std::vector<Individual> gen(Cnt);
  std::vector<Score> scores(Cnt);
  {
    std::uniform_int_distribution<int> dist(0, 1);
    for(int i = 0; i < Cnt; i++) {
      std::vector<int> x(knap.N);
      for(int j = 0; j < knap.N; j++) {
        x[j] = dist(mt);
      }
      gen[i].x = std::move(x);
      knap.fix_to_feasible(gen[i]);
      scores[i] = knap.score(gen[i]);
    }
  }

  for(int g = 0; g < Gen; g++) {
    auto F = non_dominated_sort(scores, Save);

    {
      double max_sum = 0;
      std::vector<double> maxs(knap.subs.size());
      for(int i = 0; i < Cnt; i++) {
        max_sum = std::max(max_sum, std::accumulate(scores[i].begin(), scores[i].end(), 0.0));
        for(int j = 0; j < scores[i].size(); j++) {
          maxs[j] = std::max(maxs[j], scores[i][j]);
        }
      }
      double sum_max = std::accumulate(maxs.begin(), maxs.end(), 0.0);
      std::cerr << g << "\t" << F[0].size() << "/" << F.size() << "\t" << max_sum << "\t" << sum_max << std::endl;
    }
    
    std::vector<Individual> next;
    std::vector<Score> next_scores;
    std::vector<int> rank;
    std::vector<double> crowd;
    for(int r = 0; r < F.size(); r++) {
      std::vector<Score> p;
      for(auto i: F[r]) {
        p.push_back(scores[i]);
      }
      auto cr = crowding_distances(p, 1e9);
      std::vector<int> idx(cr.size());
      std::iota(idx.begin(), idx.end(), 0);
      int need = std::min((int)idx.size(), std::max(0, Save - (int)next.size()));

      if(need < idx.size()) {
        std::sort(idx.begin(), idx.end(), [&](int i, int j) { return cr[i] > cr[j]; });
      }
      for(int k = 0; k < need; k++) {
        //std::cerr << cr[idx[k]] << " \n"[k + 1 == need];
        next.push_back(std::move(gen[F[r][idx[k]]]));
        next_scores.push_back(std::move(scores[F[r][idx[k]]]));
        rank.push_back(r);
        crowd.push_back(cr[idx[k]]);
      }
    }

    std::vector<int> idx(Save);
    std::iota(idx.begin(), idx.end(), 0);
    auto tounament_selection = [&]() {
      std::vector<int> vs(Tounament);
      std::sample(idx.begin(), idx.end(), vs.begin(), Tounament, mt);
      return *std::max_element(vs.begin(), vs.end(), [&](int i, int j) {
          if(rank[i] != rank[j]) return rank[i] > rank[j];
          else return crowd[i] < crowd[j]; 
      });
    };
    std::bernoulli_distribution crossover_dist(0.8);
    for(int i = Save; i < Cnt; i++) {
      if(crossover_dist(mt)) {
        int x = tounament_selection();
        int y = tounament_selection();
        //std::cerr << x << " " << y << std::endl;
        auto z = next[x].crossover(next[y], mt);
        knap.fix_to_feasible(z);
        next_scores.push_back(knap.score(z));
        next.push_back(std::move(z));
      }
      else {
        int x = tounament_selection();
        auto z = next[x];
        z.mutation(mt);
        knap.fix_to_feasible(z);
        next_scores.push_back(knap.score(z));
        next.push_back(std::move(z));
      }
    }

    std::swap(next, gen);
    std::swap(next_scores, scores);
  }

  {
    auto F = non_dominated_sort(scores, scores.size());
    std::sort(F[0].begin(), F[0].end(), [&](int i, int j) { return scores[i] < scores[j]; });
    for(auto i: F[0]) {
      for(int j = 0; j < scores[i].size(); j++) {
        std::cerr << scores[i][j] << "\t";
      }
      /*
      for(int j = 0; j < gen[i].x.size(); j++) {
        std::cerr << gen[i].x[j];
      }
      */
      std::cerr << std::endl;
    }
  }
}

int main() {
  std::mt19937 mt(81);

  MultiKnapsack multi;

  constexpr int Item = 500;
  constexpr int Subs = 3;

  for(int i = 0; i < Subs; i++) {
    Subject sub;
    std::uniform_real_distribution<double> v_dist(1, 100);
    std::uniform_real_distribution<double> c_dist(5 * Item, 10 * Item);
    sub.v.resize(Item);
    sub.w.resize(Item);
    for(int i = 0; i < Item; i++) {
      sub.v[i] = v_dist(mt);
      sub.w[i] = v_dist(mt);
    }
    sub.c = c_dist(mt);
    sub.build();
    std::cerr << sub.c << " " << sub.sum_v << " " << std::accumulate(sub.w.begin(), sub.w.end(), 0.0) << std::endl;
    multi.subs.push_back(std::move(sub));
  }
  multi.build();

  solve(multi);
}