제출 #770507

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
770507		cadmiumsky	카니발 티켓 (IOI20_tickets)	C++17	39 / 100	3077 ms	133924 KiB

tickets

#include <bits/stdc++.h>
#include "tickets.h"
#define all(x) (x).begin(),(x).end()
using namespace std;


using ll = long long;
using ld = long double;

#define int ll
#define sz(x) ((int)(x).size())

using pii = pair<int,int>;
using tii = tuple<int,int,int>;

const int nmax = 1500 + 5;

void partition(int k, vector<vector<int>> wsign) {
  int n = sz(wsign), m = sz(wsign[0]);
  vector<pii> freq(n, pii{0, 0});
  vector<deque<int>> sorted(n);
  vector<vector<signed>> rez(n, vector<signed>(m, -1));
  for(int i = 0; i < n; i++) {
    for(int j = 0; j < m; j++) if(wsign[i][j] == -1) sorted[i].emplace_back(j), freq[i].first++;
    for(int j = 0; j < m; j++) if(wsign[i][j] ==  1) sorted[i].emplace_back(j), freq[i].second++;      
  } 
  for(int Q = 0; Q < k; Q++) {
    vector<int> checked(n);
    
    vector<int> atr(n);
    iota(all(atr), 0);
    sort(all(atr), [&](auto a, auto b) { return freq[a].first > freq[b].first; });
    
    for(int T = 0, cnt = 0; cnt < n / 2 && T < n; T++) {
      int i = atr[T];
      if(checked[i]) continue;
      if(freq[i].first > 0) {
        rez[i][sorted[i].front()] = Q;
        sorted[i].pop_front();
        cnt++;
        checked[i] = 1;
        freq[i].first--;
      }
    }
    sort(all(atr), [&](auto a, auto b) { return freq[a].second > freq[b].second; });
    for(int T = 0, cnt = 0; cnt < n / 2 && T < n; T++) {
      int i = atr[T];
      if(checked[i]) continue;
      if(freq[i].second > 0) {
        rez[i][sorted[i].back()] = Q;
        sorted[i].pop_back();
        cnt++;
        checked[i] = 1;
        freq[i].second--;
      }
    }
  }
  
  allocate_tickets(rez);
  return;
}


const int inf = 1e9 + 5;
const ll infll = 1e18 + 5;

struct Flux {
  struct Edg {
    int other;
    ll cost;
    int flux, cap;
  };
  vector<Edg> edg;
  vector<vector<int>> g;
  vector<int> p;
  vector<ll> pot;
  vector<ll> dist;
  vector<int> inque;
  vector<int> f;
  //vector<int> 
  int S, T;
  
  void init(int s, int t, int n) {
    g.resize(n);
    pot.resize(n);
    dist.resize(n);
    inque.resize(n);
    f.resize(n);
    p.resize(n);
    S = s;
    T = t;
  }
  int addedg(int u, int v, int c, ll w) {
    g[u].emplace_back(sz(edg));
    edg.emplace_back(Edg{v, w, 0, c});
    g[v].emplace_back(sz(edg));
    edg.emplace_back(Edg{u, -w, 0, 0});
    return sz(edg) - 2;
  }
  
  void SPFA() {
    fill(all(dist), infll);
    fill(all(inque), 0);
    fill(all(f), -1);
    queue<int> que;
    inque[S] = 1;
    dist[S] = 0;
    p[S] = -1;
    f[S] = inf;
    que.emplace(S);
    while(!que.empty()) {
      auto node = que.front();
      que.pop();
      inque[node] = 0;
      for(auto e : g[node]) {
        if(edg[e].flux < edg[e].cap && dist[edg[e].other] > dist[node] + edg[e].cost) {
          dist[edg[e].other] = dist[node] + edg[e].cost;
          f[edg[e].other] = min(f[node], edg[e].cap - edg[e].flux);
          p[edg[e].other] = e;
          if(!inque[edg[e].other])
            inque[edg[e].other] = 1,
            que.emplace(edg[e].other);
        }
      }
    }
    return;
  }
  
  void dijkstra() {
    fill(all(dist), infll);
    fill(all(f), -1);
    priority_queue<pii, vector<pii>, greater<pii>> heap;
    dist[S] = 0;
    p[S] = -1;
    f[S] = inf;
    heap.emplace(0, S);
    while(!heap.empty()) {
      auto [d, node] = heap.top();
      heap.pop();
      if(d != dist[node]) continue;
      for(auto e : g[node]) {
        int d2 = d + edg[e].cost + pot[node] - pot[edg[e].other];
        if(edg[e].flux < edg[e].cap && dist[edg[e].other] > d2) {
          dist[edg[e].other] = d2;
          f[edg[e].other] = min(edg[e].cap - edg[e].flux, f[node]);
          p[edg[e].other] = e;
          heap.emplace(d2, edg[e].other);
        }
      }
    }
    for(int i = 0; i < sz(dist); i++)
      dist[i] += pot[i];
    return;
  }
  
  bool dijk = 0;
  void SP() {
    if(!dijk) SPFA();
    else dijkstra();
    dijk = 1;
  }
  
  
  
  pair<ll,int> flux() {
    ll cost = 0;
    int flow = 0;
    while(true) {      
      SP();
      if(f[T] == -1) break;
      flow += f[T];
      cost += (ll)f[T] * dist[T];
      int current_edg = p[T];
      while(current_edg != -1) {
        edg[current_edg].flux += f[T];
        edg[current_edg ^ 1].flux -= f[T];
        current_edg = p[edg[current_edg ^ 1].other];
      }
      swap(pot, dist);
    }
    return pii{cost, flow};
  }
};

int N, M;

int S() { return 0; }
int T() { return 1; }
int row(int k) { return 2 + k; }
int cellp(int x, int y) { return 2 + N + x * M + y; }
int cellm(int x, int y) { return 2 + N + N * M + x * M + y; }
int Tp() { return 2 + N + N * M + N * M; }
int Tm() { return 2 + N + N * M + N * M + 1; }

ll S2(signed k, vector<vector<signed>> d) {
  vector<pii> values;
  int n = sz(d), m = sz(d[0]);
  N = n;
  M = m;
  vector<vector<int>> atrp(n, vector<int>(m, 0));
  vector<vector<int>> atrm(n, vector<int>(m, 0));
  Flux flux;
  flux.init(S(), T(), Tm() + 5);
  
  for(int i = 0; i < n; i++) {
    flux.addedg(S(), row(i), k, 0);
    for(int j = 0; j < m; j++) {
      atrp[i][j] = flux.addedg(row(i), cellp(i, j), 1, -d[i][j]);
      flux.addedg(cellp(i, j), Tp(), 1, 0);
      atrm[i][j] = flux.addedg(row(i), cellm(i, j), 1, d[i][j]);
      flux.addedg(cellm(i, j), Tm(), 1, 0);
    }
  }
  flux.addedg(Tm(), T(), n / 2 * k, 0);
  flux.addedg(Tp(), T(), n / 2 * k, 0);
  
  auto [sum, f] = flux.flux();
  sum *= -1;
  
  
  vector<int> freq(n);
  
  vector<vector<int>> signs(n, vector<int>(m, 0));
  
  for(int i = 0; i < n; i++) {
    for(int j = 0; j < m; j++) {
      if(flux.edg[atrp[i][j]].flux == 1)
        signs[i][j] = 1;
      if(flux.edg[atrm[i][j]].flux == 1)
        signs[i][j] = -1;
      
    }
  }
  
  partition(k, signs);
  
  return sum;
}
ll S3(signed k, vector<vector<signed>> d) {
  int n = sz(d), m = sz(d[0]);
  vector<pii> freq(n, pii{0, 0});
  vector<deque<int>> sorted(n);
  vector<vector<signed>> rez(n, vector<signed>(m, -1));
  for(int i = 0; i < n; i++) {
    for(int j = 0; j < m; j++) if(d[i][j] ==  0) sorted[i].emplace_back(j), freq[i].first++;
    for(int j = 0; j < m; j++) if(d[i][j] ==  1) sorted[i].emplace_back(j), freq[i].second++;      
  } 
  ll sum = 0;
  for(int Q = 0; Q < k; Q++) {
    vector<int> checked(n);
    
    vector<int> atr(n);
    iota(all(atr), 0);
    sort(all(atr), [&](auto a, auto b) { return freq[a].first > freq[b].first; });
    
    int total = 0;
    
    for(int T = 0, cnt = 0; cnt < n / 2 && T < n; T++) {
      int i = atr[T];
      if(checked[i]) continue;
      if(freq[i].first > 0) {
        rez[i][sorted[i].front()] = Q;
        sorted[i].pop_front();
        cnt++;
        checked[i] = 1;
        freq[i].first--;
      }
    }
    sort(all(atr), [&](auto a, auto b) { return freq[a].second > freq[b].second; });
    for(int T = 0, cnt = 0; cnt < n / 2 && T < n; T++) {
      int i = atr[T];
      if(checked[i]) continue;
      if(freq[i].second > 0) {
        total++;
        rez[i][sorted[i].back()] = Q;
        sorted[i].pop_back();
        cnt++;
        checked[i] = 1;
        freq[i].second--;
      }
    }
    
    for(int T = 0; T < n; T++) {
      int i = atr[T];
      if(checked[i]) continue;
      if(freq[i].second > 0)
        total++,
        freq[i].second--;
      else
        freq[i].first--;
      rez[i][sorted[i].back()] = Q;
      sorted[i].pop_back();
      checked[i] = 1;
    }
    
    sum += min(total, n - total);
  }
  
  allocate_tickets(rez);
  return sum;
}


ll S4(signed k, vector<vector<signed>> d) { 
  vector<pii> values;
  int n = sz(d), m = sz(d[0]);
  for(int i = 0; i < n; i++) 
    for(int j = 0; j < m; j++) 
      values.emplace_back(i, j);
  sort(all(values), [&](auto a, auto b) { return d[a.first][a.second] < d[b.first][b.second]; });
  
  vector<vector<int>> signs(n, vector<int>(m, 1));
  for(int i = 0; i < n / 2 * k; i++)
    signs[values[i].first][values[i].second] = -1;
  
  partition(k, signs);
  ll sum = 0;
  for(auto [a, b] : values) {
    sum += d[a][b] * signs[a][b];
  }
  return sum;
  
}

ll S1(signed k, vector<vector<signed>> d) {
  int n = sz(d), m = 1;
  vector<vector<signed>> rez(n, vector<signed>(m, 0));
  allocate_tickets(rez);
  vector<int> v;
  for(auto a : d)
    for(auto x : a) v.emplace_back(x);
  sort(all(v));
  ll sum = 0;
  for(int i = 0; i < n; i++)
    sum += v[i];
  for(int i = 0; i < n / 2; i++)
    sum -= 2 * v[i];
  return sum;
}

long long find_maximum(signed k, std::vector<std::vector<signed>> d) {
  bool ok = 1;
  for(auto a : d)
    for(auto x : a)
      ok &= (x == 0 || x == 1);
  if(sz(d[0]) == 1) return S1(k, d);
  if(k == sz(d[0])) 
    return S4(k, d);
  if(ok)
    return S3(k, d);
  else
    return S2(k, d);
}

#undef int
/**
      Anul asta se da centroid.
-- Surse oficiale
*/

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