結果

問題 No.719 Coprime
ユーザー Min_25
提出日時 2018-07-28 19:14:20
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 3,000 ms
コード長 9,623 bytes
コンパイル時間 1,708 ms
コンパイル使用メモリ 118,196 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-07-06 04:32:49
合計ジャッジ時間 3,149 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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ファイルパターン 結果
other AC * 61
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#include <cstdio>
#include <cassert>
#include <cmath>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
#include <set>
#include <functional>
#include <stack>
#include <queue>
#include <array>
#include <tuple>
#define getchar getchar_unlocked
#define putchar putchar_unlocked
#define _rep(_1, _2, _3, _4, name, ...) name
#define rep2(i, n) rep3(i, 0, n)
#define rep3(i, a, b) rep4(i, a, b, 1)
#define rep4(i, a, b, c) for (int i = int(a); i < int(b); i += int(c))
#define rep(...) _rep(__VA_ARGS__, rep4, rep3, rep2, _)(__VA_ARGS__)
using namespace std;
using i64 = long long;
using u8 = unsigned char;
using u32 = unsigned;
using u64 = unsigned long long;
using f80 = long double;
int get_int() {
  int c, n;
  while ((c = getchar()) < '0');
  n = c - '0';
  while ((c = getchar()) >= '0') n = n * 10 + (c - '0');
  return n;
}
template <
  typename CapType, typename TotalCapType, 
  typename CostType, typename TotalCostType
>
class CostScaling {
private:
  static const int alpha = 8; // eps <- max(1, eps / alpha)
  using cap_t = CapType;
  using tcap_t = TotalCapType;
  using cost_t = CostType; // > max{|C|} * (2 * |V|)
  using tcost_t = TotalCostType;
  static constexpr cost_t Inf = (tcap_t(1) << (sizeof(tcap_t) * 8 - 2)) - 1;
  struct InputEdge { int from, to; cap_t b, c; cost_t cost; };
  struct Edge { int to, rev; cap_t cap; cost_t cost; };
  class Dinic {
  public:
    Dinic(int N, const vector<int>& ofs, vector<Edge>& edges, 
        vector<tcap_t>& capacity) 
      : N(N), ofs(ofs), edges(edges), capacity(capacity), last(N) {}
    bool succeeded() {
      // s -> u: capacity[u]
      // u -> t: capacity[u + N]
      tcap_t f = 0;
      for (int u = 0; u < N; ++u) f += capacity[u];
      vector<int> que(N);
      while (f) {
        dist.assign(N, -1);
        int qh = 0, qt = 0, lv = N;
        for (int u = 0; u < N; ++u) if (capacity[u] > 0) que[qt++] = u, dist[u] = 0;
        for (; qh < qt; ) {
          int u = que[qh++];
          if (lv == N && capacity[u + N] > 0) lv = dist[u];
          if (dist[u] > lv) break;
          for (int ei = ofs[u]; ei < ofs[u + 1]; ++ei) {
            int v = edges[ei].to;
            if (edges[ei].cap > 0 && dist[v] == -1) {
              que[qt++] = v, dist[v] = dist[u] + 1;
            }
          }
        }
        if (lv == N) break;
        for (int u = 0; u < N; ++u) last[u] = ofs[u];
        for (int u = 0; u < N; ++u) if (capacity[u] > 0) {
          auto df = block_flow(u, capacity[u]);
          f -= df, capacity[u] -= df;
        }
      }
      return f == 0;
    }
  private:
    tcap_t block_flow(int u, tcap_t f) {
      tcap_t ret = 0;
      if (capacity[u + N] > 0) {
        tcap_t df = min(f, capacity[u + N]);
        capacity[u + N] -= df;
        return df;
      }
      for (auto& ei = last[u]; ei < ofs[u + 1]; ++ei) {
        auto& e = edges[ei]; int v = e.to;
        if (e.cap == 0 || dist[v] <= dist[u]) continue;
        cap_t df = block_flow(v, min<cap_t>(e.cap, f));
        if (df == 0) continue;
        e.cap -= df, edges[e.rev].cap += df;
        f -= df, ret += df;
        if (f == 0) break;
      }
      return ret;
    }
    int N;
    const vector<int>& ofs;
    vector<Edge>& edges;
    vector<tcap_t>& capacity;
    vector<int> last, dist;
  };
public:
  CostScaling(int N, int M=0) : N(N), capacity(2 * N) {
    if (M > 0) in.reserve(M);
  }
  void add_directed_edge(int u, int v, cap_t b, cap_t c, cost_t cost) {
    if (b > 0) capacity[v] += b, capacity[u + N] += b;
    else capacity[u] += -b, capacity[v + N] += -b;
    in.push_back({u, v, b, c, cost});
  }
  pair<bool, tcost_t> minimum_cost_circulation() {
    construct();
    if (!has_feasible_circulation()) return {false, 0};
    const int cost_multiplier = 2 << __lg(N); // should be > |V|
    cost_t eps = 0;
    for (auto& e : edges) e.cost *= cost_multiplier, eps = max(eps, e.cost);
    
    while (eps > 1) refine(eps = max<cost_t>(1, eps / alpha));
    tcost_t ret = initial_cost;
    for (auto& e : edges) ret -= (e.cost / cost_multiplier) * e.cap;
    return {true, ret / 2};
  }
private:
  void refine(const cost_t eps) {
    auto cost_p = [&] (int u, const Edge& e) {
      return e.cost + potential[u] - potential[e.to];
    };
    for (int u = 0; u < N; ++u) for (int i = ofs[u]; i < ofs[u + 1]; ++i) {
      auto& e = edges[i];
      if (cost_p(u, e) < 0) edges[e.rev].cap += e.cap, e.cap = 0;
    }
    vector<tcap_t> excess(initial_excess);
    for (auto& e : edges) excess[e.to] -= e.cap;
    vector<int> stack; stack.reserve(N);
    for (int u = 0; u < N; ++u) if (excess[u] > 0) stack.push_back(u);
    auto residue = [&] (const Edge& e) -> cap_t { return e.cap; };
    auto push = [&] (int u, Edge& e, cap_t df) {
      e.cap -= df; edges[e.rev].cap += df;
      excess[e.to] += df; excess[u] -= df;
      if (excess[e.to] > 0 && excess[e.to] <= df) {
        stack.push_back(e.to);
      }
    };
    auto relabel = [&] (int u, cost_t delta) {
      potential[u] -= delta + eps;
    };
    auto relabel_in_advance = [&] (int u) {
      if (excess[u] != 0) return false;
      auto delta = Inf;
      for (int ei = ofs[u]; ei < ofs[u + 1]; ++ei) {
        auto& e = edges[ei];
        if (residue(e) == 0) continue;
        if (cost_p(u, e) < 0) return false;
        else delta = min<tcost_t>(delta, cost_p(u, e));
      }
      relabel(u, delta);
      return true;
    };
    auto discharge = [&] (int u) {
      auto delta = Inf;
      for (int ei = ofs[u]; ei < ofs[u + 1]; ++ei) {
        auto& e = edges[ei];
        if (residue(e) == 0) continue;
        if (cost_p(u, e) < 0) {
          if (relabel_in_advance(e.to)) {
            --ei; continue; // modify ei (!)
          }
          cap_t df = min<tcap_t>(excess[u], residue(e));
          push(u, e, df);
          if (!excess[u]) return;
        } else delta = min<tcost_t>(delta, cost_p(u, e));
      }
      relabel(u, delta);
      stack.push_back(u);
    };
    while (!stack.empty()) {
      auto u = stack.back(); stack.pop_back();
      discharge(u);
    }
  }
  void construct() {
    ofs.assign(N + 1, 0);
    edges.resize(2 * in.size());
    initial_excess.assign(N, 0);
    initial_cost = 0;
    potential.assign(N, 0);
    for (auto& e : in) ofs[e.from + 1]++, ofs[e.to + 1]++;
    for (int i = 1; i <= N; ++i) ofs[i] += ofs[i - 1];
    for (auto& e : in) {
      initial_excess[e.to] += e.c;
      initial_excess[e.from] += -e.b;
      initial_cost += tcost_t(e.cost) * (e.c + e.b);
      edges[ofs[e.from]++] = {e.to, ofs[e.to], e.c - e.b, e.cost};
      edges[ofs[e.to]++] = {e.from, ofs[e.from] - 1, 0, -e.cost};
    }
    for (int i = N; i > 0; --i) ofs[i] = ofs[i - 1];
    ofs[0] = 0;
  }
  bool has_feasible_circulation() {
    return Dinic(N, ofs, edges, capacity).succeeded();
  }
private:
  int N; 
  vector<InputEdge> in;
  vector<tcap_t> capacity;
  vector<int> ofs;
  vector<Edge> edges;
  tcost_t initial_cost;
  vector<tcap_t> initial_excess;
  vector<tcost_t> potential;
};
// cap, total_cap, cost * (2 * |V|), total_cost
using MCC = CostScaling<int, int64_t, int64_t, int64_t>;
// using MCC = CostScaling<int, int, int, int>;
vector<int> prime_sieve(int N) {
  if (N <= 1) return vector<int>();
  const int sieve_size = 32 << 10;
  static u8 block[sieve_size];
  const int v = sqrt(N), vv = sqrt(v);
  vector<bool> is_prime(v + 1, 1);
  vector<pair<int, int>> sprimes;
  rep(i, 2, vv + 1) if (is_prime[i]) rep(j, i * i, v + 1, i) is_prime[j] = 0;
  rep(i, 3, v + 1, 2) if (is_prime[i]) sprimes.emplace_back(i, i * i / 2);
  const int rsize = N >= 60194 ? N / (log(N) - 1.1)
                               : max(1., N / (log(N) - 1.11)) + 1;
  vector<int> primes(1, 2); primes.resize(rsize);
  int psize = 1;
  auto* pblock = block - 1;
  for (int beg = 1; beg < (N + 1) / 2; beg += sieve_size, pblock -= sieve_size) {
    int end = min(beg + sieve_size, (N + 1) / 2);
    fill(block, block + sieve_size, 1);
    rep(i, sprimes.size()) {
      int p, next; tie(p, next) = sprimes[i];
      if (p * p > N) break;
      for (; next < end; next += p) pblock[next] = 0;
      sprimes[i].second = next;
    };
    rep(i, beg, end) if (pblock[i]) primes[psize++] = 2 * i + 1;
  }
  assert(psize <= int(primes.size()));
  primes.resize(psize);
  return primes;
}
void solve() {
  /*
  10 ** 6: 37717171222 ?
  10 ** 7: 3207771163478 ?
  10 ** 8: 279332542770588 ?
  */
  int N;
  while (~scanf("%d", &N)) {
    vector<int> primes = prime_sieve(N);
    const int pcnt = primes.size();
    vector<int> max_pows(pcnt);
    i64 ans = 0;
    rep(i, primes.size()) {
      int p = primes[i];
      i64 q = p; while (q * p <= N) q *= p;
      max_pows[i] = q;
      ans += q;
    }
    const int v = sqrt(N);
    int sqi = upper_bound(primes.begin(), primes.end(), v) - primes.begin();
    auto mcc = MCC(pcnt + 2);
    rep(i, sqi) {
      i64 p = primes[i];
      rep(j, sqi, pcnt) {
        i64 q = primes[j];
        if (p * q > N) break;
        i64 t = p * q;
        while (t * p <= N) t *= p;
        i64 cost = t - max_pows[i] - max_pows[j];
        if (cost > 0) mcc.add_directed_edge(i, j, 0, 1, (int) -cost);
      }
    }
    rep(i, sqi) mcc.add_directed_edge(pcnt, i, 0, 1, 0);
    rep(i, sqi, pcnt) mcc.add_directed_edge(i, pcnt + 1, 0, 1, 0);
    mcc.add_directed_edge(pcnt + 1, pcnt, 0, sqi, 0);
    auto ans2 = mcc.minimum_cost_circulation();
    printf("%lld\n", ans - ans2.second);
  }
}
int main() {
  clock_t beg = clock();
  solve();
  clock_t end = clock();
  fprintf(stderr, "%.3f sec\n", double(end - beg) / CLOCKS_PER_SEC);
  return 0;
}
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