#755235 (C++17) No.705 ゴミ拾い Hard

提出ソース
結果

問題	No.705 ゴミ拾い Hard
コンテスト
ユーザー	maspy
提出日時	2022-04-22 16:48:48
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	91 ms / 1,500 ms
コード長	15,747 bytes
コンパイル時間	2,671 ms
コンパイル使用メモリ	216,016 KB
最終ジャッジ日時	2025-01-28 19:37:06
ジャッジサーバーID （参考情報）	judge5 / judge5
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ファイルパターン	結果
sample	AC * 4
other	AC * 40
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ソースコード

raw source code
#line 1 "/home/maspy/compro/library/my_template.hpp"
#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;

template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

#define FOR_(n) for (ll _ = 0; (_) < (ll)(n); ++(_))
#define FOR(i, n) for (ll i = 0; (i) < (ll)(n); ++(i))
#define FOR3(i, m, n) for (ll i = (m); (i) < (ll)(n); ++(i))
#define FOR_R(i, n) for (ll i = (ll)(n)-1; (i) >= 0; --(i))
#define FOR3_R(i, m, n) for (ll i = (ll)(n)-1; (i) >= (ll)(m); --(i))
#define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

template <typename T>
T SUM(vector<T> &A) {
  T sum = T(0);
  for (auto &&a: A) sum += a;
  return sum;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }

template <typename T, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}

template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}

template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

ll binary_search(function<bool(ll)> check, ll ok, ll ng) {
  assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    if (check(x))
      ok = x;
    else
      ng = x;
  }
  return ok;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

vi s_to_vi(const string& S, char first_char) {
  vi A(S.size());
  FOR(i, S.size()) { A[i] = S[i] - first_char; }
  return A;
}

template <typename T>
vector<T> cumsum(vector<T> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

template <typename CNT, typename T>
vc<CNT> bincount(const vc<T> &A, int size) {
  vc<CNT> C(size);
  for (auto &&x: A) { ++C[x]; }
  return C;
}

template <typename T>
vector<int> argsort(const vector<T> &A) {
  // stable
  vector<int> ids(A.size());
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  int n = len(A);
  assert(len(I) == n);
  vc<T> B(n);
  FOR(i, n) B[i] = A[I[i]];
  return B;
}
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>

namespace detail {
template <typename T, decltype(&T::is_modint) = &T::is_modint>
std::true_type check_value(int);
template <typename T>
std::false_type check_value(long);
} // namespace detail

template <typename T>
struct is_modint : decltype(detail::check_value<T>(0)) {};
template <typename T>
using is_modint_t = enable_if_t<is_modint<T>::value>;
template <typename T>
using is_not_modint_t = enable_if_t<!is_modint<T>::value>;

struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <class T, is_modint_t<T> * = nullptr>
  bool read_single(T &ref) {
    long long val = 0;
    bool f = read_single(val);
    ref = T(val);
    return f;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <class A, class B, class C>
  bool read_single(tuple<A, B, C> &p) {
    return (read_single(get<0>(p)) && read_single(get<1>(p))
            && read_single(get<2>(p)));
  }
  template <class A, class B, class C, class D>
  bool read_single(tuple<A, B, C, D> &p) {
    return (read_single(get<0>(p)) && read_single(get<1>(p))
            && read_single(get<2>(p)) && read_single(get<3>(p)));
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};

struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }

  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char &val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string &s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double &x) {
    ostringstream oss;
    oss << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double &x) {
    ostringstream oss;
    oss << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <class T, is_modint_t<T> * = nullptr>
  void write(T &ref) {
    write(ref.val);
  }
  template <class T>
  void write(const vector<T> &val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> &val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <class A, class B, class C>
  void write(const tuple<A, B, C> &val) {
    auto &[a, b, c] = val;
    write(a);
    write(' ');
    write(b);
    write(' ');
    write(c);
  }
  template <class A, class B, class C, class D>
  void write(const tuple<A, B, C, D> &val) {
    auto &[a, b, c, d] = val;
    write(a);
    write(' ');
    write(b);
    write(' ');
    write(c);
    write(' ');
    write(d);
  }
  template <class T, size_t S>
  void write(const array<T, S> &val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if(val < 0){
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if(negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};

Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);

void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}

void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)      \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 2 "/home/maspy/compro/library/ds/larsch.hpp"

template <class T>
class LARSCH {
  struct reduce_row;
  struct reduce_col;

  struct reduce_row {
    int n;
    std::function<T(int, int)> f;
    int cur_row;
    int state;
    std::unique_ptr<reduce_col> rec;

    reduce_row(int n_) : n(n_), f(), cur_row(0), state(0), rec() {
      const int m = n / 2;
      if (m != 0) { rec = std::make_unique<reduce_col>(m); }
    }

    void set_f(std::function<T(int, int)> f_) {
      f = f_;
      if (rec) {
        rec->set_f([&](int i, int j) -> T { return f(2 * i + 1, j); });
      }
    }

    int get_argmin() {
      const int cur_row_ = cur_row;
      cur_row += 1;
      if (cur_row_ % 2 == 0) {
        const int prev_argmin = state;
        const int next_argmin = [&]() {
          if (cur_row_ + 1 == n) {
            return n - 1;
          } else {
            return rec->get_argmin();
          }
        }();
        state = next_argmin;
        int ret = prev_argmin;
        for (int j = prev_argmin + 1; j <= next_argmin; j += 1) {
          if (f(cur_row_, ret) > f(cur_row_, j)) { ret = j; }
        }
        return ret;
      } else {
        if (f(cur_row_, state) <= f(cur_row_, cur_row_)) {
          return state;
        } else {
          return cur_row_;
        }
      }
    }
  };

  struct reduce_col {
    int n;
    std::function<T(int, int)> f;
    int cur_row;
    std::vector<int> cols;
    reduce_row rec;

    reduce_col(int n_) : n(n_), f(), cur_row(0), cols(), rec(n) {}

    void set_f(std::function<T(int, int)> f_) {
      f = f_;
      rec.set_f([&](int i, int j) -> T { return f(i, cols[j]); });
    }

    int get_argmin() {
      const int cur_row_ = cur_row;
      cur_row += 1;
      const auto cs = [&]() -> std::vector<int> {
        if (cur_row_ == 0) {
          return {{0}};
        } else {
          return {{2 * cur_row_ - 1, 2 * cur_row_}};
        }
      }();
      for (const int j: cs) {
        while ([&]() {
          const int size = cols.size();
          return size != cur_row_ && f(size - 1, cols.back()) > f(size - 1, j);
        }()) {
          cols.pop_back();
        }
        if (cols.size() != n) { cols.push_back(j); }
      }
      return cols[rec.get_argmin()];
    }
  };

  std::unique_ptr<reduce_row> base;

public:
  LARSCH(int n, std::function<T(int, int)> f)
      : base(std::make_unique<reduce_row>(n)) {
    base->set_f(f);
  }

  int get_argmin() { return base->get_argmin(); }
};
#line 2 "/home/maspy/compro/library/dp/monge.hpp"

template <typename F>
bool check_monge(int N, F f) {
  FOR(l, N + 1) FOR(k, l) FOR(j, k) FOR(i, j) {
    ll lhs = f(i, l) + f(j, k);
    ll rhs = f(i, k) + f(j, l);
    if (lhs < rhs) return false;
  }
  return true;
}

template <ll INF, typename F>
vi shortest_path_monge(ll N, F f) {
  vi dp(N + 1, INF);
  dp[0] = 0;
  LARSCH<ll> larsch(N, [&](int i, int j) {
    ++i;
    if (i <= j) return INF;
    return dp[j] + f(j, i);
  });
  FOR3(r, 1, N + 1) {
    ll l = larsch.get_argmin();
    dp[r] = dp[l] + f(l, r);
  }
  return dp;
}

/*
https://dic.kimiyuki.net/d-edge-shortest-path-monge
上凸関数 calc_L(lambda) の最大値を求める問題に帰着
|f| の上限 f_lim も渡す
*/
template <typename F>
ll d_edge_shortest_path_monge(ll N, F f, ll d, ll f_lim) {
  const ll INF = 1LL << 60;
  auto calc_L = [&](ll lambda) -> ll {
    auto cost = [&](int frm, int to) -> ll { return f(frm, to) + lambda; };
    auto dp = shortest_path_monge(N, cost);
    return dp.back() - lambda * d;
  };

  ll ANS = -INF;
  ll L = -3 * f_lim - 10;
  ll R = 3 * f_lim + 10;
  ll x = binary_search([&](ll x) { return calc_L(x - 1) <= calc_L(x); }, L, R);
  return calc_L(x);
}
#line 4 "main.cpp"

void solve() {
  LL(N);
  VEC(ll, A, N);
  VEC(ll, X, N);
  VEC(ll, Y, N);
  auto f = [&](ll i, ll j) -> ll {
    ll a = A[j - 1];
    ll x = X[i], y = Y[i];
    ll dx = abs(a - x);
    ll dy = abs(y);
    return dx * dx * dx + dy * dy * dy;
  };
  const ll INF = 1LL << 60;
  print(shortest_path_monge<INF>(N, f).back());
}

signed main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << setprecision(15);

  ll T = 1;
  // LL(T);
  FOR(_, T) solve();

  return 0;
}
yukicoder

結果

ソースコード
