結果

問題 No.2006 Decrease All to Zero
ユーザー maspymaspy
提出日時 2022-11-01 16:31:12
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 372 ms / 4,000 ms
コード長 18,125 bytes
コンパイル時間 3,557 ms
コンパイル使用メモリ 238,784 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-14 11:48:29
合計ジャッジ時間 8,037 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,816 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 21 ms
6,820 KB
testcase_03 AC 2 ms
6,820 KB
testcase_04 AC 2 ms
6,816 KB
testcase_05 AC 2 ms
6,816 KB
testcase_06 AC 6 ms
6,820 KB
testcase_07 AC 6 ms
6,816 KB
testcase_08 AC 2 ms
6,816 KB
testcase_09 AC 2 ms
6,820 KB
testcase_10 AC 368 ms
6,820 KB
testcase_11 AC 372 ms
6,820 KB
testcase_12 AC 365 ms
6,820 KB
testcase_13 AC 367 ms
6,820 KB
testcase_14 AC 369 ms
6,820 KB
testcase_15 AC 370 ms
6,820 KB
testcase_16 AC 138 ms
6,816 KB
testcase_17 AC 290 ms
6,816 KB
testcase_18 AC 2 ms
6,816 KB
testcase_19 AC 2 ms
6,816 KB
testcase_20 AC 2 ms
6,820 KB
testcase_21 AC 2 ms
6,816 KB
testcase_22 AC 2 ms
6,820 KB
testcase_23 AC 2 ms
6,820 KB
testcase_24 AC 1 ms
6,816 KB
testcase_25 AC 2 ms
6,820 KB
testcase_26 AC 366 ms
6,816 KB
testcase_27 AC 358 ms
6,816 KB
testcase_28 AC 358 ms
6,820 KB
testcase_29 AC 15 ms
6,820 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#line 1 "/home/maspy/compro/library/my_template.hpp"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#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__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) \
  overload4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#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, typename U>
T SUM(const vector<U> &A) {
  T sum = 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 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T pick(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}

template <typename T>
T pick(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}

template <typename T>
T pick(pqg<T> &que) {
  assert(que.size());
  T a = que.top();
  que.pop();
  return a;
}

template <typename T>
T pick(vc<T> &que) {
  assert(que.size());
  T a = que.back();
  que.pop_back();
  return a;
}

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};
}

template <typename F>
ll binary_search(F check, ll ok, ll ng) {
  assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return ok;
}

template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return (ok + ng) / 2;
}

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);
}

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

template <typename T, typename U>
vector<T> cumsum(vector<U> &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;
}

// stable
template <typename T>
vector<int> argsort(const vector<T> &A) {
  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(I);
  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 << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double &x) {
    ostringstream oss;
    oss << fixed << 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 A, class B, class C, class D, class E>
  void write(const tuple<A, B, C, D, E> &val) {
    auto &[a, b, c, d, e] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e);
  }
  template <class A, class B, class C, class D, class E, class F>
  void write(const tuple<A, B, C, D, E, F> &val) {
    auto &[a, b, c, d, e, f] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f);
  }
  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/disjointsparse.hpp"

template <class Monoid>
struct DisjointSparse {
  using X = typename Monoid::value_type;
  using value_type = X;
  int n, log;
  vc<vc<X>> dat;

  DisjointSparse() {}
  DisjointSparse(vc<X>& A) { build(A); }

  template <typename F>
  DisjointSparse(int n, F f) {
    vc<X> A(n);
    FOR(i, n) A[i] = f(i);
    build(A);
  }

  void build(vc<X>& A) {
    n = len(A);
    log = 1;
    while ((1 << log) < n) ++log;
    dat.assign(log, A);

    FOR(i, log) {
      auto& v = dat[i];
      int b = 1 << i;
      for (int m = b; m <= n; m += 2 * b) {
        int L = m - b, R = min(n, m + b);
        FOR3_R(j, L + 1, m) v[j - 1] = Monoid::op(v[j - 1], v[j]);
        FOR3(j, m, R - 1) v[j + 1] = Monoid::op(v[j], v[j + 1]);
      }
    }
  }

  X prod(int L, int R) {
    if (L == R) return Monoid::unit();
    --R;
    if (L == R) return dat[0][L];
    int k = 31 - __builtin_clz(L ^ R);
    return Monoid::op(dat[k][L], dat[k][R]);
  }

  template <class F>
  int max_right(const F& check, int L) {
    assert(0 <= L && L <= n && check(Monoid::unit()));
    if (L == n) return n;
    int ok = L, ng = n + 1;
    while (ok + 1 < ng) {
      int k = (ok + ng) / 2;
      if (check(prod(L, k))) {
        ok = k;
      } else {
        ng = k;
      }
    }
    return ok;
  }

  template <class F>
  int min_left(const F& check, int R) {
    assert(0 <= R && R <= n && check(Monoid::unit()));
    if (R == 0) return 0;
    int ok = R, ng = -1;
    while (ng + 1 < ok) {
      int k = (ok + ng) / 2;
      if (check(prod(k, R))) {
        ok = k;
      } else {
        ng = k;
      }
    }
    return ok;
  }

  void debug() {
    print("disjoint sparse table");
    FOR(i, log) print(dat[i]);
  }
};
#line 2 "/home/maspy/compro/library/alg/monoid/min.hpp"
template <class X>
struct Monoid_Min {
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return min(x, y); }
  static constexpr X unit() { return numeric_limits<X>::max(); }
  static constexpr bool commute = true;
};
#line 5 "main.cpp"

void solve() {
  LL(N);
  VEC(ll, X, N);
  VEC(ll, A, N);

  if (N == 1) { return print(A[0] == 1 ? 0 : -1); }

  ll LIM = MAX(A) + 5;

  /*
  ・s の左
  左方向 = 右方向
  ・[s,t] の間
  右方向 = 左方向 + 1
  ・t の右
  左方向 = 右方向

  // 3状態のどれか、左方向移動回数
  */

  const ll INF = 1LL << 60;

  auto TLE = [&]() -> void {
    vv(ll, dp, 3, LIM, INF);
    dp[0][0] = 0;
    FOR(i, N) {
      ll dx = (i + 1 == N ? 0 : X[i + 1] - X[i]);
      vv(ll, newdp, 3, LIM, INF);
      FOR(a, 3) FOR(b, 3) {
        if (a > b) continue;
        FOR(L1, LIM) FOR(L2, LIM) {
          ll R1 = L1 + (a == 1 ? 1 : 0);
          ll R2 = L2 + (b == 1 ? 1 : 0);
          if (i < N - 1 && L2 + R2 == 0) continue; // 非連結
          ll deg = L1 + R1 + L2 + R2;
          ll cnt = deg + (b - a);
          assert(cnt % 2 == 0);
          cnt /= 2;
          // 触らないで済ませられる最大回数
          ll can_omit = min(R1, R2) + min(L1, L2);
          if (cnt - can_omit <= A[i] && A[i] <= cnt) {
            chmin(newdp[b][L2], dp[a][L1] + dx * (L2 + R2));
          }
        }
      }
      swap(dp, newdp);
    }
    ll ANS = dp[2][0];
    if (ANS == INF) ANS = -1;
    print(ANS);
  };

  using Mono = Monoid_Min<ll>;

  vv(ll, dp, 3, LIM, INF);
  dp[0][0] = 0;
  FOR(i, N) {
    ll dx = (i + 1 == N ? 0 : X[i + 1] - X[i]);
    vv(ll, newdp, 3, LIM, INF);

    FOR(a, 3) FOR(b, 3) {
      if (a > b) continue;
      ll xa = (a == 1 ? 1 : 0);
      ll xb = (b == 1 ? 1 : 0);
      ll c = (xa + xb + b - a) / 2;
      assert(c == 0 || c == 1);
      /*
      FOR(L2, LIM) FOR(L1, LIM) {
        ll cnt = L1 + L2 + c;
        ll can_omit = min(L1 + xa, L2 + xb) + min(L1, L2);
        if (cnt - can_omit <= A[i] && A[i] <= cnt) {
          chmin(newdp[b][L2], dp[a][L1] + dx * (L2 + L2 + xb));
        }
      }
      */
      // L1 == L2
      FOR(L2, LIM) {
        ll cnt = L2 + L2 + c;
        ll can_omit = min(L2 + xa, L2 + xb) + min(L2, L2);
        if (cnt - can_omit <= A[i] && A[i] <= cnt) {
          chmin(newdp[b][L2], dp[a][L2] + dx * (L2 + L2 + xb));
        }
      }
      DisjointSparse<Mono> seg(dp[a]);
      // L1 < L2
      FOR(L2, LIM) {
        ll lo = max(L2 + c - xa - A[i], A[i] - L2 - c);
        if (lo < L2) {
          chmin(newdp[b][L2], seg.prod(lo, L2) + dx * (L2 + L2 + xb));
        }
      }
      // L1 > L2
      FOR(L2, LIM) {
        ll lo = max(L2 + 1, A[i] - L2 - c);
        ll hi = min(LIM - 1, A[i] - c + L2 + xb);
        if (lo <= hi) {
          chmin(newdp[b][L2], seg.prod(lo, hi + 1) + dx * (L2 + L2 + xb));
        }
      }
    }
    swap(dp, newdp);
    if (i < N - 1) dp[0][0] = dp[2][0] = INF;
  }
  ll ANS = dp[2][0];
  if (ANS == INF) ANS = -1;
  print(ANS);
}

signed main() {
  cout << fixed << setprecision(15);

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

  return 0;
}
0