結果

問題 No.2988 Min-Plus Convolution Query
コンテスト
ユーザー NyaanNyaan
提出日時 2024-12-13 01:41:48
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 18,384 bytes
コンパイル時間 17,486 ms
コンパイル使用メモリ 341,648 KB
最終ジャッジ日時 2025-02-26 12:51:55
ジャッジサーバーID
（参考情報） 		judge3 / judge3
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 2
other AC * 14 TLE * 7 -- * 19
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 # 

/**
 * date   : 2024-12-13 01:41:42
 * author : Nyaan
 */

#define NDEBUG

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")


using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tr2/dynamic_bitset>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility

namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  constexpr P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(T &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
  T res = I;
  for (; n; f(a = a * a), n >>= 1) {
    if (n & 1) f(res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
  return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
T Rev(const T &v) {
  T res = v;
  reverse(begin(res), end(res));
  return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
  using U = typename T::value_type;
  if(v.empty()) return {};
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      res[j][i] = v[i][j];
    }
  }
  return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
  using U = typename T::value_type;
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      if (clockwise) {
        res[W - 1 - j][i] = v[i][j];
      } else {
        res[j][H - 1 - i] = v[i][j];
      }
    }
  }
  return res;
}

}  // namespace Nyaan


// bit operation

namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan


// inout

namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan


// debug


#ifdef NyaanDebug
#define trc(...) (void(0))
#endif
#ifndef NyaanDebug
#define trc(...) (void(0))
#endif

#ifndef NyaanLocal
#define trc2(...) (void(0))
#endif


// macro

#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)


namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }


//

namespace nachia {

template <class Elem>
struct SmawkAlgorithm {
  template <class Gen, class Cmp = std::less<Elem>>
  std::vector<std::pair<Elem, int>> Solve(int height, int width, Gen gen,
                                          Cmp cmp = Cmp()) {
    if (height == 0) return std::vector<std::pair<Elem, int>>(0);
    auto reduce = [&](int yst,
                      const std::vector<int>& cols) -> std::vector<int> {
      int w = int(cols.size());
      std::vector<int> idx;
      int r = -1;
      for (int q = 0; q < w; q++) {
        if (idx.empty()) {
          idx.push_back(q);
          r += yst;
          continue;
        }
        int a = cols[idx.back()];
        int b = cols[q];
        if (cmp(gen(r, a), gen(r, b))) {
          if (r + yst < height) {
            idx.push_back(q);
            r += yst;
          }
        } else {
          idx.pop_back();
          q--;
          r -= yst;
        }
      }
      return idx;
    };
    auto ysts = std::vector<int>(1, 1);
    auto cols = std::vector<std::vector<int>>(1);
    for (int i = 0; i < width; i++) cols[0].push_back(i);
    cols[0] = reduce(1, cols[0]);
    while (true) {
      int nxst = ysts.back() * 2;
      if (height < nxst) break;
      auto nxc = reduce(nxst, cols.back());
      int w = nxc.size();
      for (int i = 0; i < w; i++) nxc[i] = cols.back()[nxc[i]];
      cols.push_back(move(nxc));
      ysts.push_back(nxst);
    }
    std::vector<std::pair<Elem, int>> ans(height, std::make_pair(gen(0, 0), 0));
    while (cols.size()) {
      auto x = std::move(cols.back());
      cols.pop_back();
      int st = ysts.back();
      ysts.pop_back();
      int p = 0;
      for (int y = st - 1; y < height; y += st * 2) {
        int r = y + st < height ? ans[y + st].second : width - 1;
        ans[y] = std::make_pair(gen(y, x[p]), x[p]);
        while (p + 1 < int(x.size()) && x[p + 1] <= r) {
          int xp = x[++p];
          auto fxp = gen(y, xp);
          if (!cmp(ans[y].first, fxp)) ans[y] = std::make_pair(fxp, xp);
        }
      }
    }
    return ans;
  }
};
}  // namespace nachia

namespace nachia {

template <class Elem>
std::vector<std::pair<Elem, int>> ConvexMinPlusConvolution(
    const std::vector<Elem>& a, const std::vector<Elem>& b, Elem Inf) {
  int n = a.size();
  int m = b.size();
  return nachia::SmawkAlgorithm<Elem>().Solve(
      n + m - 1, m, [&](int y, int x) -> Elem {
        return (y < x || n <= y - x) ? Inf : a[y - x] + b[x];
      });
}

}  // namespace nachia

//



using namespace std;




using namespace std;

// NxN 行列がある
// m_i := argmin_j (A_{i,j}) が単調増加であるときに m_i を列挙する
// f(i, j, k) :
// A[i][j] と A[i][k] を比較 (j < k が保証されている)
// A[i][j] <= A[i][k] のとき true を返す関数を入れる (等号はどちらでもよい)
vector<int> monotone_minima(int N, int M,
                            const function<bool(int, int, int)>& f) {
  vector<int> res(N);
  auto dfs = [&](auto rc, int is, int ie, int l, int r) -> void {
    if (is == ie) return;
    int i = (is + ie) / 2;
    int m = l;
    for (int k = l + 1; k < r; k++) {
      if (!f(i, m, k)) m = k;
    }
    res[i] = m;
    rc(rc, is, i, l, m + 1);
    rc(rc, i + 1, ie, m, r);
  };
  dfs(dfs, 0, N, 0, M);
  return res;
}

// NxM 行列がある
// m_i := argmin_j (A_{i,j}) が単調増加であるときに m_i を列挙する
// A(i, j) : A[i][j] を返す関数
template <typename T>
vector<int> monotone_minima(int N, int M, const function<T(int, int)>& A) {
  function<bool(int, int, int)> f = [&](int i, int j, int k) -> bool {
    return A(i, j) <= A(i, k);
  };
  return monotone_minima(N, M, f);
}

/**
 * @brief monotone minima
 */


// a は下に凸, b は自由
template <typename T>
vector<T> concave_min_plus_convolution(const vector<T>& a, const vector<T>& b) {
  if (a.empty() or b.empty()) return {};
  int n = a.size(), m = b.size();
  auto argmin = monotone_minima(n + m - 1, m, [&](int i, int j, int k) {
    if (i < k) return true;
    if (i - j >= n) return false;
    return a[i - j] + b[j] <= a[i - k] + b[k];
  });
  vector<T> ans(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    int j = argmin[i];
    ans[i] = a[i - j] + b[j];
  }
  return ans;
}

// a は上に凸, b は自由
template <typename T>
vector<T> concave_max_plus_convolution(const vector<T>& a, const vector<T>& b) {
  if (a.empty() or b.empty()) return {};
  int n = a.size(), m = b.size();
  auto argmin = monotone_minima(n + m - 1, m, [&](int i, int j, int k) {
    if (i < k) return true;
    if (i - j >= n) return false;
    return a[i - j] + b[j] >= a[i - k] + b[k];
  });
  vector<T> ans(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    int j = argmin[i];
    ans[i] = a[i - j] + b[j];
  }
  return ans;
}





using namespace std;

struct Timer {
  chrono::high_resolution_clock::time_point st;

  Timer() { reset(); }
  void reset() { st = chrono::high_resolution_clock::now(); }

  long long elapsed() {
    auto ed = chrono::high_resolution_clock::now();
    return chrono::duration_cast<chrono::milliseconds>(ed - st).count();
  }
  long long operator()() { return elapsed(); }
};


using namespace Nyaan;

using u32 = unsigned int;
int N, Q;
vl A, B;

ll B2[TEN(6)];

void q() {
  Timer timer;
  in(N, Q);
  A.resize(N), B.resize(N);
  in(A, B);

  rep(i, TEN(6)) B2[i] = infLL;
  ll* b = B2 + 5 * TEN(5);
  rep(i, N) b[i] = B[i];

  vl P(Q), X(Q), K(Q);
  in3(P, X, K);
  each(p, P)-- p;
  each(k, K) k -= 2;

  int S = 1800;
  for (int is = 0; is < Q; is += S) {
    int ie = min(Q, is + S);
    vl A2 = A;
    vector<int> pos;
    reg(i, is, ie) {
      pos.push_back(P[i]);
      A2[P[i]] = TEN(10);
    }
    auto C = nachia::ConvexMinPlusConvolution<ll>(B, A2, TEN(11));
    pos = mkuni(pos);

    /*
    reg(i, is, ie) {
      ll ans = C[K[i]].fi;
      A[P[i]] = X[i];
      each(p, pos) {
        int q = K[i] - p;
        if ((0 <= q and q < N)) amin(ans, A[p] + B[q]);
      }
      out(ans);
    }
    */
    reg(i, is, ie) {
      ll ans[8];
      rep(ii, 8) ans[ii] = infLL;
      ans[0] = C[K[i]].fi;
      A[P[i]] = X[i];
      int j = 0;
      for (; j + 4 <= sz(pos); j += 4) {
        ans[0] = min(ans[0], A[pos[j + 0]] + b[K[i] - pos[j + 0]]);
        ans[1] = min(ans[1], A[pos[j + 1]] + b[K[i] - pos[j + 1]]);
        ans[2] = min(ans[2], A[pos[j + 2]] + b[K[i] - pos[j + 2]]);
        ans[3] = min(ans[3], A[pos[j + 3]] + b[K[i] - pos[j + 3]]);
      }
      for (; j < sz(pos); j++) {
        int p = pos[j];
        ans[0] = min(ans[0], A[p] + b[K[i] - p]);
      }
      out(*min_element(ans, ans + 8));
    }
  }

  trc2(timer());

  /*
  struct Line {
    int x, i;
    Line() : i(-1), x(0) {}
    Line(int _i, int _x) : i(_i), x(_x) {}
    ll operetor(ll k) {
      if (i == -1) return infLL;
      int j = k - i;
      if (!(0 <= j and j < N)) return infLL;
      return x + B[j];
    }
  };
  */
  /*
  int len = 1;
  while (len < Q) len *= 2;
  DivideInterval di{len};
  // (p,x)
  VV<pi> qs(2 * len);
  {
    vi lastA = A;
    vi lastT(N);
    rep(t, Q) {
      int p = P[t], x = X[t];
      di.apply(lastT[p], t, [&](int i) { qs[i].emplace_back(p, lastA[p]); });
      lastA[p] = x;
      lastT[p] = t;
    }
    rep(p, N) {
      di.apply(lastT[p], Q, [&](int i) { qs[i].emplace_back(p, lastA[p]); });
    }
  }

  vl xs;
  rep(i, 2 * N - 1) xs.push_back(i);
  LiChaoTree<Line, true, false> lct(xs, Line{});
  */
}

void Nyaan::solve() {
  int t = 1;
  // in(t);
  while (t--) q();
}
0