verify/convolution/LC_min_plus_convolution_convex_arbitrary.test.cpp

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• Last update: 2025-10-21 21:13:36+09:00
• Problem: https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary

Depends on

• monotone minima (algorithm/monotone-minima.hpp)
• min-plus 畳み込み (convex) (convolution/min-plus-convex.hpp)
• template/debug.hpp
• template/inout.hpp
• template/macro.hpp
• template/template.hpp
• template/util.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary"

#include "template/template.hpp"
#include "convolution/min-plus-convex.hpp"

int main() {
  int n, m;
  in(n, m);
  vector<int> a(n), b(m);
  in(a, b);
  auto c = MinPlusConvolutionConvexArbitrary(a, b);
  out(c);
}

#line 1 "verify/convolution/LC_min_plus_convolution_convex_arbitrary.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary"

#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"

#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <class T, class S = T>
S SUM(const vector<T> &a) {
  return accumulate(ALL(a), S(0));
}
template <class T>
inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

template <class T>
int popcnt(T x) {
  return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
  return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
  return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"

#line 2 "template/inout.hpp"
struct Fast {
  Fast() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} fast;

template <class T1, class T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  return os << p.first << " " << p.second;
}
template <class T>
istream &operator>>(istream &is, vector<T> &a) {
  for (auto &v : a) is >> v;
  return is;
}
template <class T>
ostream &operator<<(ostream &os, const vector<T> &a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T>
ostream &operator<<(ostream &os, const set<T> &st) {
  os << "{";
  for (auto it = st.begin(); it != st.end();) {
    os << *it;
    if (++it != st.end()) os << ",";
  }
  os << "}";
  return os;
}
template <class T1, class T2>
ostream &operator<<(ostream &os, const map<T1, T2> &mp) {
  os << "{";
  for (auto it = mp.begin(); it != mp.end();) {
    os << it->first << ":" << it->second;
    if (++it != mp.end()) os << ",";
  }
  os << "}";
  return os;
}

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...);
}
#line 10 "template/template.hpp"

#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int i, T name) {
  cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
  for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
  cerr << ":" << b << " ";
  _show(i + 1, a, c...);
}
#line 2 "convolution/min-plus-convex.hpp"

#line 2 "algorithm/monotone-minima.hpp"

vector<int> MonotoneMinima(int n, int m, const function<bool(int, int, int)> &f) {
  vector<int> res(n);
  auto dfs = [&](auto rc, int il, int ir, int l, int r) -> void {
    if (il == ir) return;
    int i = (il + ir) / 2;
    int m = l;
    for (int k = l + 1; k < r; k++)
      if (!f(i, m, k)) m = k;
    res[i] = m;
    rc(rc, il, i, l, m + 1);
    rc(rc, i + 1, ir, m, r);
  };
  dfs(dfs, 0, n, 0, m);
  return res;
}

// 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
template <class T>
vector<int> MonotoneMinima(int N, int M, const function<T(int, int)> &A) {
  const auto f = [&](int i, int j, int k) -> bool {
    return A(i, j) <= A(i, k);
  };
  return MonotoneMinima(N, M, f);
}

/**
 * @brief monotone minima
 * @docs docs/algorithm/monotone-minima.md
 */
#line 4 "convolution/min-plus-convex.hpp"

// a : 下に凸, b : 自由
template <class T>
vector<T> MinPlusConvolutionConvexArbitrary(const vector<T> &a, const vector<T> &b) {
  if (a.empty() || b.empty()) return {};
  int n = a.size(), m = b.size();
  auto argmin = MonotoneMinima(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> c(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    int j = argmin[i];
    c[i] = a[i - j] + b[j];
  }
  return c;
}

// a,b : 下に凸
template <class T>
vector<T> MinPlusConvolutionConvexConvex(const vector<T> &a, const vector<T> &b) {
  if (a.empty() || b.empty()) return {};
  int n = a.size(), m = b.size();
  vector<T> c(n + m - 1);
  c[0] = a[0] + b[0];
  for (int k = 0, i = 0; k < n + m - 2; k++) {
    int j = k - i;
    if (j == m - 1 || (i < n - 1 && a[i + 1] + b[j] < a[i] + b[j + 1])) {
      c[k + 1] = a[++i] + b[j];
    } else {
      c[k + 1] = a[i] + b[++j];
    }
  }
  return c;
}

/**
 * @brief min-plus 畳み込み (convex)
 * @docs docs/convolution/min-plus-convex.md
 */
#line 5 "verify/convolution/LC_min_plus_convolution_convex_arbitrary.test.cpp"

int main() {
  int n, m;
  in(n, m);
  vector<int> a(n), b(m);
  in(a, b);
  auto c = MinPlusConvolutionConvexArbitrary(a, b);
  out(c);
}

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