結果

問題 No.913 木の燃やし方
ユーザー 👑 emthrm
提出日時 2019-11-26 18:28:01
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 263 ms / 3,000 ms
コード長 4,862 bytes
コンパイル時間 2,871 ms
コンパイル使用メモリ 128,584 KB
最終ジャッジ日時 2025-01-08 05:39:44
ジャッジサーバーID
（参考情報） 		judge1 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 34
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 #
プレゼンテーションモードにする

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cctype>
#include <chrono>
#define _USE_MATH_DEFINES
#include <cmath>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iostream>
#include <iomanip>
#include <iterator>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
const int INF = 0x3f3f3f3f;
const long long LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 1000000007;
// const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
// const int dy[] = {1, 1, 0, -1, -1, -1, 0, 1},
//           dx[] = {0, -1, -1, -1, 0, 1, 1, 1};
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(10);
  }
} iosetup;
/*-------------------------------------------------*/
template <typename T>
struct CHT {
  using Line = pair<T, T>;
  CHT(bool is_minimized = true) : is_minimized(is_minimized) {}
  void add(T a, T b) {
    Line now(a, b);
    if (deq.empty()) {
      deq.emplace_back(now);
    } else if (deq.back().first <= a) {
      if (deq.back().first == a) {
        if (is_minimized) {
          if (b >= deq.back().second) return;
          deq.pop_back();
        } else {
          if (b <= deq.back().second) return;
          deq.pop_back();
        }
      }
      while (deq.size() >= 2 && !is_necessary(deq[deq.size() - 2], deq.back(), now)) deq.pop_back();
      deq.emplace_back(now);
    } else {
      if (deq.front().first == a) {
        if (is_minimized) {
          if (b >= deq.front().second) return;
          deq.pop_front();
        } else {
          if (b <= deq.front().second) return;
          deq.pop_front();
        }
      }
      while (deq.size() >= 2 && !is_necessary(now, deq[0], deq[1])) deq.pop_front();
      deq.emplace_front(now);
    }
  }
  T query(T x) {
    int lb = -1, ub = deq.size() - 1;
    while (ub - lb > 1) {
      int mid = (lb + ub) >> 1;
      if (is_minimized) {
        (f(deq[mid], x) < f(deq[mid + 1], x) ? ub : lb) = mid;
      } else {
        (f(deq[mid], x) > f(deq[mid + 1], x) ? ub : lb) = mid;
      }
    }
    return f(deq[ub], x);
  }
  T monotone_inc_query(T x) {
    if (is_minimized) {
      while (deq.size() >= 2 && f(deq[deq.size() - 2], x) <= f(deq.back(), x)) deq.pop_back();
      return f(deq.back(), x);
    } else {
      while (deq.size() >= 2 && f(deq[0], x) <= f(deq[1], x)) deq.pop_front();
      return f(deq.front(), x);
    }
  }
  T monotone_dec_query(T x) {
    if (is_minimized) {
      while (deq.size() >= 2 && f(deq[0], x) >= f(deq[1], x)) deq.pop_front();
      return f(deq.front(), x);
    } else {
      while (deq.size() >= 2 && f(deq[deq.size() - 2], x) >= f(deq.back(), x)) deq.pop_back();
      return f(deq.back(), x);
    }
  }
private:
  bool is_minimized;
  deque<Line> deq;
  using Real = long double;
  bool is_necessary(const Line &l1, const Line &l2, const Line &l3) {
    Real lhs = static_cast<Real>(l3.second - l2.second) / (l2.first - l3.first);
    Real rhs = static_cast<Real>(l2.second - l1.second) / (l1.first - l2.first);
    // T lhs = (l1.first - l2.first) * (l3.second - l2.second);
    // T rhs = (l2.first - l3.first) * (l2.second - l1.second);
    return is_minimized ? lhs < rhs : lhs > rhs;
  }
  T f(const Line &l, T x) { return l.first * x + l.second; }
};
int main() {
  int n; cin >> n;
  vector<long long> a(n); REP(i, n) cin >> a[i];
  FOR(i, 1, n) a[i] += a[i - 1];
  vector<long long> ans(n, LINF);
  function<void(int, int)> rec = [&](int l, int r) {
    if (r <= l) return;
    if (l + 1 == r) {
      ans[l] = min(ans[l], a[l] - (l > 0 ? a[l - 1] : 0) + 1);
      return;
    }
    int mid = (l + r) / 2;
    rec(l, mid);
    rec(mid, r);
    CHT<long long> cht1;
    FOR(i, mid, r) cht1.add(-2 * i, 1LL * i * i + 2 * i + a[i]);
    vector<long long> memo1(mid - l);
    FOR(i, l, mid) memo1[i - l] = cht1.monotone_inc_query(i) + 1LL * i * i - 2 * i - (i > 0 ? a[i - 1] : 0) + 1;
    FOR(i, 1, mid - l) memo1[i] = min(memo1[i], memo1[i - 1]);
    FOR(i, l, mid) ans[i] = min(ans[i], memo1[i - l]);
    CHT<long long> cht2;
    FOR(i, l, mid + 1) cht2.add(-2 * i, 1LL * i * i - 2 * i - (i > 0 ? a[i - 1] : 0));
    vector<long long> memo2(r - mid);
    FOR(i, mid, r) memo2[i - mid] = cht2.monotone_inc_query(i) + 1LL * i * i + 2 * i + a[i] + 1;
    for (int i = r - mid - 2; i >= 0; --i) memo2[i] = min(memo2[i], memo2[i + 1]);
    FOR(i, mid, r) ans[i] = min(ans[i], memo2[i - mid]);
  };
  rec(0, n);
  REP(i, n) cout << ans[i] << '\n';
  return 0;
}
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