結果

問題 No.2078 魔抜けなパープル
コンテスト
ユーザー miscalc
提出日時 2022-09-25 21:09:54
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 49 ms / 2,000 ms
コード長 4,800 bytes
コンパイル時間 4,250 ms
コンパイル使用メモリ 256,280 KB
最終ジャッジ日時 2025-02-07 15:09:20
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
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ファイルパターン 結果
sample AC * 1
other AC * 7
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 # 

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using pll = pair<ll, ll>;
using tlll = tuple<ll, ll, ll>;
constexpr ll INF = 1LL << 60;
template<class T> bool chmin(T& a, T b) {if (a > b) {a = b; return true;} return false;}
template<class T> bool chmax(T& a, T b) {if (a < b) {a = b; return true;} return false;}
ll safemod(ll A, ll M) {ll res = A % M; if (res < 0) res += M; return res;}
ll divfloor(ll A, ll B) {if (B < 0) {return divfloor(-A, -B);} return (A - safemod(A, B)) / B;}
ll divceil(ll A, ll B) {if (B < 0) {return divceil(-A, -B);} return divfloor(A + B - 1, B);}
ll pow_ll(ll A, ll B) {if (A == 0 || A == 1) {return A;} if (A == -1) {return B & 1 ? -1 : 1;} ll res = 1; for (int i = 0; i < B; i++) {res *= A;} return res;}
ll logfloor(ll A, ll B) {assert(A >= 2); ll res = 0; for (ll tmp = 1; tmp <= B / A; tmp *= A) {res++;} return res;}
ll logceil(ll A, ll B) {assert(A >= 2); ll res = 0; for (ll tmp = 1; tmp < B; tmp *= A) {res++;} return res;}
ll arisum_ll(ll a, ll d, ll n) { return n * a + (n & 1 ? ((n - 1) >> 1) * n : (n >> 1) * (n - 1)) * d; }
ll arisum2_ll(ll a, ll l, ll n) { return n & 1 ? ((a + l) >> 1) * n : (n >> 1) * (a + l); }
ll arisum3_ll(ll a, ll l, ll d) { assert((l - a) % d == 0); return arisum2_ll(a, l, (l - a) / d + 1); }
template<class T> void unique(vector<T> &V) {V.erase(unique(V.begin(), V.end()), V.end());}
template<class T> void sortunique(vector<T> &V) {sort(V.begin(), V.end()); V.erase(unique(V.begin(), V.end()), V.end());}
#define FINALANS(A) do {cout << (A) << '\n'; exit(0);} while (false)
template<class T> void printvec(const vector<T> &V) {int _n = V.size(); for (int i = 0; i < _n; i++) cout << V[i] << (i == _n - 1 ? "" : " ");cout << '\n';}
template<class T> void printvect(const vector<T> &V) {for (auto v : V) cout << v << '\n';}
template<class T> void printvec2(const vector<vector<T>> &V) {for (auto &v : V) printvec(v);}
//*
#include <atcoder/all>
using namespace atcoder;
//using mint = modint998244353;
using mint = modint1000000007;
//using mint = modint;
//*/

template<class T>
struct ConvexHullTrickDeque
{
private:
  deque<pair<T, T>> deq;
  bool need_sub(T a, T b, T a1, T b1, T a2, T b2)
  {
    if (a1 > a2)
      swap(a1, a2), swap(b1, b2);
    return __int128_t(a - a1) * (b2 - b1) > __int128_t(b - b1) * (a2 - a1);
  }

public:
  void add_line(T a, T b) // 追加する直線の傾きが広義単調減少または広義単調増加
  {
    if (deq.empty())
      deq.emplace_back(make_pair(a, b));
    else if (a <= deq.front().first)
    {
      if (a == deq.front().first && b >= deq.front().second)
        return;
      while ((int)deq.size() >= 2)
      {
        auto [a2, b2] = deq.front();
        auto [a3, b3] = deq[1];
        if (!need_sub(a2, b2, a, b, a3, b3))
          deq.pop_front();
        else
          break;
      }
      deq.emplace_front(make_pair(a, b));
    }
    else if (deq.back().first <= a)
    {
      if (a == deq.back().first && b >= deq.back().second)
        return;
      while ((int)deq.size() >= 2)
      {
        auto [a2, b2] = deq[(int)deq.size() - 2];
        auto [a3, b3] = deq.back();
        if (!need_sub(a3, b3, a2, b2, a, b))
          deq.pop_back();
        else
          break;
      }
      deq.emplace_back(make_pair(a, b));
    }
    else
      assert(false);
  }

  T get_min(T p)
  {
    int l = 0, r = (int)deq.size() - 1;
    while (r - l > 1)
    {
      int c = (l + r) / 2;
      auto [a1, b1] = deq[c - 1];
      auto [a2, b2] = deq[c];
      if (a1 * p + b1 > a2 * p + b2)
        l = c;
      else
        r = c;
    }
    auto [al, bl] = deq[l];
    auto [ar, br] = deq[r];
    return min(al * p + bl, ar * p + br);
  }

  T get_min_light_inc(T p) // クエリで問われる x 座標が広義単調増加
  {
    while ((int)deq.size() >= 2)
    {
      auto [a1, b1] = deq[(int)deq.size() - 2];
      auto [a2, b2] = deq.back();
      if (a1 * p + b1 < a2 * p + b2)
        deq.pop_back();
      else
        break;
    }
    auto [a, b] = deq.back();
    return a * p + b;
  }

  T get_min_light_dec(T p) // クエリで問われる x 座標が広義単調減少
  {
    while ((int)deq.size() >= 2)
    {
      auto [a1, b1] = deq.front();
      auto [a2, b2] = deq[1];
      if (a1 * p + b1 > a2 * p + b2)
        deq.pop_front();
      else
        break;
    }
    auto [a, b] = deq.front();
    return a * p + b;
  }
};

int main()
{
  int T;
  cin >> T;
  vector<ll> dp(100010);
  while (T--)
  {
    int X, A;
    cin >> X >> A;

    ConvexHullTrickDeque<ll> cht;

    dp[0] = 0;
    for (ll i = 1; i <= A; i++)
    {
      cht.add_line(-2 * (i - 1), (i - 1) * (i - 1) + dp[i - 1]);
      dp[i] = i * i + X + cht.get_min_light_inc(i);
    }
    ll ans = dp[A];
    cout << ans << '\n';
  }
}
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