#273081 (C++14) No.703 ゴミ拾い Easy

• 問題: No.703 ゴミ拾い Easy
• ユーザー: potoooooooo
• 提出日時: 2018-07-16 04:36:43
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 102 ms / 1,500 ms
• コード長: 2,869 bytes
• コンパイル時間: 1,860 ms
• コンパイル使用メモリ: 167,184 KB
• 実行使用メモリ: 12,800 KB
• 最終ジャッジ日時: 2025-01-02 13:57:42
• 合計ジャッジ時間: 6,266 ms
• ジャッジサーバーID （参考情報）: judge1 / judge2

ファイルパターン	結果
sample	AC * 4
other	AC * 46

ソースコード

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#include <bits/stdc++.h>
using namespace std;
template<class Numeric> struct ConvexHullTrick {
  struct Line { // f: y=ax+b
    Numeric a; Numeric b;
    Line(Numeric _a, Numeric _b) : a(_a), b(_b) {}
    bool operator< (Line &l) {
      if (a != l.a) return a < l.a;
      else return b < l.b;
    }
  };
  private:
    vector<Line> lines;
    bool isMinimumQuery;
    bool isMonotonicQuery;
    bool compare(Numeric a, Numeric b, bool equal = true) {
      if (equal) {
        if (isMinimumQuery) return b <= a;
        else return a <= b;
      } else {
        if (isMinimumQuery) return b < a;
        else return a < b;
      }
    }
  public:
    // constructor
    ConvexHullTrick(bool monotonic, bool minimum = true) :
      isMinimumQuery(minimum), isMonotonicQuery(monotonic) {}
    // check the necessity of line2
    bool check(Line l1, Line l2, Line l3) {
      if (l1 < l3) swap(l3, l1);
      return compare((l3.b-l2.b)*(l2.a-l1.a), (l2.b-l1.b)*(l3.a-l2.a));
    }
    // add the line: y=ax+b
    void add(Numeric a, Numeric b) {
      Line line(a, b);
      int size = (int) lines.size();
      if (size >= 1 && lines[size-1].a == line.a){
        if (!compare(lines[size-1].b, line.b)) return;
      }
      while (size >= 2 && check(lines[size-2], lines[size-1], line)){
        lines.pop_back(); --size;
      }
      lines.emplace_back(line);
    }
    // get the value of line(x)
    Numeric f(Line line, Numeric x) {
      return line.a * x + line.b;
    }
    // solve
    Numeric solve(Numeric x) {
      if (isMonotonicQuery) {
        static int head = 0;
        if ((int) lines.size() <= head) head = lines.size()-1;
        while (head > 0 && compare(f(lines[head], x), f(lines[head-1], x), false)) --head;
        while (lines.size() - head >= 2 && compare(f(lines[head], x), f(lines[head+1], x))) ++head;
        return f(lines[head], x);
      }
      else {
        int low = -1; int high = lines.size()-1;
        while (high - low > 1) {
          int mid = (high+low)/2;
          if (compare(f(lines[mid], x), f(lines[mid+1], x))) low = mid;
          else high = mid;
        }
        return f(lines[high], x);
      }
    }
};
int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n; cin >> n;
  vector<long long> a(n), x(n), y(n);
  for (int i = 0; i < n; i++) {
    cin >> a[n-i-1];
  }
  for (int i = 0; i < n; i++) {
    cin >> x[n-i-1];
  }
  for (int i = 0; i < n; i++) {
    cin >> y[n-i-1];
  }
  ConvexHullTrick<long long> convexhulltrick(true);
  vector<long long> dp(n+1, 0);
  for (int i = 0; i < n; i++) {
    convexhulltrick.add(2*a[i], dp[i]+a[i]*a[i]);
    dp[i+1] = convexhulltrick.solve(-x[i]) + x[i]*x[i] + y[i]*y[i];
  }
  long long ans = dp[n];
  for (int i = 0; i < n; i++) {
    ans = min(ans, dp[i] + (x[n-1]-a[i])*(x[n-1]-a[i]) + y[n-1] * y[n-1]);
  }
  cout << ans << endl;
  return 0;
}
 
 
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