Submission #7289875


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#define DEBUG 0
/**
 * File    : F.cpp
 * Author  : Kazune Takahashi
 * Created : 2019/9/1 21:42:35
 * Powered by Visual Studio Code
 */
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <vector>
#include <string>
#include <complex>
#include <tuple>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
#include <functional>
#include <random>
#include <chrono>
#include <cctype>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstdlib>
using namespace std;
#define maxs(x, y) (x = max(x, y))
#define mins(x, y) (x = min(x, y))
using ll = long long;
class mint
{
public:
  static ll MOD;
  ll x;
  mint() : x(0) {}
  mint(ll x) : x(x % MOD) {}
  mint operator-() const { return x ? MOD - x : 0; }
  mint &operator+=(const mint &a)
  {
    if ((x += a.x) >= MOD)
    {
      x -= MOD;
    }
    return *this;
  }
  mint &operator-=(const mint &a) { return *this += -a; }
  mint &operator*=(const mint &a)
  {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint &operator/=(const mint &a)
  {
    mint b{a};
    return *this *= b.power(MOD - 2);
  }
  mint operator+(const mint &a) const { return mint(*this) += a; }
  mint operator-(const mint &a) const { return mint(*this) -= a; }
  mint operator*(const mint &a) const { return mint(*this) *= a; }
  mint operator/(const mint &a) const { return mint(*this) /= a; }
  bool operator<(const mint &a) const { return x < a.x; }
  bool operator==(const mint &a) const { return x == a.x; }
  const mint power(ll N)
  {
    if (N == 0)
    {
      return 1;
    }
    else if (N % 2 == 1)
    {
      return *this * power(N - 1);
    }
    else
    {
      mint half = power(N / 2);
      return half * half;
    }
  }
};
ll mint::MOD = 1e9 + 7;
istream &operator>>(istream &stream, mint &a) { return stream >> a.x; }
ostream &operator<<(ostream &stream, const mint &a) { return stream << a.x; }
class combination
{
public:
  vector<mint> inv, fact, factinv;
  static int MAX_SIZE;
  combination() : inv(MAX_SIZE), fact(MAX_SIZE), factinv(MAX_SIZE)
  {
    inv[1] = 1;
    for (auto i = 2; i < MAX_SIZE; i++)
    {
      inv[i] = (-inv[mint::MOD % i]) * (mint::MOD / i);
    }
    fact[0] = factinv[0] = 1;
    for (auto i = 1; i < MAX_SIZE; i++)
    {
      fact[i] = mint(i) * fact[i - 1];
      factinv[i] = inv[i] * factinv[i - 1];
    }
  }
  mint operator()(int n, int k)
  {
    if (n >= 0 && k >= 0 && n - k >= 0)
    {
      return fact[n] * factinv[k] * factinv[n - k];
    }
    return 0;
  }
};
int combination::MAX_SIZE = 3000010;
ll gcd(ll x, ll y) { return y ? gcd(y, x % y) : x; }
// constexpr double epsilon = 1e-10;
// constexpr ll infty = 1000000000000000LL;
// constexpr int dx[4] = {1, 0, -1, 0};
// constexpr int dy[4] = {0, 1, 0, -1};
void Yes()
{
  cout << "Yes" << endl;
  exit(0);
}
void No()
{
  cout << "No" << endl;
  exit(0);
}

int N;
ll X[110];
ll Y[110];
ll ans{0};
random_device seed_gen;
mt19937 engine(seed_gen());

using point = complex<ll>;

void solve2()
{
  vector<bool> used(N, false);
  vector<point> V(N);
  for (auto i = 0; i < N; i++)
  {
    V[i] = point(X[i], Y[i]);
  }
  shuffle(V.begin(), V.end(), engine);
  point v{};
  for (auto i = 0; i < N; i++)
  {
    if (X[i] >= 0 && Y[i] >= 0)
    {
      v += V[i];
      used[i] = true;
    }
    if (X[i] < 0 && Y[i] < 0)
    {
      used[i] = true;
    }
  }
  int cnt{0};
  maxs(ans, norm(v));
  do
  {
    cnt = 0;
    for (auto i = 0; i < N; i++)
    {
      if (used[i])
      {
        continue;
      }
      if (norm(V[i] + v) >= norm(v))
      {
        v += V[i];
        used[i] = true;
        ++cnt;
      }
    }
    maxs(ans, norm(v));
  } while (cnt > 0);
}

void solve()
{
  vector<bool> used(N, false);
  vector<point> V(N);
  for (auto i = 0; i < N; i++)
  {
    V[i] = point(X[i], Y[i]);
  }
  shuffle(V.begin(), V.end(), engine);
  point v{};
  for (auto i = 0; i < N; i++)
  {
    if (X[i] >= 0 && Y[i] >= 0)
    {
      v += V[i];
      used[i] = true;
    }
    if (X[i] < 0 && Y[i] < 0)
    {
      used[i] = true;
    }
  }
  int cnt{0};
  maxs(ans, norm(v));
  do
  {
    cnt = 0;
    for (auto i = 0; i < N; i++)
    {
      if (used[i])
      {
        continue;
      }
      if (norm(V[i] + v) >= norm(v))
      {
        v += V[i];
        used[i] = true;
        ++cnt;
      }
    }
    maxs(ans, norm(v));
  } while (cnt > 0);
}

int main()
{
  cin >> N;
  for (auto i = 0; i < N; i++)
  {
    cin >> X[i] >> Y[i];
  }
  auto start{chrono::system_clock::now()};
  auto goal{chrono::system_clock::now()};
  double dif{0};
  solve2();
  for (auto i = 0; i < N; i++)
  {
    X[i] = -X[i];
  }
  solve2();
  for (auto i = 0; i < N; i++)
  {
    Y[i] = -Y[i];
  }
  solve2();
  for (auto i = 0; i < N; i++)
  {
    X[i] = -X[i];
  }
  solve2();
  for (auto i = 0; i < N; i++)
  {
    Y[i] = -Y[i];
  }
  while (true)
  {
    goal = chrono::system_clock::now();
    dif = chrono::duration_cast<chrono::milliseconds>(goal - start).count();
    if (dif >= 1990)
    {
      break;
    }
    solve();
    for (auto i = 0; i < N; i++)
    {
      X[i] = -X[i];
    }
    solve();
    for (auto i = 0; i < N; i++)
    {
      Y[i] = -Y[i];
    }
    solve();
    for (auto i = 0; i < N; i++)
    {
      X[i] = -X[i];
    }
    solve();
    for (auto i = 0; i < N; i++)
    {
      Y[i] = -Y[i];
    }
  }
  cout << fixed << setprecision(18) << sqrt(ans) << endl;
}

Submission Info

Submission Time
Task F - Engines
User kazunetakahashi
Language C++14 (GCC 5.4.1)
Score 0
Code Size 5729 Byte
Status
Exec Time 1992 ms
Memory 384 KB

Test Cases

Set Name Score / Max Score Test Cases
Sample 0 / 0 00-sample-01.txt, 00-sample-02.txt, 00-sample-03.txt, 00-sample-04.txt, 00-sample-05.txt, 00-sample-06.txt, 00-sample-07.txt
All 0 / 600 00-sample-01.txt, 00-sample-02.txt, 00-sample-03.txt, 00-sample-04.txt, 00-sample-05.txt, 00-sample-06.txt, 00-sample-07.txt, 01-random-very-small-01.txt, 01-random-very-small-02.txt, 01-random-very-small-03.txt, 02-random-small-01.txt, 02-random-small-02.txt, 02-random-small-03.txt, 03-random-01.txt, 03-random-02.txt, 03-random-03.txt, 04-zero-01.txt, 05-same-01.txt, 05-same-02.txt, 06-linear-01.txt, 06-linear-02.txt, 06-linear-03.txt, 07-linear-positive-01.txt, 07-linear-positive-02.txt, 07-linear-positive-03.txt, 08-90-degree-01.txt, 08-90-degree-02.txt, 09-180-degree-01.txt, 09-180-degree-02.txt, 10-sandglass-01.txt, 10-sandglass-02.txt, 11-circle-01.txt, 11-circle-02.txt, 11-circle-03.txt, 11-circle-04.txt, 11-circle-05.txt, 12-square-01.txt, 12-square-02.txt, 12-square-03.txt, 13-corner-01.txt, 13-corner-02.txt
Case Name Status Exec Time Memory
00-sample-01.txt 1991 ms 256 KB
00-sample-02.txt 1991 ms 256 KB
00-sample-03.txt 1991 ms 256 KB
00-sample-04.txt 1991 ms 256 KB
00-sample-05.txt 1991 ms 384 KB
00-sample-06.txt 1991 ms 256 KB
00-sample-07.txt 1991 ms 256 KB
01-random-very-small-01.txt 1991 ms 256 KB
01-random-very-small-02.txt 1991 ms 256 KB
01-random-very-small-03.txt 1991 ms 256 KB
02-random-small-01.txt 1991 ms 256 KB
02-random-small-02.txt 1991 ms 256 KB
02-random-small-03.txt 1991 ms 256 KB
03-random-01.txt 1991 ms 256 KB
03-random-02.txt 1991 ms 256 KB
03-random-03.txt 1991 ms 256 KB
04-zero-01.txt 1991 ms 256 KB
05-same-01.txt 1991 ms 256 KB
05-same-02.txt 1991 ms 256 KB
06-linear-01.txt 1991 ms 384 KB
06-linear-02.txt 1991 ms 256 KB
06-linear-03.txt 1991 ms 256 KB
07-linear-positive-01.txt 1991 ms 384 KB
07-linear-positive-02.txt 1991 ms 256 KB
07-linear-positive-03.txt 1991 ms 256 KB
08-90-degree-01.txt 1991 ms 256 KB
08-90-degree-02.txt 1992 ms 256 KB
09-180-degree-01.txt 1991 ms 256 KB
09-180-degree-02.txt 1991 ms 256 KB
10-sandglass-01.txt 1991 ms 256 KB
10-sandglass-02.txt 1991 ms 256 KB
11-circle-01.txt 1991 ms 256 KB
11-circle-02.txt 1991 ms 256 KB
11-circle-03.txt 1991 ms 256 KB
11-circle-04.txt 1991 ms 256 KB
11-circle-05.txt 1991 ms 256 KB
12-square-01.txt 1991 ms 256 KB
12-square-02.txt 1991 ms 256 KB
12-square-03.txt 1991 ms 256 KB
13-corner-01.txt 1991 ms 256 KB
13-corner-02.txt 1991 ms 256 KB