Luzhiled's Library

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:heavy_check_mark: test/verify/aoj-1254.test.cpp

Depends on

Code

// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1254
// clang-format on

#include <algorithm>
#include <cmath>
#include <iostream>
#include <map>
#include <string>
#include <vector>

#include "../../graph/others/chromatic-number.hpp"
#include "../../math/matrix/square-matrix.hpp"

using namespace std;

const double EPS = 1e-10;

struct Point {
  double x, y;

  Point() {}

  Point(double x, double y) : x(x), y(y) {}

  Point operator+(Point p) { return Point(x + p.x, y + p.y); }

  Point operator-(Point p) { return Point(x - p.x, y - p.y); }

  Point operator*(double k) { return Point(x * k, y * k); }

  Point operator/(double k) { return Point(x / k, y / k); }
};

typedef Point Vector;
typedef vector<Point> Polygon;

double norm(Vector a) { return a.x * a.x + a.y * a.y; }

double abs(Vector a) { return sqrt(norm(a)); }

double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

bool calc(Point a1, Point a2, Point b1, Point b2) {
  if (abs(cross(a2 - a1, b1 - a1)) > EPS) return 0;
  if (abs(cross(a2 - a1, b2 - a1)) > EPS) return 0;
  double ml = 0;
  ml = max(ml, abs(a1 - a2));
  ml = max(ml, abs(a1 - b1));
  ml = max(ml, abs(a1 - b2));
  ml = max(ml, abs(a2 - b1));
  ml = max(ml, abs(a2 - b2));
  ml = max(ml, abs(b1 - b2));
  return (ml + EPS < abs(a1 - a2) + abs(b1 - b2));
}

int main() {
  int n;
  while (cin >> n, n) {
    vector<Polygon> p(n);
    vector<string> name(n);
    map<string, int> m;
    for (int i = 0; i < n; i++) {
      cin >> name[i];
      if (!m.count(name[i])) {
        int k = m.size();
        m[name[i]] = k;
      }
      int x, y;
      while (cin >> x, ~x) {
        cin >> y;
        p[i].push_back(Point(x, y));
      }
    }

    SquareMatrix<bool, 10> G{};
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        if (name[i] == name[j]) continue;
        for (int k = 0; k < (int)p[i].size(); k++) {
          for (int l = 0; l < (int)p[j].size(); l++) {
            if (calc(p[i][k], p[i][(k + 1) % p[i].size()], p[j][l],
                     p[j][(l + 1) % p[j].size()])) {
              G[m[name[j]]][m[name[i]]] = true;
              G[m[name[i]]][m[name[j]]] = true;
            }
          }
        }
      }
    }
    cout << chromatic_number(G) << endl;
  }
}

#line 1 "test/verify/aoj-1254.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1254
// clang-format on

#include <algorithm>
#include <cmath>
#include <iostream>
#include <map>
#include <string>
#include <vector>

#line 2 "graph/others/chromatic-number.hpp"

#include <cstdint>
#include <utility>
#line 6 "graph/others/chromatic-number.hpp"

/**
 * @brief Chromatic Number(彩色数)
 *
 * @see https://www.slideshare.net/wata_orz/ss-12131479
 */
template <typename Matrix>
int chromatic_number(Matrix& g) {
  int N = (int)g.size();
  std::vector<int> es(N);
  for (int i = 0; i < (int)g.size(); i++) {
    for (int j = 0; j < (int)g.size(); j++) {
      if (g[i][j] != 0) es[i] |= 1 << j;
    }
  }
  std::vector<int> ind(1 << N);
  ind[0] = 1;
  for (int S = 1; S < (1 << N); S++) {
    int u = __builtin_ctz(S);
    ind[S] = ind[S ^ (1 << u)] + ind[(S ^ (1 << u)) & ~es[u]];
  }
  std::vector<int> cnt((1 << N) + 1);
  for (int i = 0; i < (1 << N); i++) {
    cnt[ind[i]] += __builtin_parity(i) ? -1 : 1;
  }
  std::vector<std::pair<unsigned, int> > hist;
  for (int i = 1; i <= (1 << N); i++) {
    if (cnt[i]) hist.emplace_back(i, cnt[i]);
  }
  constexpr int mods[] = {1000000007, 1000000011, 1000000021};
  int ret = N;
  for (int k = 0; k < 3; k++) {
    auto buf = hist;
    for (int c = 1; c < ret; c++) {
      std::int64_t sum = 0;
      for (auto& [i, x] : buf) {
        sum += (x = std::int64_t(x) * i % mods[k]);
      }
      if (sum % mods[k]) ret = c;
    }
  }
  return ret;
}
#line 2 "math/matrix/square-matrix.hpp"

#include <array>
#include <cstddef>
#line 7 "math/matrix/square-matrix.hpp"

/**
 * @brief Square-Matrix(正方行列)
 */
template <class T, std::size_t N>
struct SquareMatrix {
  std::array<std::array<T, N>, N> A;

  SquareMatrix() : A{{}} {}

  SquareMatrix(const std::array<std::array<T, N>, N>& A) : A(A) {}

  std::size_t size() const { return N; }

  inline const std::array<T, N>& operator[](int k) const { return (A.at(k)); }

  inline std::array<T, N>& operator[](int k) { return (A.at(k)); }

  static SquareMatrix add_identity() { return SquareMatrix(); }

  static SquareMatrix mul_identity() {
    SquareMatrix mat;
    for (std::size_t i = 0; i < N; i++) mat[i][i] = 1;
    return mat;
  }

  SquareMatrix& operator+=(const SquareMatrix& B) {
    for (std::size_t i = 0; i < N; i++) {
      for (std::size_t j = 0; j < N; j++) {
        (*this)[i][j] += B[i][j];
      }
    }
    return *this;
  }

  SquareMatrix& operator-=(const SquareMatrix& B) {
    for (std::size_t i = 0; i < N; i++) {
      for (std::size_t j = 0; j < N; j++) {
        (*this)[i][j] -= B[i][j];
      }
    }
    return *this;
  }

  SquareMatrix& operator*=(const SquareMatrix& B) {
    std::array<std::array<T, N>, N> C;
    for (std::size_t i = 0; i < N; i++) {
      for (std::size_t j = 0; j < N; j++) {
        for (std::size_t k = 0; k < N; k++) {
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
        }
      }
    }
    A.swap(C);
    return (*this);
  }

  SquareMatrix& operator^=(std::uint64_t k) {
    SquareMatrix B = SquareMatrix::mul_identity();
    while (k > 0) {
      if (k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return *this;
  }

  SquareMatrix operator+(const SquareMatrix& B) const {
    return SquareMatrix(*this) += B;
  }

  SquareMatrix operator-(const SquareMatrix& B) const {
    return SquareMatrix(*this) -= B;
  }

  SquareMatrix operator*(const SquareMatrix& B) const {
    return SquareMatrix(*this) *= B;
  }

  SquareMatrix operator^(std::uint64_t k) const {
    return SquareMatrix(*this) ^= k;
  }

  friend std::ostream& operator<<(std::ostream& os, SquareMatrix& p) {
    for (int i = 0; i < N; i++) {
      os << "[";
      for (int j = 0; j < N; j++) {
        os << p[i][j] << (j + 1 == N ? "]\n" : ",");
      }
    }
    return os;
  }
};
#line 14 "test/verify/aoj-1254.test.cpp"

using namespace std;

const double EPS = 1e-10;

struct Point {
  double x, y;

  Point() {}

  Point(double x, double y) : x(x), y(y) {}

  Point operator+(Point p) { return Point(x + p.x, y + p.y); }

  Point operator-(Point p) { return Point(x - p.x, y - p.y); }

  Point operator*(double k) { return Point(x * k, y * k); }

  Point operator/(double k) { return Point(x / k, y / k); }
};

typedef Point Vector;
typedef vector<Point> Polygon;

double norm(Vector a) { return a.x * a.x + a.y * a.y; }

double abs(Vector a) { return sqrt(norm(a)); }

double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

bool calc(Point a1, Point a2, Point b1, Point b2) {
  if (abs(cross(a2 - a1, b1 - a1)) > EPS) return 0;
  if (abs(cross(a2 - a1, b2 - a1)) > EPS) return 0;
  double ml = 0;
  ml = max(ml, abs(a1 - a2));
  ml = max(ml, abs(a1 - b1));
  ml = max(ml, abs(a1 - b2));
  ml = max(ml, abs(a2 - b1));
  ml = max(ml, abs(a2 - b2));
  ml = max(ml, abs(b1 - b2));
  return (ml + EPS < abs(a1 - a2) + abs(b1 - b2));
}

int main() {
  int n;
  while (cin >> n, n) {
    vector<Polygon> p(n);
    vector<string> name(n);
    map<string, int> m;
    for (int i = 0; i < n; i++) {
      cin >> name[i];
      if (!m.count(name[i])) {
        int k = m.size();
        m[name[i]] = k;
      }
      int x, y;
      while (cin >> x, ~x) {
        cin >> y;
        p[i].push_back(Point(x, y));
      }
    }

    SquareMatrix<bool, 10> G{};
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        if (name[i] == name[j]) continue;
        for (int k = 0; k < (int)p[i].size(); k++) {
          for (int l = 0; l < (int)p[j].size(); l++) {
            if (calc(p[i][k], p[i][(k + 1) % p[i].size()], p[j][l],
                     p[j][(l + 1) % p[j].size()])) {
              G[m[name[j]]][m[name[i]]] = true;
              G[m[name[i]]][m[name[j]]] = true;
            }
          }
        }
      }
    }
    cout << chromatic_number(G) << endl;
  }
}

Test cases

Env Name Status Elapsed Memory
g++ judge_data :heavy_check_mark: AC 8 ms 4 MB
clang++ judge_data :heavy_check_mark: AC 8 ms 4 MB
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