/*
    Copyright 2007-2012 Janez Konc 

    If you use this program, please cite: 
    Janez Konc and Dusanka Janezic. An improved branch and bound algorithm for the 
    maximum clique problem. MATCH Commun. Math. Comput. Chem., 2007, 58, 569-590.

    More information at: http://www.sicmm.org/~konc

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/

#ifndef MCQD
#define MCQD

#include <iostream>
#include <algorithm>
#include <assert.h>
#ifdef DBG
using namespace std;
#endif

class Maxclique {
  const bool* const* e;
  int pk, level;
  const float Tlimit;
  class Vertices {
    class Vertex {
      int i, d;
    public:
      void set_i(const int ii)  { i = ii; }
      int get_i() const { return i; }
      void set_degree(int dd) { d = dd; }
      int get_degree() const { return d; }
    };
    Vertex *v;
    int sz;
    static bool desc_degree(const Vertex vi, const Vertex vj) { return (vi.get_degree() > vj.get_degree()); }
  public:
#ifdef DBG
    void dbg_v(const string msg="") const {
      std::cout << msg << " Vertices: [";
      for (int i=0; i < sz; i++) 
	std::cout << "(" << v[i].get_i() << "," << v[i].get_degree() << ") ";
      std::cout << "]" << std::endl;
    }
#endif
    Vertices(int size) : sz(0) { v = new Vertex[size]; }
    ~Vertices () {}
    void dispose() { if (v) delete [] v; }
    void sort() { std::sort(v, v+sz, desc_degree); }
    void init_colors();
    void set_degrees(Maxclique&);
    int size() const { return sz; }
    void push(const int ii) { v[sz++].set_i(ii); };
    void pop() { sz--; };
    Vertex& at(const int ii) const { return v[ii]; };
    Vertex& end() const { return v[sz - 1]; };
  };
  class ColorClass {
    int *i;
    int sz;
  public:
#ifdef DBG
    void dbg_i(const string msg="") const {
      std::cout << msg << " Class: [";
      for (int ii=0; ii < sz; ii++) 
	std::cout << i[ii] << " ";
      std::cout << "]" << std::endl;
    }
#endif
    ColorClass() : sz(0), i(0) {}
    ColorClass(const int sz) : sz(sz), i(0) { init(sz); }
    ~ColorClass() { if (i) delete [] i;
    }
    void init(const int sz) { i = new int[sz]; rewind(); }
    void push(const int ii) { i[sz++] = ii; };
    void pop() { sz--; };
    void rewind() { sz = 0; };
    int size() const { return sz; }
    int& at(const int ii) const { return i[ii]; }
    ColorClass& operator=(const ColorClass& dh) {
      for (int j = 0; j < dh.sz; j++) i[j] = dh.i[j];
      sz = dh.sz;
      return *this;
    }
  };
  Vertices V;
  ColorClass *C, QMAX, Q;
  class StepCount {
    int i1, i2;
  public:
    StepCount() : i1(0), i2(0) {}
    void set_i1(const int ii)  { i1 = ii; }
    int get_i1() const { return i1; }
    void set_i2(const int ii)  { i2 = ii; }
    int get_i2() const { return i2; }
    void inc_i1()  { i1++; }
  };
  StepCount *S;
  bool connection(const int i, const int j) const { return e[i][j]; }
  bool cut1(const int, const ColorClass&);
  void cut2(const Vertices&, Vertices&);
  void color_sort(Vertices&);
  void expand(Vertices);
  void expand_dyn(Vertices);
  void _mcq(int*&, int&, bool);
  void degree_sort(Vertices &R) { R.set_degrees(*this); R.sort(); }
public:
#ifdef DBG
  void dbg_C() const {
    for (int i=0; i < V.size(); i++) {
      std::cout << "C["<< i << "] : ";
      C[i].dbg_i();
    }
  }
  void dbg_conn() const {
    for (int i=0; i < V.size(); i++) {
      for (int j=0; j < V.size(); j++) {
	std::cout <<e[i][j];
      }
      std::cout<< std::endl;
    }
  }
#endif
  Maxclique(const bool* const*, const int, const float=0.025);
  int steps() const { return pk; }
  void mcq(int* &maxclique, int &sz) { _mcq(maxclique, sz, false); }
  void mcqdyn(int* &maxclique, int &sz) { _mcq(maxclique, sz, true); }
  ~Maxclique() {
    if (C) delete [] C;
    if (S) delete [] S;
    V.dispose();
  };
};

Maxclique::Maxclique (const bool* const* conn, const int sz, const float tt) : pk(0), level(1), Tlimit(tt), V(sz), Q(sz), QMAX(sz) {
  assert(conn!=0 && sz>0);
  for (int i=0; i < sz; i++) V.push(i);
  e = conn;
  C = new ColorClass[sz + 1];
  for (int i=0; i < sz + 1; i++) C[i].init(sz + 1);
  S = new StepCount[sz + 1];
}

void Maxclique::_mcq(int* &maxclique, int &sz, bool dyn) { 
  V.set_degrees(*this);
  V.sort();
  V.init_colors();
  if (dyn) {
    for (int i=0; i < V.size() + 1; i++) {
      S[i].set_i1(0);
      S[i].set_i2(0);
    }
    expand_dyn(V);
  }
  else
    expand(V);
  maxclique = new int[QMAX.size()]; 
  for (int i=0; i<QMAX.size(); i++) { 
    maxclique[i] = QMAX.at(i);
  }
  sz = QMAX.size();
}

void Maxclique::Vertices::init_colors() { 
  const int max_degree = v[0].get_degree();
  for (int i = 0; i < max_degree; i++)
    v[i].set_degree(i + 1);
  for (int i = max_degree; i < sz; i++)
    v[i].set_degree(max_degree + 1);
}

void Maxclique::Vertices::set_degrees(Maxclique &m) { 
  for (int i=0; i < sz; i++) {
    int d = 0;
    for (int j=0; j < sz; j++)
      if (m.connection(v[i].get_i(), v[j].get_i())) d++;
    v[i].set_degree(d);
  }
}

bool Maxclique::cut1(const int pi, const ColorClass &A) {
  for (int i = 0; i < A.size(); i++)
    if (connection(pi, A.at(i)))
      return true;
  return false;
}

void Maxclique::cut2(const Vertices &A, Vertices &B) {
  for (int i = 0; i < A.size() - 1; i++) {
    if (connection(A.end().get_i(), A.at(i).get_i()))
      B.push(A.at(i).get_i());
  }
}

void Maxclique::color_sort(Vertices &R) {
  int j = 0;
  int maxno = 1;
  int min_k = QMAX.size() - Q.size() + 1;
  C[1].rewind();
  C[2].rewind();
  int k = 1;
  for (int i=0; i < R.size(); i++) {
    int pi = R.at(i).get_i();
    k = 1;
    while (cut1(pi, C[k]))
      k++;
    if (k > maxno) {
      maxno = k;
      C[maxno + 1].rewind();
    }
    C[k].push(pi);
    if (k < min_k) {
      R.at(j++).set_i(pi);
    }
  }
  if (j > 0) R.at(j-1).set_degree(0);
  if (min_k <= 0) min_k = 1;
  for (k = min_k; k <= maxno; k++)
    for (int i = 0; i < C[k].size(); i++) {
      R.at(j).set_i(C[k].at(i));
      R.at(j++).set_degree(k);
    }
}

void Maxclique::expand(Vertices R) {
  while (R.size()) {
    if (Q.size() + R.end().get_degree() > QMAX.size()) {
      Q.push(R.end().get_i());
      Vertices Rp(R.size());
      cut2(R, Rp);
      if (Rp.size()) {
        color_sort(Rp);
	pk++;
        expand(Rp);
      }
      else if (Q.size() > QMAX.size()) { 
        std::cout << "step = " << pk << " current max. clique size = " << Q.size() << std::endl; 
	QMAX = Q;
      }    
      Rp.dispose();
      Q.pop();
    }
    else {
      return;
    }
    R.pop();
  }
}

void Maxclique::expand_dyn(Vertices R) {
  S[level].set_i1(S[level].get_i1() + S[level - 1].get_i1() - S[level].get_i2());
  S[level].set_i2(S[level - 1].get_i1());
  while (R.size()) {
    if (Q.size() + R.end().get_degree() > QMAX.size()) {
      Q.push(R.end().get_i());
      Vertices Rp(R.size());
      cut2(R, Rp);
      if (Rp.size()) {
        if ((float)S[level].get_i1()/++pk < Tlimit) {
          degree_sort(Rp);
        }
        color_sort(Rp);
	S[level].inc_i1();
	level++;
	expand_dyn(Rp);
	level--;
      }
      else if (Q.size() > QMAX.size()) { 
        std::cout << "step = " << pk << " current max. clique size = " << Q.size() << std::endl; 
	QMAX = Q;
      }    
      Rp.dispose();
      Q.pop();
    }
    else {
      return;
    }
    R.pop();
  }
}

#endif