/*
  Copyright (c) 2017 Microsoft Corporation
  Author: Nikolaj Bjorner
  Lev Nachmanson


  A mon_eq represents a definition m_v = v1*v2*...*vn, 
  where m_vs = [v1, v2, .., vn]
      
  A monic contains a mon_eq and variables in canonized form.

*/

#pragma once
#include "math/lp/lp_settings.h"
#include "util/vector.h"
#include "math/lp/lar_solver.h"
#include "math/lp/nla_defs.h"
#include <algorithm>
namespace nla {

class mon_eq {
    // fields
    lp::var_index          m_v;
    svector<lp::var_index> m_vs;
public:
    // constructors
    mon_eq(lp::var_index v, unsigned sz, lp::var_index const* vs):
        m_v(v), m_vs(sz, vs) {
        std::sort(m_vs.begin(), m_vs.end());
    }
    mon_eq(lp::var_index v, const svector<lp::var_index> &vs):
        m_v(v), m_vs(vs) {
        std::sort(m_vs.begin(), m_vs.end());
    }
    mon_eq(): m_v(UINT_MAX) {}
        
    unsigned var() const { return m_v; }
    unsigned size() const { return m_vs.size(); }
    const svector<lp::var_index>& vars() const { return m_vs; }
    bool empty() const { return m_vs.empty(); }
    bool is_sorted() const {
        for (unsigned i = 0; i + 1 < size(); i++)
            if (m_vs[i] > m_vs[i + 1])
                return false;
        return true;
    }
    bool contains_var(lpvar j) const {
        return std::binary_search(m_vs.begin(), m_vs.end(), j);
    }
protected:
    svector<lp::var_index>& vars1() { return m_vs; }
};

// support the congruence    
class monic: public mon_eq {
    // fields
    svector<lpvar>   m_rvars;
    bool             m_rsign;
    mutable unsigned m_visited;
public:
    // constructors
    monic(lpvar v, unsigned sz, lpvar const* vs, unsigned idx):  
        monic(v, svector<lpvar>(sz, vs), idx) {}
    monic(lpvar v, const svector<lpvar> &vs, unsigned idx): 
        mon_eq(v, vs), m_rsign(false),  m_visited(0) {
        std::sort(vars1().begin(), vars1().end());
    }

    unsigned visited() const { return m_visited; }
    void set_visited(unsigned v) { m_visited = v; }
    svector<lpvar> const& rvars() const { return m_rvars; }
    bool rsign() const { return m_rsign; }
    void reset_rfields() { m_rsign = false; m_rvars.reset(); SASSERT(m_rvars.size() == 0); }
    void push_rvar(signed_var sv) { m_rsign ^= sv.sign(); m_rvars.push_back(sv.var()); }
    void sort_rvars() { std::sort(m_rvars.begin(), m_rvars.end()); }
    
    svector<lpvar>::const_iterator begin() const { return vars().begin(); }
    svector<lpvar>::const_iterator end() const { return vars().end(); }

    rational rat_sign() const { return m_rsign ? rational(-1) : rational(1); }
};

inline std::ostream& operator<<(std::ostream& out, monic const& m) {
    return out << m.var() << " := " << m.vars() 
               << " r ( " << (m.rsign()?"- ":"") << m.rvars() << ")";
}


typedef std::unordered_map<lpvar, rational> variable_map_type;
template <typename T>
bool check_assignment(T const& m, variable_map_type & vars);
template <typename K>
bool check_assignments(const K & monomimials,
                       const lp::lar_solver& s,
                       variable_map_type & vars);

} // end of namespace nla