/*
  Copyright (c) 2017 Microsoft Corporation
  Author: Lev Nachmanson
*/
#include "math/lp/int_solver.h"
#include "math/lp/lar_solver.h"
#include "math/lp/lp_utils.h"
#include "math/lp/monic.h"
#include "math/lp/gomory.h"
#include "math/lp/int_branch.h"
#include "math/lp/int_cube.h"

namespace lp {

    int_solver::patcher::patcher(int_solver& lia):
        lia(lia),
        lra(lia.lra),
        lrac(lia.lrac)
    {}
    
    void int_solver::patcher::remove_fixed_vars_from_base() {
        unsigned num = lra.A_r().column_count();
        for (unsigned v = 0; v < num; v++) {
            if (!lia.is_base(v) || !lia.is_fixed(v))
                continue;
            auto const & r = lra.basic2row(v);
            for (auto const& c : r) {
                if (c.var() != v && !lia.is_fixed(c.var())) {
                    lra.pivot(c.var(), v); 
                    break;
                }
            }        
        }
    }


    unsigned int_solver::patcher::count_non_int() {
        unsigned non_int = 0;
        for (auto j : lra.r_basis()) 
            if (lra.column_is_int(j) && !lra.column_value_is_int(j))
                ++non_int;
        return non_int;
    }

    lia_move int_solver::patcher::patch_basic_columns() {
        remove_fixed_vars_from_base();
        lia.settings().stats().m_patches++;
        lp_assert(lia.is_feasible());
        
       // unsigned non_int_before, non_int_after;

       // non_int_before = count_non_int();


        // unsigned num = lra.A_r().column_count();
        for (unsigned j : lra.r_basis()) 
            if (!lra.get_value(j).is_int())
                patch_basic_column(j);
        // non_int_after = count_non_int();
        // verbose_stream() << non_int_before << " -> " << non_int_after << "\n";

        if (!lia.has_inf_int()) {
            lia.settings().stats().m_patches_success++;
            return lia_move::sat;
        }
        return lia_move::undef;
    }

    // clang-format on
    /**
     * \brief find integral and minimal, in the absolute values, deltas such that x - alpha*delta is integral too.
     */
    bool get_patching_deltas(const rational& x, const rational& alpha,
                             rational& delta_plus, rational& delta_minus) {
        auto a1 = numerator(alpha);
        auto a2 = denominator(alpha);
        auto x1 = numerator(x);
        auto x2 = denominator(x);
        if (!divides(x2, a2))
            return false;

        // delta has to be integral.
        // We need to find delta such that x1/x2 + (a1/a2)*delta is integral (we are going to flip the delta sign later).
        // Then a2*x1/x2 + a1*delta is integral, but x2 and x1 are coprime:
        // that means that t = a2/x2 is
        // integral. We established that a2 = x2*t Then x1 + a1*delta*(x2/a2)  = x1
        // + a1*(delta/t)  is integral. Taking into account that t and a1 are
        // coprime we have delta = t*k, where k is an integer.
        rational t = a2 / x2;
        // std::cout << "t = " << t << std::endl;
        // Now we have x1/x2 + (a1/x2)*k is integral, or (x1 + a1*k)/x2 is integral.
        // It is equivalent to x1 + a1*k = x2*m, where m is an integer
        // We know that a2 and a1 are coprime, and x2 divides a2, so x2 and a1 are
        // coprime. We can find u and v such that u*a1 + v*x2 = 1.
        rational u, v;
        gcd(a1, x2, u, v);
        lp_assert(gcd(a1, x2, u, v).is_one());
        // std::cout << "u = " << u << ", v = " << v << std::endl;
        // std::cout << "x= " << (x1 / x2) << std::endl;
        // std::cout << "x + (a1 / a2) * (-u * t) * x1 = "
        //           << x + (a1 / a2) * (-u * t) * x1 << std::endl;
        lp_assert((x + (a1 / a2) * (-u * t) * x1).is_int());
        // 1 = (u- l*x2 ) * a1 + (v + l*a1)*x2, for every integer l.
        rational d = u * t * x1;
        // We can prove that x+alpha*d is integral,
        // and any other delta, satisfying x+alpha*delta, is equal to d modulo a2.
        delta_plus = mod(d, a2);
        lp_assert(delta_plus > 0);
        delta_minus = delta_plus - a2;
        lp_assert(delta_minus < 0);

        return true;
    }
    /**
     * \brief try to patch the basic column v
     */
    bool int_solver::patcher::patch_basic_column_on_row_cell(unsigned v, row_cell<mpq> const& c) {
        if (v == c.var())
            return false;
        if (!lra.column_is_int(c.var()))  // could use real to patch integer
            return false;
        if (c.coeff().is_int())
            return false;
        mpq a = fractional_part(c.coeff());
        mpq r = fractional_part(lra.get_value(v));
        lp_assert(0 < r && r < 1);
        lp_assert(0 < a && a < 1);
        mpq delta_plus, delta_minus;
        if (!get_patching_deltas(r, a, delta_plus, delta_minus))
            return false;

        if (lia.random() % 2) {
            return try_patch_column(v, c.var(), delta_plus) ||
                   try_patch_column(v, c.var(), delta_minus);
        } else {
            return try_patch_column(v, c.var(), delta_minus) ||
                   try_patch_column(v, c.var(), delta_plus);
        }
    }
        
    bool int_solver::patcher::try_patch_column(unsigned v, unsigned j, mpq const& delta) {
        const auto & A = lra.A_r();
        if (delta < 0) {
            if (lia.has_lower(j) && lia.get_value(j) + impq(delta) < lra.get_lower_bound(j))
                return false;
        }
        else {
            if (lia.has_upper(j) && lia.get_value(j) + impq(delta) > lra.get_upper_bound(j))
                return false;
        }
        for (auto const& c : A.column(j)) {
            unsigned row_index = c.var();
            unsigned bj = lrac.m_r_basis[row_index];
            auto old_val = lia.get_value(bj);
            auto new_val = old_val - impq(c.coeff()*delta);
            if (lia.has_lower(bj) && new_val < lra.get_lower_bound(bj))
                return false;
            if (lia.has_upper(bj) && new_val > lra.get_upper_bound(bj))
                return false;
            if (old_val.is_int() && !new_val.is_int()){
                return false; // do not waste resources on this case
            }
            // if bj == v, then, because we are patching the lra.get_value(v),
            // we just need to assert that the lra.get_value(v) would be integral.
            lp_assert(bj != v || lra.from_model_in_impq_to_mpq(new_val).is_int());
        }
        
        lra.set_value_for_nbasic_column(j, lia.get_value(j) + impq(delta));
        return true;
    }
    
    void int_solver::patcher::patch_basic_column(unsigned v) {
        SASSERT(!lia.is_fixed(v));
        for (auto const& c : lra.basic2row(v))
            if (patch_basic_column_on_row_cell(v, c))
                return;                                       
    }



int_solver::int_solver(lar_solver& lar_slv) :
    lra(lar_slv),
    lrac(lra.m_mpq_lar_core_solver),
    m_gcd(*this),
    m_patcher(*this),
    m_number_of_calls(0),
    m_hnf_cutter(*this),
    m_hnf_cut_period(settings().hnf_cut_period()) {
    lra.set_int_solver(this);
}

// this will allow to enable and disable tracking of the pivot rows
struct check_return_helper {
    lar_solver&      lra;
    bool             m_track_touched_rows;
    check_return_helper(lar_solver& ls) :
        lra(ls),
        m_track_touched_rows(lra.touched_rows_are_tracked()) {
        lra.track_touched_rows(false);
    }
    ~check_return_helper() {
        lra.track_touched_rows(m_track_touched_rows);
    }
};

lia_move int_solver::check(lp::explanation * e) {
    SASSERT(lra.ax_is_correct());
    if (!has_inf_int()) return lia_move::sat;

    m_t.clear();
    m_k.reset();
    m_ex = e;
    m_ex->clear();
    m_upper = false;
    lia_move r = lia_move::undef;

    if (m_gcd.should_apply()) r = m_gcd();

    check_return_helper pc(lra);

    if (settings().get_cancel_flag())
        return lia_move::undef;

    ++m_number_of_calls;
    if (r == lia_move::undef && m_patcher.should_apply()) r = m_patcher();
    if (r == lia_move::undef && should_find_cube()) r = int_cube(*this)();
    if (r == lia_move::undef && should_hnf_cut()) r = hnf_cut();
    if (r == lia_move::undef && should_gomory_cut()) r = gomory(*this)();
    if (r == lia_move::undef) r = int_branch(*this)();
    return r;
}

std::ostream& int_solver::display_inf_rows(std::ostream& out) const {
    unsigned num = lra.A_r().column_count();
    for (unsigned v = 0; v < num; v++) {
        if (column_is_int(v) && !get_value(v).is_int()) {
            display_column(out, v);
        }
    }

    num = 0;
    for (unsigned i = 0; i < lra.A_r().row_count(); i++) {
        unsigned j = lrac.m_r_basis[i];
        if (column_is_int_inf(j)) {
            num++;
            lra.print_row(lra.A_r().m_rows[i], out);
            out << "\n";
        }
    }
    out << "num of int infeasible: " << num << "\n";
    return out;
}

bool int_solver::cut_indices_are_columns() const {
    for (lar_term::ival p : m_t) {
        if (p.column().index() >= lra.A_r().column_count())
            return false;
    }
    return true;
}

bool int_solver::current_solution_is_inf_on_cut() const {
    SASSERT(cut_indices_are_columns());
    const auto & x = lrac.m_r_x;
    impq v = m_t.apply(x);
    mpq sign = m_upper ? one_of_type<mpq>()  : -one_of_type<mpq>();
    CTRACE("current_solution_is_inf_on_cut", v * sign <= impq(m_k) * sign,
           tout << "m_upper = " << m_upper << std::endl;
           tout << "v = " << v << ", k = " << m_k << std::endl;
          );
    return v * sign > impq(m_k) * sign;
}

bool int_solver::has_inf_int() const {
    return lra.has_inf_int();
}

constraint_index int_solver::column_upper_bound_constraint(unsigned j) const {
    return lra.get_column_upper_bound_witness(j);
}

constraint_index int_solver::column_lower_bound_constraint(unsigned j) const {
    return lra.get_column_lower_bound_witness(j);
}

unsigned int_solver::row_of_basic_column(unsigned j) const {
    return lra.row_of_basic_column(j);
}

lp_settings& int_solver::settings() {
    return lra.settings();
}

const lp_settings& int_solver::settings() const {
    return lra.settings();
}

bool int_solver::column_is_int(column_index const& j) const {
    return lra.column_is_int(j);
}

bool int_solver::is_real(unsigned j) const {
    return !column_is_int(j);
}

bool int_solver::value_is_int(unsigned j) const {
    return lra.column_value_is_int(j);
}

unsigned int_solver::random() {
    return settings().random_next();
}

const impq& int_solver::upper_bound(unsigned j) const {
    return lra.column_upper_bound(j);
}

const impq& int_solver::lower_bound(unsigned j) const {
    return lra.column_lower_bound(j);
}

bool int_solver::is_term(unsigned j) const {
    return lra.column_corresponds_to_term(j);
}

unsigned int_solver::column_count() const  {
    return lra.column_count();
}

bool int_solver::should_find_cube() {
    return m_number_of_calls % settings().m_int_find_cube_period == 0;
}


bool int_solver::should_gomory_cut() {
    return m_number_of_calls % settings().m_int_gomory_cut_period == 0;
}

bool int_solver::should_hnf_cut() {
    return settings().enable_hnf() && m_number_of_calls % m_hnf_cut_period == 0;
}

lia_move int_solver::hnf_cut() {
    lia_move r = m_hnf_cutter.make_hnf_cut();
    if (r == lia_move::undef) {
        m_hnf_cut_period *= 2;
    }
    else {
        m_hnf_cut_period = settings().hnf_cut_period();
    }
    return r;
}

bool int_solver::has_lower(unsigned j) const {
    switch (lrac.m_column_types()[j]) {
    case column_type::fixed:
    case column_type::boxed:
    case column_type::lower_bound:
        return true;
    default:
        return false;
    }
}

bool int_solver::has_upper(unsigned j) const {
    switch (lrac.m_column_types()[j]) {
    case column_type::fixed:
    case column_type::boxed:
    case column_type::upper_bound:
        return true;
    default:
        return false;
    }
}

static void set_lower(impq & l, bool & inf_l, impq const & v ) {
    if (inf_l || v > l) {
        l = v;
        inf_l = false;
    }
}

static void set_upper(impq & u, bool & inf_u, impq const & v) {
    if (inf_u || v < u) {
        u = v;
        inf_u = false;
    }
}

// this function assumes that all basic columns dependend on j are feasible
bool int_solver::get_freedom_interval_for_column(unsigned j, bool & inf_l, impq & l, bool & inf_u, impq & u, mpq & m) {
    if (lrac.m_r_heading[j] >= 0 || is_fixed(j)) // basic or fixed var
        return false;

    TRACE("random_update", display_column(tout, j) << ", is_int = " << column_is_int(j) << "\n";);
    impq const & xj = get_value(j);

    inf_l = true;
    inf_u = true;
    l = u = zero_of_type<impq>();
    m = mpq(1);

    if (has_lower(j)) 
        set_lower(l, inf_l, lower_bound(j) - xj);
    
    if (has_upper(j)) 
        set_upper(u, inf_u, upper_bound(j) - xj);
    

    const auto & A = lra.A_r();
    TRACE("random_update", tout <<  "m = " << m << "\n";);

    auto delta = [](mpq const& x, impq const& y, impq const& z) {
        if (x.is_one())
            return y - z;
        if (x.is_minus_one())
            return z - y;
        return (y - z) / x;
    };

    for (auto c : A.column(j)) {
        unsigned row_index = c.var();
        const mpq & a = c.coeff();
        unsigned i = lrac.m_r_basis[row_index];
        impq const & xi = get_value(i);
        lp_assert(lrac.m_r_solver.column_is_feasible(i));
        if (column_is_int(i) && !a.is_int() && xi.is_int()) 
            m = lcm(m, denominator(a));
        
        if (!inf_l && !inf_u) {
            if (l == u) 
                continue;            
        }

        if (a.is_neg()) {
            if (has_lower(i)) 
                set_lower(l, inf_l, delta(a, xi, lra.get_lower_bound(i)));
            if (has_upper(i)) 
                set_upper(u, inf_u, delta(a, xi, lra.get_upper_bound(i)));
        }
        else {
            if (has_upper(i)) 
                set_lower(l, inf_l, delta(a, xi, lra.get_upper_bound(i)));
            if (has_lower(i)) 
                set_upper(u, inf_u, delta(a, xi, lra.get_lower_bound(i)));
        }
    }

    l += xj;
    u += xj;

    TRACE("freedom_interval",
          tout << "freedom variable for:\n";
          tout << lra.get_variable_name(j);
          tout << "[";
          if (inf_l) tout << "-oo"; else tout << l;
          tout << "; ";
          if (inf_u) tout << "oo";  else tout << u;
          tout << "]\n";
          tout << "val = " << get_value(j) << "\n";
          tout << "return " << (inf_l || inf_u || l <= u);
          );
    return (inf_l || inf_u || l <= u);
}


bool int_solver::is_feasible() const {
    lp_assert(
        lrac.m_r_solver.calc_current_x_is_feasible_include_non_basis() ==
        lrac.m_r_solver.current_x_is_feasible());
    return lrac.m_r_solver.current_x_is_feasible();
}

const impq & int_solver::get_value(unsigned j) const {
    return lrac.m_r_x[j];
}

std::ostream& int_solver::display_column(std::ostream & out, unsigned j) const {
    return lrac.m_r_solver.print_column_info(j, out);
}

bool int_solver::column_is_int_inf(unsigned j) const {
    return column_is_int(j) && (!value_is_int(j));
}

bool int_solver::is_base(unsigned j) const {
    return lrac.m_r_heading[j] >= 0;
}

bool int_solver::is_boxed(unsigned j) const {
    return lrac.m_column_types[j] == column_type::boxed;
}

bool int_solver::is_fixed(unsigned j) const {
    return lrac.m_column_types[j] == column_type::fixed;
}

bool int_solver::is_free(unsigned j) const {
    return lrac.m_column_types[j] == column_type::free_column;
}

bool int_solver::at_bound(unsigned j) const {
    auto & mpq_solver = lrac.m_r_solver;
    switch (mpq_solver.m_column_types[j] ) {
    case column_type::fixed:
    case column_type::boxed:
        return
            mpq_solver.m_lower_bounds[j] == get_value(j) ||
            mpq_solver.m_upper_bounds[j] == get_value(j);
    case column_type::lower_bound:
        return mpq_solver.m_lower_bounds[j] == get_value(j);
    case column_type::upper_bound:
        return  mpq_solver.m_upper_bounds[j] == get_value(j);
    default:
        return false;
    }
}

bool int_solver::at_lower(unsigned j) const {
    auto & mpq_solver = lrac.m_r_solver;
    switch (mpq_solver.m_column_types[j] ) {
    case column_type::fixed:
    case column_type::boxed:
    case column_type::lower_bound:
        return mpq_solver.m_lower_bounds[j] == get_value(j);
    default:
        return false;
    }
}

bool int_solver::at_upper(unsigned j) const {
    auto & mpq_solver = lrac.m_r_solver;
    switch (mpq_solver.m_column_types[j] ) {
    case column_type::fixed:
    case column_type::boxed:
    case column_type::upper_bound:
        return mpq_solver.m_upper_bounds[j] == get_value(j);
    default:
        return false;
    }
}

std::ostream & int_solver::display_row(std::ostream & out, lp::row_strip<rational> const & row) const {
    bool first = true;
    auto & rslv = lrac.m_r_solver;
    for (const auto &c : row) {
        if (is_fixed(c.var())) {
            if (!get_value(c.var()).is_zero()) {
                impq val = get_value(c.var()) * c.coeff();
                if (!first && val.is_pos())
                    out << "+";
                if (val.y.is_zero())
                    out << val.x << " ";
                else
                    out << val << " ";
            }
            first = false;
            continue;
        }
        if (c.coeff().is_one())
        {
            if (!first)
                out << "+";
        }
        else if (c.coeff().is_minus_one())
            out << "-";
        else {
            if (c.coeff().is_pos() && !first)
                out << "+";
            if (c.coeff().is_big())
                out << " b*";
            else
                out << c.coeff();
        }
        out << rslv.column_name(c.var()) << " ";
        first = false;
    }
    out << "\n";
    for (const auto &c : row) {
        if (is_fixed(c.var()))
            continue;
        rslv.print_column_info(c.var(), out);
        if (is_base(c.var()))
            out << "j" << c.var() << " base\n";
    }
    return out;
}
    
std::ostream& int_solver::display_row_info(std::ostream & out, unsigned row_index) const  {    
    auto & rslv = lrac.m_r_solver;
    auto const& row = rslv.m_A.m_rows[row_index];
    return display_row(out, row);
}

bool int_solver::shift_var(unsigned j, unsigned range) {
    if (is_fixed(j) || is_base(j))
        return false;
    if (settings().get_cancel_flag())
        return false;
    bool inf_l = false, inf_u = false;
    impq l, u;
    mpq m;
    if (!get_freedom_interval_for_column(j, inf_l, l, inf_u, u, m))
        return false;
    if (settings().get_cancel_flag())
        return false;
    const impq & x = get_value(j);
    // x, the value of j column, might be shifted on a multiple of m

    if (inf_l && inf_u) {
        impq new_val = m * impq(random() % (range + 1)) + x;
        lra.set_value_for_nbasic_column(j, new_val);
        return true;
    }
    if (column_is_int(j)) {
        if (!inf_l) {
            l = impq(ceil(l));
        }
        if (!inf_u) {
            u = impq(floor(u));
        }
    }
    if (!inf_l && !inf_u && l >= u)
        return false;


    if (inf_u) {
        SASSERT(!inf_l);
        impq new_val = x + m * impq(random() % (range + 1));
        lra.set_value_for_nbasic_column(j, new_val);
        return true;
    }

    if (inf_l) {
        SASSERT(!inf_u);
        impq new_val = x - m * impq(random() % (range + 1));
        lra.set_value_for_nbasic_column(j, new_val);
        return true;
    }

    SASSERT(!inf_l && !inf_u);
    // The shift has to be a multiple of m: let us look for s, such that the shift is m*s.
    // We have new_val = x+m*s <= u, so m*s <= u-x and, finally, s <= floor((u- x)/m) = a
    // The symmetric reasoning gives us s >= ceil((l-x)/m) = b
    // We randomly pick s in the segment [b, a]
    mpq a = floor((u - x) / m);
    mpq b = ceil((l - x) / m);
    mpq r = a - b;
    if (!r.is_pos())
        return false;
    TRACE("int_solver", tout << "a = " << a << ", b = " << b << ", r = " << r<< ", m = " << m << "\n";);
    if (r < mpq(range))
        range = static_cast<unsigned>(r.get_uint64());

    mpq s = b + mpq(random() % (range + 1));
    impq new_val = x + m * impq(s);
    TRACE("int_solver", tout << "new_val = " << new_val << "\n";);
    SASSERT(l <= new_val && new_val <= u);
    lra.set_value_for_nbasic_column(j, new_val);
    return true;
}

// not used:
bool int_solver::non_basic_columns_are_at_bounds() const {
    for (unsigned j : lrac.m_r_nbasis) {
        auto & val = lrac.m_r_x[j];
        switch (lrac.m_column_types()[j]) {
        case column_type::boxed:
            if (val != lrac.m_r_lower_bounds()[j] && val != lrac.m_r_upper_bounds()[j])
                return false;
            break;
        case column_type::lower_bound:
            if (val != lrac.m_r_lower_bounds()[j])
                return false;
            break;
        case column_type::upper_bound:
            if (val != lrac.m_r_upper_bounds()[j])
                return false;
            break;
        default:
            if (column_is_int(j) && !val.is_int()) {
                return false;
            }
        }
    }
    return true;
}

int int_solver::select_int_infeasible_var() {
    int result = -1;
    mpq range;
    mpq new_range;
    mpq small_value(1024);
    unsigned n = 0;
    lar_core_solver & lcs = lra.m_mpq_lar_core_solver;
    unsigned prev_usage = 0; // to quiet down the compile

    enum state { small_box, is_small_value,  any_value, not_found };
    state st = not_found;

    for (unsigned j : lra.r_basis()) {
        if (!column_is_int_inf(j))
            continue;
        unsigned usage = lra.usage_in_terms(j);
        if (is_boxed(j) && (new_range = lcs.m_r_upper_bounds()[j].x - lcs.m_r_lower_bounds()[j].x - rational(2*usage)) <= small_value) {
            SASSERT(!is_fixed(j));
            if (st != small_box) {
                n = 0;
                st = small_box;
            }
            if (n == 0 || new_range < range) {
                result = j;
                range = new_range;
                n = 1;
            }
            else if (new_range == range && (random() % (++n) == 0)) {
                result = j;
            }
            continue;
        }
        if (st == small_box)
            continue;
        impq const& value = get_value(j);
        if (abs(value.x) < small_value ||
            (has_upper(j) && small_value > upper_bound(j).x - value.x) ||
            (has_lower(j) && small_value > value.x - lower_bound(j).x)) {
            if (st != is_small_value) {
                n = 0;
                st = is_small_value;
            }
            if (random() % (++n) == 0)
                result = j;
        }
        if (st == is_small_value)
            continue;
        SASSERT(st == not_found || st == any_value);
        st = any_value;
        if (n == 0 || usage > prev_usage) {
            result = j;
            prev_usage = usage;
            n = 1;
        } 
        else if (usage > 0 && usage == prev_usage && (random() % (++n) == 0)) 
            result = j;
    }
    
    return result;
}


}