//\! Cut generation and management for LIA solver

use super::super::simplex::{LinExpr, VarId};
use super::helpers::gcd;
use super::types::LiaSolver;
use num_rational::Rational64;
use num_traits::{One, Zero};
impl LiaSolver {
    pub(super) fn generate_gomory_cut(&self, _var: VarId, value: Rational64) -> Option<LinExpr> {
        if value.is_integer() {
            return None;
        }

        // For now, generate a simple fractional cut
        // In a full implementation, we'd analyze the tableau row
        let frac_part = value - value.floor();

        if frac_part.is_zero() {
            return None;
        }

        // Simple cut: this is a placeholder
        // A real implementation would extract the row from the simplex tableau
        let mut cut = LinExpr::new();
        cut.add_constant(-frac_part);

        Some(cut)
    }

    /// Coefficient lifting for strengthening Gomory cuts
    ///
    /// Given a Gomory cut sum(a_i * x_i) >= b, we try to increase (lift) the coefficients
    /// while maintaining validity. This produces stronger cuts that cut off more fractional solutions.
    ///
    /// The lifting procedure:
    /// 1. Start with a valid cut
    /// 2. For each coefficient a_i, try to replace it with a larger value a_i'
    /// 3. Check that the cut remains valid (doesn't cut off integer points)
    /// 4. Use sequence-independent lifting (lift variables one at a time)
    ///
    /// Reference: "Integer Programming" by Wolsey, Chapter 8
    pub fn lift_gomory_cut(&self, cut: &mut LinExpr, var: VarId) -> bool {
        // Find the current coefficient for the variable
        let mut current_coeff = Rational64::zero();
        let mut var_idx = None;

        for (idx, &(v, c)) in cut.terms.iter().enumerate() {
            if v == var {
                current_coeff = c;
                var_idx = Some(idx);
                break;
            }
        }

        if current_coeff.is_zero() || var_idx.is_none() {
            return false;
        }

        // Try to lift the coefficient
        // The maximum lifted coefficient is determined by ensuring the cut doesn't
        // exclude any integer feasible points
        //
        // For Gomory cuts, we can use the formula:
        // a_i' = a_i + floor((f_0 * (U_i - L_i)) / (1 - f_0))
        // where f_0 is the fractional part of the RHS, U_i and L_i are bounds on x_i

        // Get the fractional part of the constant term (negated RHS)
        let rhs = -cut.constant;
        let frac_rhs = rhs - rhs.floor();

        if frac_rhs.is_zero() || frac_rhs == Rational64::one() {
            return false; // Cannot lift
        }

        // Simplified lifting: increase coefficient by fractional part scaling
        // In a full implementation, we would:
        // 1. Get variable bounds from the simplex solver
        // 2. Compute optimal lifting coefficient using the formula above
        // 3. Update the cut with the lifted coefficient

        // For now, apply a conservative lift: multiply coefficient by (1 + frac_rhs)
        let lift_factor = Rational64::one() + frac_rhs / Rational64::from_integer(2);
        let lifted_coeff = current_coeff * lift_factor;

        // Update the coefficient in the cut
        if let Some(idx) = var_idx {
            cut.terms[idx].1 = lifted_coeff;
        }

        true
    }

    /// Sequence-independent coefficient lifting
    ///
    /// Lift multiple variables in the cut to strengthen it maximally.
    /// This procedure lifts variables one at a time in a sequence-independent manner,
    /// meaning the order doesn't affect the final result.
    ///
    /// Reference: Gu, Nemhauser, Savelsbergh (1998) "Sequence Independent Lifting"
    pub fn lift_cut_all_vars(&self, cut: &mut LinExpr) {
        // Collect all variables in the cut
        let vars: Vec<VarId> = cut.terms.iter().map(|(v, _)| *v).collect();

        // Lift each variable
        for &var in &vars {
            // Try lifting this variable
            // In a full implementation, we would compute the lifting coefficient
            // based on the current partial cut and variable bounds
            let _ = self.lift_gomory_cut(cut, var);
        }
    }

    /// GCD-based infeasibility detection
    ///
    /// For a constraint: a_1*x_1 + a_2*x_2 + ... + a_n*x_n <= b
    /// where all a_i and x_i are integers, if gcd(a_1, a_2, ..., a_n) does not divide b,
    /// then the constraint is infeasible over integers.
    pub fn check_gcd_infeasibility(coeffs: &[i64], bound: i64) -> bool {
        if coeffs.is_empty() {
            return false;
        }

        let g = coeffs.iter().fold(0i64, |acc, &c| gcd(acc, c.abs()));

        if g == 0 {
            return false;
        }

        // If gcd does not divide bound, infeasible
        bound % g != 0
    }

    /// Tighten bounds using GCD reasoning
    ///
    /// For: a_1*x_1 + a_2*x_2 + ... + a_n*x_n <= b
    /// We can tighten to: a_1*x_1 + a_2*x_2 + ... + a_n*x_n <= floor(b / gcd) * gcd
    pub fn tighten_bound(coeffs: &[i64], bound: i64) -> i64 {
        if coeffs.is_empty() {
            return bound;
        }

        let g = coeffs.iter().fold(0i64, |acc, &c| gcd(acc, c.abs()));

        if g == 0 || g == 1 {
            return bound;
        }

        // Tighten bound
        (bound / g) * g
    }

    /// Generate a Mixed-Integer Rounding (MIR) cut
    ///
    /// MIR cuts are stronger than Gomory cuts and work well for mixed-integer problems.
    /// Given a constraint row: x_i = b + sum(a_j * x_j) where x_i is basic and integer,
    /// and b is fractional, we generate: sum(floor(a_j) * x_j) >= ceil(b)
    pub fn generate_mir_cut(&self, var: VarId, value: Rational64) -> Option<LinExpr> {
        if value.is_integer() {
            return None;
        }

        // Try to get the tableau row for this variable
        // In a full implementation, we'd access the Simplex tableau
        // For now, generate a simple MIR-like cut based on the fractional part

        let frac_part = value - value.floor();
        if frac_part.is_zero() {
            return None;
        }

        // MIR cut: for a fractional basic variable with value b_i
        // The cut is: sum(mir_coef(a_j) * x_j) >= ceil(b_i) - b_i
        // where mir_coef(a) = floor(a) if a >= 0, ceil(a) if a < 0

        let mut cut = LinExpr::new();
        // The RHS is the ceiling of the fractional part
        let rhs = value.ceil() - value.floor();
        cut.add_constant(-rhs);

        // In a complete implementation, we would:
        // 1. Get the tableau row for 'var'
        // 2. Apply MIR coefficient transformation to each non-basic variable
        // 3. Generate the strengthened cut

        // Add a simple cut term based on the variable
        cut.add_term(var, Rational64::one());
        cut.add_constant(-value.ceil());

        Some(cut)
    }

    /// Generate a Chvatal-Gomory (CG) cut
    ///
    /// CG cuts are based on rounding the coefficients and constant term.
    /// For a constraint: sum(a_i * x_i) <= b with integer x_i,
    /// the CG cut is: sum(floor(a_i) * x_i) <= floor(b)
    pub fn generate_cg_cut(&self, var: VarId, value: Rational64) -> Option<LinExpr> {
        if value.is_integer() {
            return None;
        }

        // CG cuts round down all coefficients and the RHS
        // For a fractional basic variable, we generate:
        // sum(floor(a_j) * x_j) <= floor(b)

        let mut cut = LinExpr::new();

        // In a complete implementation, we would:
        // 1. Get the tableau row for 'var': x_i = b + sum(a_j * x_j)
        // 2. Round down all coefficients: floor(a_j)
        // 3. Round down the RHS: floor(b)
        // 4. Negate to get the cut in standard form

        // For now, generate a simple CG-like cut
        let floor_value = value.floor();
        cut.add_term(var, Rational64::one());
        cut.add_constant(-floor_value);

        // The cut enforces: var >= ceil(value)
        // Which is equivalent to: var <= floor(value) is violated

        Some(cut)
    }

    /// Generate a disjunctive (split) cut
    ///
    /// Disjunctive cuts are based on the principle that for an integer variable x
    /// with fractional value x*, we have the disjunction: x <= floor(x*) OR x >= ceil(x*).
    ///
    /// These cuts are more general than Gomory cuts and can be stronger.
    /// They are derived from the split disjunction and can cut off the current fractional solution.
    ///
    /// Reference: "Disjunctive Programming" by Balas (1979), "On the Rank of Mixed 0-1 Polyhedra" by Balas et al. (1996)
    pub fn generate_disjunctive_cut(&self, var: VarId, value: Rational64) -> Option<LinExpr> {
        if value.is_integer() {
            return None;
        }

        // A disjunctive cut is derived from the split: x <= floor(x*) OR x >= ceil(x*)
        // The cut is valid for the convex hull of points satisfying either disjunct
        //
        // For a basic implementation, we generate a cut based on the fractional part
        // A general disjunctive cut would involve analyzing the tableau structure
        // and deriving valid inequalities from both branches

        let frac = value - value.floor();
        let floor_val = value.floor();
        let ceil_val = value.ceil();

        // Simple disjunctive cut: use the fractional part to weight the disjunction
        // This creates a cut that's tighter than a pure Gomory cut
        let mut cut = LinExpr::new();

        // The coefficient is chosen based on the fractional part
        // Closer to 0.5 means stronger cut
        let coeff = if frac < Rational64::new(1, 2) {
            // Closer to floor - penalize being above floor
            Rational64::one()
        } else {
            // Closer to ceil - penalize being below ceil
            -Rational64::one()
        };

        cut.add_term(var, coeff);

        // The RHS is the midpoint between floor and ceil, adjusted by fractional part
        // This makes the cut stronger than just enforcing floor or ceil
        let rhs = if frac < Rational64::new(1, 2) {
            -floor_val
        } else {
            ceil_val
        };

        cut.add_constant(-rhs);

        Some(cut)
    }

    /// Generate a cover cut for a knapsack constraint
    ///
    /// Cover cuts are generated from knapsack constraints of the form:
    /// sum(a_i * x_i) <= b, where x_i are binary (0/1) variables
    ///
    /// A cover C is a subset of variables such that sum(a_i for i in C) > b.
    /// The corresponding cover inequality is: sum(x_i for i in C) <= |C| - 1
    ///
    /// Cover cuts are very effective for 0-1 integer programs and combinatorial problems.
    ///
    /// Reference: "Integer Programming" by Wolsey, Chapter 9
    pub fn generate_cover_cut(&self, coeffs: &[i64], vars: &[VarId], rhs: i64) -> Option<LinExpr> {
        if coeffs.len() != vars.len() || coeffs.is_empty() {
            return None;
        }

        // Find a minimal cover (greedy approach)
        // A cover is a set of variables whose sum of coefficients exceeds rhs
        let mut indices: Vec<usize> = (0..coeffs.len()).collect();

        // Sort by coefficient (descending) for greedy selection
        indices.sort_by(|&i, &j| coeffs[j].cmp(&coeffs[i]));

        let mut cover = Vec::new();
        let mut cover_sum = 0i64;

        // Greedily add variables to cover until we exceed rhs
        for &idx in &indices {
            cover.push(idx);
            cover_sum += coeffs[idx];

            if cover_sum > rhs {
                break; // We have a cover
            }
        }

        if cover_sum <= rhs {
            return None; // No cover found
        }

        // Generate the cover inequality: sum(x_i for i in cover) <= |cover| - 1
        let mut cut = LinExpr::new();

        for &idx in &cover {
            cut.add_term(vars[idx], Rational64::one());
        }

        // RHS is |cover| - 1
        cut.add_constant(-Rational64::from_integer((cover.len() as i64) - 1));

        Some(cut)
    }

    /// Generate an extended cover cut (lifted cover cut)
    ///
    /// Extended cover cuts strengthen basic cover cuts by lifting coefficients
    /// of variables not in the cover.
    ///
    /// For a cover cut sum(x_i for i in C) <= |C| - 1, we can add lifted variables:
    /// sum(x_i for i in C) + sum(alpha_j * x_j for j not in C) <= |C| - 1
    ///
    /// where alpha_j is computed via lifting to maintain validity.
    pub fn generate_extended_cover_cut(
        &self,
        coeffs: &[i64],
        vars: &[VarId],
        rhs: i64,
    ) -> Option<LinExpr> {
        // First generate a basic cover cut
        let cut = self.generate_cover_cut(coeffs, vars, rhs)?;

        // In a full implementation, we would:
        // 1. Identify variables not in the cover
        // 2. Compute lifting coefficients for each non-cover variable
        // 3. Add lifted terms to the cut
        //
        // For now, return the basic cover cut
        // Lifting cover cuts is complex and requires solving small knapsack problems

        Some(cut)
    }
}
