//\! Heuristic methods for LIA solver

use super::super::simplex::VarId;
use super::types::{CutInfo, LiaSolver};
use num_rational::Rational64;
use oxiz_core::error::Result;
impl LiaSolver {
    /// Feasibility Pump heuristic for finding integer-feasible solutions
    /// Feasibility Pump heuristic for finding integer-feasible solutions
    pub fn feasibility_pump(&mut self, max_iterations: usize) -> Result<Option<Vec<i64>>> {
        // Start by solving the LP relaxation
        if self.simplex.check().is_err() {
            return Ok(None); // LP infeasible, can't use feasibility pump
        }

        let mut prev_rounded: Option<Vec<i64>> = None;

        for _iteration in 0..max_iterations {
            // Step 1: Round current solution to nearest integers
            let rounded = self.round_solution();

            // Check if we've found an integer solution (all fractional parts are 0)
            if self.find_fractional_var().is_none() {
                // Success! Current solution is integer-feasible
                return Ok(Some(self.get_integer_solution()));
            }

            // Check for cycling (same rounded solution as before)
            if let Some(ref prev) = prev_rounded
                && *prev == rounded
            {
                // Cycle detected - perturb the solution slightly
                // In a more sophisticated implementation, we would add random perturbations
                // For now, just bail out
                return Ok(None);
            }

            // Step 2: Project back to LP feasible region by solving:
            // minimize sum_i |x_i - rounded_i|
            //
            // This is approximated by temporarily modifying the bounds to pull toward rounded values
            // In a full implementation, we would solve a new LP with distance minimization objective
            //
            // For simplicity, we'll just re-solve the LP, which will give us a feasible solution
            self.simplex.push();

            // Add soft constraints pulling toward rounded values (approximation)
            // In practice, this would be done via an objective function
            for (&var, &target) in self.int_vars.keys().zip(rounded.iter()) {
                let target_rational = Rational64::from_integer(target);
                // Don't override bounds, but bias toward target if possible
                // (This is a simplified version - full implementation needs objective function)
                if let Some(ub) = self.simplex.get_upper(var)
                    && target_rational <= ub.value.real
                {
                    // Target is within upper bound, good
                }
            }

            // Re-solve LP
            if self.simplex.check().is_err() {
                self.simplex.pop();
                return Ok(None); // Became infeasible
            }

            self.simplex.pop();

            // Save current rounded solution for cycle detection
            prev_rounded = Some(rounded);

            // Check for integer solution again after projection
            if self.find_fractional_var().is_none() {
                return Ok(Some(self.get_integer_solution()));
            }
        }

        // Max iterations reached without finding integer solution
        Ok(None)
    }

    /// Round the current solution to nearest integers
    pub fn round_solution(&self) -> Vec<i64> {
        self.int_vars
            .keys()
            .map(|&var| {
                let value = self.simplex.value(var);
                value.round().to_integer()
            })
            .collect()
    }

    /// Get the current integer solution
    fn get_integer_solution(&self) -> Vec<i64> {
        self.int_vars
            .keys()
            .map(|&var| {
                let value = self.simplex.value(var);
                value.floor().to_integer()
            })
            .collect()
    }

    /// Probing: Tentatively fix variables to derive tighter bounds
    ///
    /// Probing (also called lookahead) is a preprocessing technique that:
    /// 1. Tentatively fixes a variable to one of its bounds (lower or upper)
    /// 2. Propagates this fixation through the constraints
    /// 3. Observes what bounds can be tightened on other variables
    /// 4. Detects infeasibilities early (if fixing leads to contradiction)
    ///
    /// Algorithm:
    /// ```text
    /// for each integer variable x with bounds [lb, ub]:
    ///   # Probe x = lb (lower bound)
    ///   push()
    ///   set x = lb
    ///   if infeasible:
    ///     tighten: x >= lb + 1  (lower bound failed, must be higher)
    ///   else:
    ///     record tightened bounds on other variables
    ///   pop()
    ///
    ///   # Probe x = ub (upper bound)
    ///   push()
    ///   set x = ub
    ///   if infeasible:
    ///     tighten: x <= ub - 1  (upper bound failed, must be lower)
    ///   else:
    ///     record tightened bounds on other variables
    ///   pop()
    /// ```
    ///
    /// Benefits:
    /// - Tightens variable bounds before branching (reduces search space)
    /// - Detects infeasibilities early (prunes infeasible branches)
    /// - Can fix variables when probing proves unique value
    /// - Particularly effective on structured problems (scheduling, routing)
    ///
    /// Cost:
    /// - Each probe requires solving an LP (2 LPs per variable)
    /// - Typically done once at root node or periodically
    /// - Parameterized by max_probes to control overhead
    ///
    /// Reference:
    /// - Savelsbergh, "Preprocessing and Probing Techniques for MIP" (1994)
    /// - Achterberg, "Constraint Integer Programming" (2007), Section 4.4
    /// - CPLEX and Gurobi both use probing extensively
    ///
    /// Returns the number of bounds tightened.
    #[allow(dead_code)]
    pub fn probe_variables(&mut self, max_probes: usize) -> Result<usize> {
        let mut bounds_tightened = 0;

        // Get list of integer variables to probe (prioritize fractional variables)
        let mut candidates: Vec<VarId> = self.int_vars.keys().copied().collect();

        // Limit number of probes to avoid excessive overhead
        let num_probes = candidates.len().min(max_probes);
        candidates.truncate(num_probes);

        for &var in &candidates {
            // Get current bounds and copy data we need (to avoid borrow checker issues)
            let (lb_int, ub_int, lb_reason, ub_reason) = {
                let lower = self.simplex.get_lower(var);
                let upper = self.simplex.get_upper(var);

                if let (Some(lb), Some(ub)) = (lower, upper) {
                    let lb_int = lb.value.real.ceil().to_integer();
                    let ub_int = ub.value.real.floor().to_integer();

                    // Skip if variable is already fixed
                    if lb_int == ub_int {
                        continue;
                    }

                    (lb_int, ub_int, lb.reason, ub.reason)
                } else {
                    continue; // No bounds, skip
                }
            };

            // Probe lower bound: try x = lb_int
            self.simplex.push();
            let lb_val = Rational64::from_integer(lb_int);
            self.simplex.set_lower(var, lb_val, lb_reason);
            self.simplex.set_upper(var, lb_val, lb_reason); // Fix to lb

            let lb_feasible = self.simplex.check().is_ok();
            self.simplex.pop();

            if !lb_feasible {
                // Lower bound is infeasible, tighten: x >= lb + 1
                let new_lb = Rational64::from_integer(lb_int + 1);
                self.simplex.set_lower(var, new_lb, lb_reason);
                bounds_tightened += 1;
            }

            // Probe upper bound: try x = ub_int
            self.simplex.push();
            let ub_val = Rational64::from_integer(ub_int);
            self.simplex.set_lower(var, ub_val, ub_reason);
            self.simplex.set_upper(var, ub_val, ub_reason); // Fix to ub

            let ub_feasible = self.simplex.check().is_ok();
            self.simplex.pop();

            if !ub_feasible {
                // Upper bound is infeasible, tighten: x <= ub - 1
                let new_ub = Rational64::from_integer(ub_int - 1);
                self.simplex.set_upper(var, new_ub, ub_reason);
                bounds_tightened += 1;
            }

            // Check if probing fixed the variable (both bounds infeasible)
            if !lb_feasible && !ub_feasible {
                // Both bounds failed - problem is infeasible
                return Ok(bounds_tightened);
            }
        }

        Ok(bounds_tightened)
    }

    /// Manage cuts: age and delete ineffective cuts
    ///
    /// Cut management is crucial for LP solver efficiency. As branch-and-bound progresses,
    /// many cuts become ineffective (slack, never binding). Keeping too many cuts:
    /// - Increases LP solve time (larger constraint matrix)
    /// - Increases memory usage
    /// - Slows down warm-starting
    ///
    /// Strategy:
    /// 1. **Aging**: Increment age of all cuts after each LP solve
    /// 2. **Activity tracking**: Track how often cuts are tight/binding
    /// 3. **Deletion criteria**:
    ///    - Age > threshold AND activity == 0 (never binding)
    ///    - Age > high_threshold (old regardless of activity)
    ///    - Keep at most max_cuts most recent/active cuts
    ///
    /// Deletion heuristics:
    /// - Delete cuts with age > 100 and activity == 0
    /// - Delete cuts with age > 1000 regardless of activity
    /// - Keep only the 10,000 most recent cuts
    ///
    /// Reference:
    /// - Bixby & Rothberg, "Progress in Computational MIP" (2007)
    /// - Achterberg, "Constraint Integer Programming" (2007), Section 7.6
    /// - Modern solvers maintain ~5,000-50,000 active cuts
    ///
    /// Returns the number of cuts deleted.
    #[allow(dead_code)]
    pub fn manage_cuts(&mut self) -> usize {
        const AGE_THRESHOLD: u32 = 100;
        const HIGH_AGE_THRESHOLD: u32 = 1000;
        const MAX_CUTS: usize = 10_000;

        let mut deleted_count = 0;

        // Age all cuts
        for cut in &mut self.active_cuts {
            cut.age += 1;
        }

        // TODO: Update activity by checking if cuts are binding
        // This would require querying simplex for slack variable values
        // For now, we use a simpler age-based strategy

        // Delete cuts based on criteria
        self.active_cuts.retain(|cut| {
            let should_delete =
                // Delete old inactive cuts
                (cut.age > AGE_THRESHOLD && cut.activity == 0) ||
                // Delete very old cuts regardless of activity
                (cut.age > HIGH_AGE_THRESHOLD);

            if should_delete {
                deleted_count += 1;
                // TODO: Actually remove constraint from simplex tableau
                // This would require simplex API for constraint deletion
                false
            } else {
                true
            }
        });

        // Limit total number of cuts (keep most recent)
        if self.active_cuts.len() > MAX_CUTS {
            let to_remove = self.active_cuts.len() - MAX_CUTS;
            // Remove oldest cuts (they're at the beginning)
            self.active_cuts.drain(0..to_remove);
            deleted_count += to_remove;
        }

        deleted_count
    }

    /// Record that a cut was added (for tracking)
    #[allow(dead_code)]
    pub fn record_cut(&mut self, slack_var: VarId) {
        self.active_cuts.push(CutInfo {
            slack_var,
            age: 0,
            activity: 0,
            generation: self.cuts_generated,
        });
    }
}
