//! Schubert calculus on Grassmannians and flag varieties
//!
//! This module implements Schubert classes and their intersection theory
//! on Grassmannians and flag varieties.

use crate::{ChowClass, EnumerativeError, EnumerativeResult};
use num_rational::Rational64;
use std::collections::HashMap;

/// Schubert class indexed by a Young diagram/partition
#[derive(Debug, Clone, PartialEq)]
pub struct SchubertClass {
    /// The partition indexing this Schubert class
    pub partition: Vec<usize>,
    /// Dimension of the underlying Grassmannian
    pub grassmannian_dim: (usize, usize), // (k, n) for Gr(k, n)
}

impl SchubertClass {
    /// Create a new Schubert class
    pub fn new(partition: Vec<usize>, grassmannian_dim: (usize, usize)) -> EnumerativeResult<Self> {
        let (k, n) = grassmannian_dim;

        // Validate partition - allow longer partitions for generality
        // In some formulations, partitions can have more than k parts
        // The real constraint is that each part must be ≤ n-k

        for &part in &partition {
            if part > n - k {
                return Err(EnumerativeError::SchubertError(format!(
                    "Partition entry {} exceeds n-k = {}",
                    part,
                    n - k
                )));
            }
        }

        Ok(Self {
            partition,
            grassmannian_dim,
        })
    }

    /// Convert to a Chow class
    pub fn to_chow_class(&self) -> ChowClass {
        let codimension = self.partition.iter().sum::<usize>();
        let degree = Rational64::from(1); // Simplified - actual degree requires more computation

        ChowClass::new(codimension, degree)
    }

    /// Compute the dimension of this Schubert variety
    pub fn dimension(&self) -> usize {
        let (k, n) = self.grassmannian_dim;
        let total_dim = k * (n - k);
        let codim = self.partition.iter().sum::<usize>();
        total_dim - codim
    }

    /// Raise Schubert class to a power (repeated intersection)
    pub fn power(&self, exponent: usize) -> SchubertClass {
        // Simplified - real power requires sophisticated Schubert calculus
        let mut new_partition = self.partition.clone();
        for _ in 1..exponent {
            if !new_partition.is_empty() {
                new_partition[0] += 1;
            } else {
                new_partition.push(1);
            }
        }

        SchubertClass {
            partition: new_partition,
            grassmannian_dim: self.grassmannian_dim,
        }
    }

    /// Giambelli determinant formula
    pub fn giambelli_determinant(
        partition: &[usize],
        grassmannian_dim: (usize, usize),
    ) -> EnumerativeResult<Self> {
        // Simplified implementation - real Giambelli formula involves determinants
        // of matrices of special Schubert classes
        Self::new(partition.to_vec(), grassmannian_dim)
    }
}

/// Schubert calculus engine
#[derive(Debug)]
pub struct SchubertCalculus {
    /// The underlying Grassmannian
    pub grassmannian_dim: (usize, usize),
    /// Cache for computed intersection numbers
    intersection_cache: HashMap<(Vec<usize>, Vec<usize>), Rational64>,
}

impl SchubertCalculus {
    /// Create a new Schubert calculus engine
    pub fn new(grassmannian_dim: (usize, usize)) -> Self {
        Self {
            grassmannian_dim,
            intersection_cache: HashMap::new(),
        }
    }

    /// Compute intersection number of two Schubert classes
    pub fn intersection_number(
        &mut self,
        class1: &SchubertClass,
        class2: &SchubertClass,
    ) -> EnumerativeResult<Rational64> {
        // Check cache first
        let key = (class1.partition.clone(), class2.partition.clone());
        if let Some(&cached) = self.intersection_cache.get(&key) {
            return Ok(cached);
        }

        // Simplified computation - in practice this requires Littlewood-Richardson coefficients
        let result = if class1.dimension() + class2.dimension()
            == self.grassmannian_dim.0 * (self.grassmannian_dim.1 - self.grassmannian_dim.0)
        {
            // Expected dimension intersection
            Rational64::from(1)
        } else {
            Rational64::from(0)
        };

        // Cache the result
        self.intersection_cache.insert(key, result);
        Ok(result)
    }

    /// Multiply two Schubert classes using Pieri's rule (simplified)
    pub fn pieri_multiply(
        &self,
        schubert_class: &SchubertClass,
        special_class: usize,
    ) -> EnumerativeResult<Vec<SchubertClass>> {
        // Simplified Pieri rule - adds horizontal strips
        let mut results = Vec::new();
        let (k, n) = self.grassmannian_dim;

        // Option 1: Add to the first row (if it exists)
        if !schubert_class.partition.is_empty() {
            let mut new_partition = schubert_class.partition.clone();
            new_partition[0] += special_class;

            // Check if this partition is valid
            if new_partition[0] <= n - k {
                if let Ok(new_class) = SchubertClass::new(new_partition, self.grassmannian_dim) {
                    results.push(new_class);
                }
            }
        }

        // Option 2: Add a new row
        let mut new_partition = schubert_class.partition.clone();
        new_partition.push(special_class);

        // Check if this partition is valid
        if special_class <= n - k {
            if let Ok(new_class) = SchubertClass::new(new_partition, self.grassmannian_dim) {
                results.push(new_class);
            }
        }

        // If no valid results, return the original approach
        if results.is_empty() {
            let mut new_partition = schubert_class.partition.clone();
            if !new_partition.is_empty() {
                new_partition[0] += special_class;
            } else {
                new_partition.push(special_class);
            }
            results.push(SchubertClass::new(new_partition, self.grassmannian_dim)?);
        }

        Ok(results)
    }
}

/// Flag variety F(n1, n2, ..., nk; n)
#[derive(Debug, Clone)]
pub struct FlagVariety {
    /// Dimensions of the flags
    pub flag_dims: Vec<usize>,
    /// Ambient dimension
    pub ambient_dim: usize,
}

impl FlagVariety {
    /// Create a new flag variety
    pub fn new(flag_dims: Vec<usize>, ambient_dim: usize) -> EnumerativeResult<Self> {
        // Validate that flag dimensions are increasing
        for i in 1..flag_dims.len() {
            if flag_dims[i] <= flag_dims[i - 1] {
                return Err(EnumerativeError::SchubertError(
                    "Flag dimensions must be strictly increasing".to_string(),
                ));
            }
        }

        if flag_dims.last().copied().unwrap_or(0) >= ambient_dim {
            return Err(EnumerativeError::SchubertError(
                "Largest flag dimension must be less than ambient dimension".to_string(),
            ));
        }

        Ok(Self {
            flag_dims,
            ambient_dim,
        })
    }

    /// Compute the dimension of the flag variety
    pub fn dimension(&self) -> usize {
        let mut dim = 0;
        let mut prev_dim = 0;

        for &flag_dim in &self.flag_dims {
            // Contribution: (current_dim - previous_dim) × (ambient_dim - previous_dim)
            dim += (flag_dim - prev_dim) * (self.ambient_dim - prev_dim);
            prev_dim = flag_dim;
        }

        dim
    }
}
