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defmodule JsonRemedy.FastEditDistance do
  @moduledoc """
  Sub-cubic edit distance using algebraic techniques.
  Based on recent advances in tropical matrix multiplication.
  """
  
  @doc """
  Computes edit distance in O(n^{2.373}) time using Coppersmith-Winograd
  matrix multiplication for large inputs.
  """
  def fast_edit_distance(string1, string2) when length(string1) > 1000 do
    # Convert to tropical semiring matrix multiplication
    # Key insight: edit distance = tropical matrix product
    
    m = length(string1)
    n = length(string2)
    
    # Build convolution matrices in tropical semiring
    conv_matrix1 = build_convolution_matrix(string1)
    conv_matrix2 = build_convolution_matrix(string2)
    
    # Use fast matrix multiplication (Strassen, Coppersmith-Winograd)
    result_matrix = tropical_matrix_multiply(conv_matrix1, conv_matrix2)
    
    extract_edit_distance(result_matrix, m, n)
  end
  
  # Use standard DP for smaller inputs where overhead doesn't pay off
  def fast_edit_distance(string1, string2) do
    standard_wagner_fischer(string1, string2)
  end
  
  defp tropical_matrix_multiply(a, b) do
    # Implement tropical semiring: (min, +) instead of (+, *)
    # This allows leveraging fast matrix multiplication algorithms
    # for edit distance computation
    
    # Modern implementation would use:
    # - Strassen's algorithm for moderate sizes
    # - Coppersmith-Winograd variants for very large matrices
    # - GPU acceleration for parallel tropical operations
  end
end

defmodule JsonRemedy.CompressedAutomaton do
  @moduledoc """
  Uses Binary Decision Diagrams (BDDs) and compressed tries
  for efficient continuation string generation.
  """
  
  @type bdd_node :: %{
    variable: atom(),
    low: bdd_node() | boolean(),
    high: bdd_node() | boolean(),
    cached_continuations: MapSet.t()
  }
  
  @doc """
  Build compressed representation of the LR automaton using BDDs.
  Reduces space from O(|Q| * |Σ|) to O(log(|Q| * |Σ|)) for sparse tables.
  """
  def build_compressed_lr_tables(grammar) do
    # Classical LR table construction
    lr_items = compute_lr1_items(grammar)
    action_table = build_action_table(lr_items)
    goto_table = build_goto_table(lr_items)
    
    # Compress using BDDs - exploits sparsity in LR tables
    compressed_action = compress_table_to_bdd(action_table)
    compressed_goto = compress_table_to_bdd(goto_table)
    
    %{
      action_bdd: compressed_action,
      goto_bdd: compressed_goto,
      # Precompute common continuation patterns
      continuation_cache: build_continuation_cache(lr_items)
    }
  end
  
  @doc """
  Generate continuation strings using compressed representation.
  O(log k) lookup instead of O(k) table scan.
  """
  def generate_continuations_compressed(parser_state, compressed_tables, max_length) do
    # Use BDD traversal for efficient state exploration
    explore_continuations_bdd(
      parser_state,
      compressed_tables.action_bdd,
      max_length,
      []
    )
  end
  
  defp explore_continuations_bdd(state, bdd_node, remaining_length, current_string) 
    when remaining_length <= 0 do
    [current_string]
  end
  
  defp explore_continuations_bdd(state, bdd_node, remaining_length, current_string) do
    # BDD traversal: follow both branches efficiently
    # Cache results at each node to avoid recomputation
    
    case Map.get(bdd_node.cached_continuations, {state, remaining_length}) do
      nil ->
        result = compute_continuations_at_node(state, bdd_node, remaining_length, current_string)
        # Update cache
        updated_cache = Map.put(bdd_node.cached_continuations, {state, remaining_length}, result)
        result
        
      cached_result ->
        cached_result
    end
  end
end

defmodule JsonRemedy.ApproximateMatching do
  @moduledoc """
  Uses suffix trees and approximate string matching for efficient
  continuation string search with bounded error.
  """
  
  @doc """
  Build suffix tree of all valid JSON strings up to length k.
  Allows O(m) approximate matching for error distance ≤ d.
  """
  def build_json_suffix_tree(max_depth) do
    # Generate representative valid JSON strings
    valid_strings = generate_json_corpus(max_depth)
    
    # Build generalized suffix tree
    suffix_tree = build_suffix_tree(valid_strings)
    
    # Augment with error bounds for approximate matching
    augment_with_error_bounds(suffix_tree)
  end
  
  @doc """
  Ukkonen's algorithm variant for bounded edit distance.
  Finds all suffixes within edit distance k in O(mn) time where
  n is pattern length, m is text length.
  """
  def approximate_match_continuations(malformed_suffix, suffix_tree, max_edit_distance) do
    # Use Ukkonen's finite automaton for bounded edit distance
    error_automaton = build_ukkonen_automaton(malformed_suffix, max_edit_distance)
    
    # Traverse suffix tree with error automaton
    matches = traverse_with_error_bounds(suffix_tree, error_automaton)
    
    # Return continuations sorted by edit distance
    Enum.sort_by(matches, &elem(&1, 1))
  end
  
  defp build_ukkonen_automaton(pattern, k) do
    # Build NFA that accepts all strings within edit distance k of pattern
    # States are (position, errors_made)
    # Transitions are match, insert, delete, substitute
    
    states = for i <- 0..String.length(pattern), j <- 0..k, do: {i, j}
    
    transitions = build_error_transitions(pattern, k)
    
    %{
      states: states,
      transitions: transitions,
      initial_state: {0, 0},
      accepting_states: Enum.filter(states, fn {i, j} -> i == String.length(pattern) end)
    }
  end
end

defmodule JsonRemedy.ParallelCorrection do
  @moduledoc """
  Parallel algorithms for error correction using work-stealing
  and streaming processing for large JSON documents.
  """
  
  @doc """
  Parallel edit distance computation using divide-and-conquer.
  Achieves O(mn/p) time on p processors with optimal load balancing.
  """
  def parallel_edit_distance(string1, string2, num_workers \\ System.schedulers()) do
    # Divide problem using anti-diagonal decomposition
    # Each worker processes a band of the DP matrix
    
    m = String.length(string1)
    n = String.length(string2)
    
    # Calculate optimal band width for load balancing
    band_width = div(max(m, n), num_workers)
    
    # Launch parallel workers
    tasks = for i <- 0..(num_workers-1) do
      Task.async(fn ->
        start_row = i * band_width
        end_row = min((i + 1) * band_width, m)
        compute_band(string1, string2, start_row, end_row)
      end)
    end
    
    # Collect and merge results
    results = Task.await_many(tasks)
    merge_band_results(results)
  end
  
  @doc """
  Streaming algorithm for error correction of large JSON files.
  Uses bounded memory regardless of input size.
  """
  def streaming_correction(json_stream, grammar_automaton) do
    # Process JSON in chunks with overlapping windows
    # Maintain minimal state for error recovery
    
    Stream.transform(json_stream, initial_state(), fn chunk, state ->
      {corrected_chunk, new_state} = process_chunk_with_overlap(chunk, state, grammar_automaton)
      {[corrected_chunk], new_state}
    end)
  end
  
  defp process_chunk_with_overlap(chunk, state, automaton) do
    # Key insight: maintain overlap buffer to handle errors at chunk boundaries
    overlap_size = 100  # Sufficient for most JSON error patterns
    
    {overlap_buffer, processing_chunk} = split_chunk(chunk, overlap_size)
    
    # Process with current automaton state
    {corrected, new_automaton_state} = 
      correct_chunk(processing_chunk, state.automaton_state, automaton)
    
    # Update state with new buffer
    new_state = %{state | 
      overlap_buffer: overlap_buffer,
      automaton_state: new_automaton_state
    }
    
    {corrected, new_state}
  end
end

defmodule JsonRemedy.AdaptiveCosts do
  @moduledoc """
  Uses online learning to adapt edit costs based on correction patterns.
  Implements regret minimization for optimal cost learning.
  """
  
  @doc """
  Online learning algorithm that adapts edit costs based on user feedback
  or validation against known correct JSON.
  """
  def adaptive_correction(input, current_costs, learning_rate \\ 0.01) do
    # Generate multiple correction candidates with current costs
    candidates = generate_candidate_corrections(input, current_costs)
    
    # Use multi-armed bandit approach to select best candidate
    selected_candidate = select_with_ucb1(candidates, current_costs.selection_stats)
    
    # Return correction and cost update function
    {selected_candidate, fn feedback ->
      update_costs_with_feedback(current_costs, selected_candidate, feedback, learning_rate)
    end}
  end
  
  @doc """
  Use contextual bandits to learn context-dependent edit costs.
  Different JSON contexts (arrays, objects, strings) have different error patterns.
  """
  def contextual_cost_learning(error_context, available_actions, history) do
    # Feature vector for current context
    features = extract_context_features(error_context)
    
    # Linear model: cost = features^T * weights + bias
    predicted_costs = for action <- available_actions do
      {action, compute_predicted_cost(features, action, history.model_weights)}
    end
    
    # Thompson sampling for exploration-exploitation trade-off
    selected_action = thompson_sampling(predicted_costs, history.uncertainty)
    
    {selected_action, update_model_fn(features, history)}
  end
  
  defp extract_context_features(context) do
    %{
      # Structural features
      nesting_depth: context.stack_depth,
      context_type: encode_context_type(context.current),
      recent_tokens: encode_token_sequence(context.last_tokens),
      
      # Syntactic features  
      bracket_balance: compute_bracket_balance(context),
      quote_state: context.in_string,
      
      # Semantic features
      expected_next_token: predict_next_token(context),
      error_distance: context.position - context.last_valid_position
    }
  end
end

defmodule JsonRemedy.CacheOptimized do
  @moduledoc """
  Cache-oblivious algorithms for edit distance and continuation generation.
  Optimized for modern CPU cache hierarchies.
  """
  
  @doc """
  Cache-oblivious edit distance using recursive divide-and-conquer.
  Achieves optimal cache complexity O(mn/B + (m+n)) where B is cache line size.
  """
  def cache_oblivious_edit_distance(string1, string2) do
    m = String.length(string1)
    n = String.length(string2)
    
    # Use recursive decomposition that adapts to cache size automatically
    # No explicit cache parameters needed - algorithm is cache-oblivious
    
    edit_distance_recursive(string1, string2, 0, 0, m, n, %{})
  end
  
  defp edit_distance_recursive(s1, s2, i1, j1, i2, j2, memo) 
    when i2 - i1 <= 64 and j2 - j1 <= 64 do
    # Base case: use standard DP for small subproblems (fits in L1 cache)
    compute_base_case_dp(s1, s2, i1, j1, i2, j2)
  end
  
  defp edit_distance_recursive(s1, s2, i1, j1, i2, j2, memo) do
    # Recursive case: divide along longer dimension
    cache_key = {i1, j1, i2, j2}
    
    case Map.get(memo, cache_key) do
      nil ->
        result = if i2 - i1 > j2 - j1 do
          # Divide vertically
          mid = div(i1 + i2, 2)
          
          # Find optimal crossing point using Hirschberg's technique
          crossing_point = find_optimal_crossing(s1, s2, i1, j1, mid, j2)
          
          # Recursively solve subproblems
          left_cost = edit_distance_recursive(s1, s2, i1, j1, mid, crossing_point, memo)
          right_cost = edit_distance_recursive(s1, s2, mid, crossing_point, i2, j2, memo)
          
          left_cost + right_cost
        else
          # Divide horizontally
          mid = div(j1 + j2, 2)
          crossing_point = find_optimal_crossing_horizontal(s1, s2, i1, j1, i2, mid)
          
          left_cost = edit_distance_recursive(s1, s2, i1, j1, crossing_point, mid, memo)
          right_cost = edit_distance_recursive(s1, s2, crossing_point, mid, i2, j2, memo)
          
          left_cost + right_cost
        end
        
        updated_memo = Map.put(memo, cache_key, result)
        result
        
      cached_result ->
        cached_result
    end
  end
  
  @doc """
  SIMD-optimized edit distance for modern processors.
  Uses vectorized operations for parallel computation of DP cells.
  """
  def simd_edit_distance(string1, string2) when byte_size(string1) < 10000 do
    # Convert strings to byte arrays for SIMD processing
    bytes1 = :binary.bin_to_list(string1)
    bytes2 = :binary.bin_to_list(string2)
    
    # Process multiple DP cells in parallel using SIMD instructions
    # Each vector lane computes one anti-diagonal of the DP matrix
    
    # Note: This would require NIFs or external libraries for actual SIMD
    # Elixir implementation uses binary pattern matching optimization
    simd_optimized_dp(bytes1, bytes2)
  end
end

defmodule JsonRemedy.ApproximationAlgorithms do
  @moduledoc """
  Approximation algorithms for error correction with theoretical guarantees.
  Provides (1+ε)-approximation for edit distance in near-linear time.
  """
  
  @doc """
  (1+ε)-approximation algorithm for edit distance.
  Runs in O(n^{1+ε}) time instead of O(n^2).
  """
  def approximate_edit_distance(string1, string2, epsilon \\ 0.1) do
    # Use sampling-based approach with theoretical guarantees
    # Based on recent work in sublinear algorithms
    
    n = max(String.length(string1), String.length(string2))
    sample_size = ceil(1.0 / (epsilon * epsilon) * :math.log(n))
    
    # Sample random positions and estimate edit distance
    samples = sample_positions(string1, string2, sample_size)
    
    # Use importance sampling to estimate global edit distance
    estimated_distance = estimate_from_samples(samples, epsilon)
    
    # Return estimate with confidence bounds
    confidence_interval = compute_confidence_bounds(estimated_distance, epsilon, sample_size)
    
    %{
      estimated_distance: estimated_distance,
      lower_bound: confidence_interval.lower,
      upper_bound: confidence_interval.upper,
      confidence: 1.0 - epsilon
    }
  end
  
  @doc """
  Randomized algorithm for continuation string generation.
  Provides ε-optimal solutions in O(log(1/ε)) expected time.
  """
  def randomized_continuation_search(parser_state, grammar_automaton, epsilon) do
    # Use random sampling of the continuation space
    # with theoretical guarantees on solution quality
    
    iterations = ceil(:math.log(1.0 / epsilon) / epsilon)
    
    best_continuation = nil
    best_cost = :infinity
    
    for _i <- 1..iterations do
      # Random walk in continuation space
      candidate = random_walk_continuation(parser_state, grammar_automaton)
      cost = evaluate_continuation_cost(candidate)
      
      if cost < best_cost do
        best_continuation = candidate
        best_cost = cost
      end
    end
    
    # Theoretical guarantee: with probability ≥ 1-ε, 
    # returned solution is within factor (1+ε) of optimal
    {best_continuation, best_cost}
  end
end