# models a set of identical dice, that can be "rolled" and combined into a simple integer result. The
# dice are identical in number of sides, and any re-roll or mapping rules that apply to them
class GamesDice::Bunch
  # attributes is a hash of symbols used to set attributes of the new Bunch object. Each
  # attribute is explained in more detail in its own section. The following hash keys and values
  # are mandatory:
  #  :ndice
  #  :sides
  # The following are optional, and modify the behaviour of the Bunch object
  #  :name
  #  :prng
  #  :rerolls
  #  :maps
  #  :keep_mode
  #  :keep_number
  # Any other keys provided to the constructor are ignored
  def initialize( attributes )
    @name = attributes[:name].to_s
    @ndice = Integer(attributes[:ndice])
    raise ArgumentError, ":ndice must be 1 or more, but got #{@ndice}" unless @ndice > 0
    @sides = Integer(attributes[:sides])
    raise ArgumentError, ":sides must be 1 or more, but got #{@sides}" unless @sides > 0

    options = Hash.new

    if attributes[:prng]
      # We deliberately do not clone this object, it will often be intended that it is shared
      prng = attributes[:prng]
      raise ":prng does not support the rand() method" if ! prng.respond_to?(:rand)
    end

    needs_complex_die = false

    if attributes[:rerolls]
      needs_complex_die = true
      options[:rerolls] = attributes[:rerolls].clone
    end

    if attributes[:maps]
      needs_complex_die = true
      options[:maps] = attributes[:maps].clone
    end

    if needs_complex_die
      options[:prng] = prng
      @single_die = GamesDice::ComplexDie.new( @sides, options )
    else
      @single_die = GamesDice::Die.new( @sides, prng )
    end

    case attributes[:keep_mode]
    when nil then
      @keep_mode = nil
    when :keep_best then
      @keep_mode = :keep_best
      @keep_number = Integer(attributes[:keep_number] || 1)
    when :keep_worst then
      @keep_mode = :keep_worst
      @keep_number = Integer(attributes[:keep_number] || 1)
    else
      raise ArgumentError, ":keep_mode can be nil, :keep_best or :keep_worst. Got #{attributes[:keep_mode].inspect}"
    end
  end

  # the string name as provided to the constructor, it will appear in explain_result
  attr_reader :name

  # integer number of dice to roll (initially, before re-rolls etc)
  attr_reader :ndice

  # individual die that will be rolled, #ndice times, an GamesDice::Die or GamesDice::ComplexDie object.
  attr_reader :single_die

  # may be nil, :keep_best or :keep_worst
  attr_reader :keep_mode

  # number of "best" or "worst" results to select when #keep_mode is not nil. This attribute is
  # 1 by default if :keep_mode is supplied, or nil by default otherwise.
  attr_reader :keep_number

  # after calling #roll, this is set to the final integer value from using the dice as specified
  attr_reader :result

  # Needs refinement. Returns best available string description of the bunch.
  def label
    return @name if @name != ''
    return @ndice.to_s + 'd' + @sides.to_s
  end

  # either nil, or an array of GamesDice::RerollRule objects that are assessed on each roll of #single_die
  # Reroll types :reroll_new_die and :reroll_new_keeper do not affect the #single_die, but are instead
  # assessed in this container object
  def rerolls
    @single_die.rerolls
  end

  # either nil, or an array of GamesDice::MapRule objects that are assessed on each result of #single_die (after rerolls are completed)
  def maps
    @single_die.rerolls
  end

  # after calling #roll, this is an array of GamesDice::DieResult objects, one from each #single_die rolled,
  # allowing inspection of how the result was obtained.
  def result_details
    return nil unless @raw_result_details
    @raw_result_details.map { |r| r.is_a?(Fixnum) ? GamesDice::DieResult.new(r) : r }
  end

  # minimum possible integer value
  def min
    n = @keep_mode ? [@keep_number,@ndice].min : @ndice
    return n * @single_die.min
  end

  # maximum possible integer value
  def max
    n = @keep_mode ? [@keep_number,@ndice].min : @ndice
    return n * @single_die.max
  end

  # returns a hash of value (Integer) => probability (Float) pairs. Warning: Some dice schemes
  # cause this method to take a long time, and use a lot of memory. The worst-case offenders are
  # dice schemes with a #keep_mode of :keep_best or :keep_worst.
  def probabilities
    return @probabilities if @probabilities
    @probabilities_complete = true

    # TODO: It is possible to optimise this slightly by combining already-calculated values
    # Adding dice is same as multiplying probability sets for that number of dice
    # Combine(probabililities_3_dice, probabililities_single_die) == Combine(probabililities_2_dice, probabililities_2_dice)
    # It is possible to minimise the total number of multiplications, gaining about 30% efficiency, with careful choices
    single_roll_probs = @single_die.probabilities.to_h
    if @keep_mode && @ndice > @keep_number
      preadd_probs = {}
      single_roll_probs.each { |k,v| preadd_probs[k.to_s] = v }

      (@keep_number-1).times do
        preadd_probs = prob_accumulate_combinations preadd_probs, single_roll_probs
      end
      extra_dice = @ndice - @keep_number
      extra_dice.times do
        preadd_probs = prob_accumulate_combinations preadd_probs, single_roll_probs, @keep_mode
      end
      combined_probs = {}
      preadd_probs.each do |k,v|
        total = k.split(';').map { |s| s.to_i }.inject(:+)
        combined_probs[total] ||= 0.0
        combined_probs[total] += v
      end
    else
      combined_probs = single_roll_probs.clone
      (@ndice-1).times do
        combined_probs = prob_accumulate combined_probs, single_roll_probs
      end
    end

    @probabilities_min, @probabilities_max = combined_probs.keys.minmax
    @probabilities = GamesDice::Probabilities.new( combined_probs )
  end

  # simulate dice roll according to spec. Returns integer final total, and also stores it in #result
  def roll
    @result = 0
    @raw_result_details = []

    @ndice.times do
      @result += @single_die.roll
      @raw_result_details << @single_die.result
    end

    if ! @keep_mode
      return @result
    end

    use_dice = if @keep_mode && @keep_number < @ndice
      case @keep_mode
      when :keep_best then @raw_result_details.sort[-@keep_number..-1]
      when :keep_worst then @raw_result_details.sort[0..(@keep_number-1)]
      end
    else
      @raw_result_details
    end

    @result = use_dice.inject(0) { |so_far, die_result| so_far + die_result }
  end

  def explain_result
    return nil unless @result

    explanation = ''

    # With #keep_mode, we may need to show unused and used dice separately
    used_dice = result_details
    unused_dice = []

    # Pick highest numbers and their associated details
    if @keep_mode && @keep_number < @ndice
      full_dice = result_details.sort_by { |die_result| die_result.total }
      case @keep_mode
      when :keep_best then
        used_dice = full_dice[-@keep_number..-1]
        unused_dice = full_dice[0..full_dice.length-1-@keep_number]
      when :keep_worst then
        used_dice = full_dice[0..(@keep_number-1)]
        unused_dice = full_dice[@keep_number..(full_dice.length-1)]
      end
    end

    # Show unused dice (if any)
    if @keep_mode || @single_die.maps
      explanation += result_details.map do |die_result|
        die_result.explain_value
      end.join(', ')
      if @keep_mode
        separator = @single_die.maps ? ', ' : ' + '
        explanation += ". Keep: " + used_dice.map do |die_result|
          die_result.explain_total
        end.join( separator )
      end
      if @single_die.maps
        explanation += ". Successes: #{@result}"
      end
      explanation += " = #{@result}" if @keep_mode && ! @single_die.maps && @keep_number > 1
    else
      explanation += used_dice.map do |die_result|
        die_result.explain_value
      end.join(' + ')
      explanation += " = #{@result}" if @ndice > 1
    end

    explanation
  end

  private

  # combines two sets of probabilities where the end result is the first set of keys plus
  # the second set of keys, at the associated probailities of the values
  def prob_accumulate first_probs, second_probs
    accumulator = Hash.new

    first_probs.each do |v1,p1|
      second_probs.each do |v2,p2|
        v3 = v1 + v2
        p3 = p1 * p2
        accumulator[v3] ||= 0.0
        accumulator[v3] += p3
      end
    end

    accumulator
  end

  # combines two sets of probabilities, as above, except tracking unique permutations
  def prob_accumulate_combinations so_far, die_probs, keep_rule = nil
    accumulator = Hash.new

    so_far.each do |sig,p1|
      combo = sig.split(';').map { |s| s.to_i }

      case keep_rule
      when nil then
        die_probs.each do |v2,p2|
          new_sig = (combo + [v2]).sort.join(';')
          p3 = p1 * p2
          accumulator[new_sig] ||= 0.0
          accumulator[new_sig] += p3
        end
      when :keep_best then
        need_more_than = combo.min
        die_probs.each do |v2,p2|
          if v2 > need_more_than
            new_sig = (combo + [v2]).sort[1..combo.size].join(';')
          else
            new_sig = sig
          end
          p3 = p1 * p2
          accumulator[new_sig] ||= 0.0
          accumulator[new_sig] += p3
        end
      when :keep_worst then
        need_less_than = combo.max
        die_probs.each do |v2,p2|
          if v2 < need_less_than
            new_sig = (combo + [v2]).sort[0..(combo.size-1)].join(';')
          else
            new_sig = sig
          end
          p3 = p1 * p2
          accumulator[new_sig] ||= 0.0
          accumulator[new_sig] += p3
        end
      end
    end

    accumulator
  end

  # Generates all sets of [throw_away,may_keep_exactly,keep_preferentially,combinations] that meet
  # criteria for correct total number of dice and keep dice. These then need to be assessed for every
  # die value by the caller to get a full set of probabilities
  def generate_item_counts total_dice, keep_dice
    # Constraints are:
    # may_keep_exactly must be at least 1, and at most is all the dice
    # keep_preferentially plus may_keep_exactly must be >= keep_dice, but keep_preferentially < keep dice
    # sum of all three always == total_dice
    item_counts = []
    (1..total_dice).each do |may_keep_exactly|
      min_kp = [keep_dice - may_keep_exactly, 0].max
      max_kp = [keep_dice - 1, total_dice - may_keep_exactly].min
      (min_kp..max_kp).each do |keep_preferentially|
        counts = [ total_dice - may_keep_exactly - keep_preferentially, may_keep_exactly, keep_preferentially ]
        counts << combinations(counts)
        item_counts << counts
      end
    end
    item_counts
  end

  # How many unique ways can a set of items, some of which are identical, be arranged?
  def combinations item_counts
    item_counts = item_counts.map { |i| Integer(i) }.select { |i| i > 0 }
    total_items = item_counts.inject(:+)
    numerator = 1.upto(total_items).inject(:*)
    denominator = item_counts.map { |i| 1.upto(i).inject(:*) }.inject(:*)
    numerator / denominator
  end

end # class Bunch