canvas-lms/lib/grade_calculator.rb

#
# Copyright (C) 2011 - present Instructure, Inc.
#
# This file is part of Canvas.
#
# Canvas is free software: you can redistribute it and/or modify it under
# the terms of the GNU Affero General Public License as published by the Free
# Software Foundation, version 3 of the License.
#
# Canvas is distributed in the hope that it will be useful, but WITHOUT ANY
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
# A PARTICULAR PURPOSE. See the GNU Affero General Public License for more
# details.
#
# You should have received a copy of the GNU Affero General Public License along
# with this program. If not, see <http://www.gnu.org/licenses/>.
#

class GradeCalculator
  attr_accessor :assignments, :groups

  def initialize(user_ids, course, opts = {})
    opts = opts.reverse_merge(
      ignore_muted: true,
      update_all_grading_period_scores: true,
      update_course_score: true,
      only_update_course_gp_metadata: false
    )

    Rails.logger.info("GRADES: calc args: user_ids=#{user_ids.inspect}")
    Rails.logger.info("GRADES: calc args: course=#{course.inspect}")
    Rails.logger.info("GRADES: calc args: opts=#{opts.inspect}")

    @course = course.is_a?(Course) ? course : Course.find(course)

    @groups = opts[:groups] || @course.assignment_groups.active.to_a
    @grading_period = opts[:grading_period]
    # if we're updating an overall course score (no grading period specified), we
    # want to first update all grading period scores for the users
    @update_all_grading_period_scores = @grading_period.nil? && opts[:update_all_grading_period_scores]
    # if we're updating a grading period score, we also need to update the
    # overall course score
    @update_course_score = @grading_period.present? && opts[:update_course_score]
    @assignments = opts[:assignments] || @course.assignments.published.gradeable.to_a

    @user_ids = Array(user_ids).map { |id| Shard.relative_id_for(id, Shard.current, @course.shard) }
    @current_updates = {}
    @final_updates = {}
    @dropped_updates = {}
    @current_groups = {}
    @final_groups = {}
    # The developers of the future, I leave you this gift:
    #   If you add a new options here, make sure you also update the
    #   opts in the compute_branch method
    @ignore_muted = opts[:ignore_muted]
    @effective_due_dates = opts[:effective_due_dates]
    @enrollments = opts[:enrollments]
    @periods = opts[:periods]
    @submissions = opts[:submissions]
    @only_update_course_gp_metadata = opts[:only_update_course_gp_metadata]
  end

  # recomputes the scores and saves them to each user's Enrollment
  def self.recompute_final_score(user_ids, course_id, compute_score_opts = {})
    user_ids = Array(user_ids).uniq.map(&:to_i)
    return if user_ids.empty?
    course = course_id.is_a?(Course) ? course_id : Course.active.where(id: course_id).take
    return unless course

    assignments = compute_score_opts[:assignments] || course.assignments.published.gradeable.to_a
    groups = compute_score_opts[:groups] || course.assignment_groups.active.to_a
    periods = compute_score_opts[:periods] || GradingPeriod.for(course)
    grading_period_id = compute_score_opts.delete(:grading_period_id)
    grading_period = periods.find_by(id: grading_period_id) if grading_period_id
    opts = compute_score_opts.reverse_merge(
      grading_period: grading_period,
      assignments: assignments,
      groups: groups,
      periods: periods
    )
    user_ids.in_groups_of(1000, false) do |user_ids_group|
      GradeCalculator.new(user_ids_group, course, opts).compute_and_save_scores
    end
  end

  def submissions
    @submissions ||= @course.submissions.
      except(:order, :select).
      for_user(@user_ids).
      where(assignment_id: @assignments).
      select("submissions.id, user_id, assignment_id, score, excused, submissions.workflow_state")
  end

  def compute_scores
    scores_and_group_sums = []
    @user_ids.each_slice(100) do |batched_ids|
      scores_and_group_sums_batch = compute_scores_and_group_sums_for_batch(batched_ids)
      scores_and_group_sums.concat(scores_and_group_sums_batch)
    end
    scores_and_group_sums
  end

  def compute_and_save_scores
    calculate_grading_period_scores if @update_all_grading_period_scores
    compute_scores
    save_scores
    invalidate_caches
    # The next line looks weird, but it is intended behaviour.  Its
    # saying "if we're on the branch not calculating muted scores, run
    # the branch that does."
    calculate_muted_scores if @ignore_muted
    calculate_course_score if @update_course_score
  end

  private

  def effective_due_dates
    @effective_due_dates ||= EffectiveDueDates.for_course(@course, @assignments).filter_students_to(@user_ids)
  end

  def compute_scores_and_group_sums_for_batch(user_ids)
    user_ids.map do |user_id|
      next unless enrollments_by_user[user_id].first
      group_sums = compute_group_sums_for_user(user_id)
      scores = compute_scores_for_user(user_id, group_sums)
      update_changes_hash_for_user(user_id, scores, group_sums)
      {
        current: scores[:current],
        current_groups: group_sums[:current].index_by { |group| group[:id] },
        final: scores[:final],
        final_groups: group_sums[:final].index_by { |group| group[:id] }
      }
    end.compact
  end

  def assignment_visible_to_student?(assignment_id, user_id)
    effective_due_dates.find_effective_due_date(user_id, assignment_id).key?(:due_at)
  end

  def compute_group_sums_for_user(user_id)
    user_submissions = submissions_by_user.fetch(user_id, []).select do |submission|
      assignment_visible_to_student?(submission.assignment_id, user_id)
    end

    {
      current: create_group_sums(user_submissions, user_id, ignore_ungraded: true),
      final: create_group_sums(user_submissions, user_id, ignore_ungraded: false)
    }
  end

  def compute_scores_for_user(user_id, group_sums)
    if compute_course_scores_from_weighted_grading_periods?
      scores = calculate_total_from_weighted_grading_periods(user_id)
    else
      scores = {
        current: calculate_total_from_group_scores(group_sums[:current]),
        final: calculate_total_from_group_scores(group_sums[:final])
      }
    end
    Rails.logger.info "GRADES: calculated: #{scores.inspect}"
    scores
  end

  def update_changes_hash_for_user(user_id, scores, group_sums)
    @current_updates[user_id] = scores[:current][:grade]
    @final_updates[user_id] = scores[:final][:grade]
    @current_groups[user_id] = group_sums[:current]
    @final_groups[user_id] = group_sums[:final]
    @dropped_updates[user_id] = {
      current: {dropped: scores[:current][:dropped]},
      final: {dropped: scores[:final][:dropped]}
    }
  end

  def grading_period_scores(enrollment_id)
    @grading_period_scores ||= Score.active.where(
      enrollment: enrollments.map(&:id),
      grading_period: grading_periods_for_course.map(&:id)
    ).group_by(&:enrollment_id)
    @grading_period_scores[enrollment_id] || []
  end

  def calculate_total_from_weighted_grading_periods(user_id)
    enrollment = enrollments_by_user[user_id].first
    grading_period_scores = grading_period_scores(enrollment.id)
    scores = apply_grading_period_weights_to_scores(grading_period_scores)
    scale_and_round_scores(scores, grading_period_scores)
  end

  def apply_grading_period_weights_to_scores(grading_period_scores)
    grading_period_scores.each_with_object(
      { current: { full_weight: 0.0, grade: 0.0 }, final: { full_weight: 0.0, grade: 0.0 } }
    ) do |score, scores|
      weight = grading_period_weights[score.grading_period_id] || 0.0
      scores[:final][:full_weight] += weight
      scores[:current][:full_weight] += weight if score.current_score
      scores[:current][:grade] += (score.current_score || 0.0) * (weight / 100.0)
      scores[:final][:grade] += (score.final_score || 0.0) * (weight / 100.0)
    end
  end

  def scale_and_round_scores(scores, grading_period_scores)
    [:current, :final].each_with_object({ current: {}, final: {} }) do |score_type, adjusted_scores|
      score = scores[score_type][:grade]
      full_weight = scores[score_type][:full_weight]
      score = scale_score_up(score, full_weight) if full_weight < 100
      if score == 0.0 && score_type == :current && grading_period_scores.none?(&:current_score)
        score = nil
      end
      adjusted_scores[score_type][:grade] = score ? score.round(2) : score
    end
  end

  def scale_score_up(score, weight)
    return 0.0 if weight.zero?
    (score * 100.0) / weight
  end

  def compute_course_scores_from_weighted_grading_periods?
    return @compute_from_weighted_periods if @compute_from_weighted_periods.present?

    if @grading_period || grading_periods_for_course.empty?
      @compute_from_weighted_periods = false
    else
      @compute_from_weighted_periods = grading_periods_for_course.first.grading_period_group.weighted?
    end
  end

  def grading_periods_for_course
    @periods ||= GradingPeriod.for(@course)
  end

  def grading_period_weights
    @grading_period_weights ||= grading_periods_for_course.each_with_object({}) do |period, weights|
        weights[period.id] = period.weight
    end
  end

  def submissions_by_user
    @submissions_by_user ||= submissions.group_by {|s| Shard.relative_id_for(s.user_id, Shard.current, @course.shard) }
  end

  def compute_branch(opts = {})
    opts = opts.reverse_merge(
      groups: @groups,
      grading_period: @grading_period,
      update_all_grading_period_scores: false,
      update_course_score: false,
      assignments: @assignments,
      ignore_muted: @ignore_muted,
      periods: grading_periods_for_course,
      effective_due_dates: effective_due_dates,
      enrollments: enrollments,
      submissions: submissions,
      only_update_course_gp_metadata: @only_update_course_gp_metadata
    )
    GradeCalculator.new(@user_ids, @course, opts).compute_and_save_scores
  end

  def calculate_muted_scores
    # re-run this calculator, except include muted assignments
    compute_branch(ignore_muted: false)
  end

  def calculate_grading_period_scores
    grading_periods_for_course.each do |grading_period|
      # update this grading period score
      compute_branch(grading_period: grading_period)
    end

    # delete any grading period scores that are no longer relevant
    grading_period_ids = grading_periods_for_course.empty? ? nil : grading_periods_for_course.map(&:id)
    @course.shard.activate do
      Score.active.joins(:enrollment).
        where(enrollments: {user_id: @user_ids, course_id: @course.id}).
        where.not(grading_period_id: grading_period_ids).
        update_all(workflow_state: :deleted)
    end
  end

  def calculate_course_score
    # update the overall course score now that we've finished
    # updating the grading period score
    compute_branch(grading_period: nil)
  end

  def enrollments
    @enrollments ||= Enrollment.shard(@course.shard).active.
      where(user_id: @user_ids, course_id: @course.id).
      select(:id, :user_id, :workflow_state)
  end

  def joined_enrollment_ids
    # use local_id because we'll exec the query on the enrollment's shard
    @joined_enrollment_ids ||= enrollments.map(&:local_id).join(',')
  end

  def enrollments_by_user
    @enrollments_by_user ||= begin
      hsh = enrollments.group_by {|e| Shard.relative_id_for(e.user_id, Shard.current, @course.shard) }
      hsh.default = []
      hsh
    end
  end

  def number_or_null(score)
    # GradeCalculator sometimes divides by 0 somewhere,
    # resulting in NaN. Treat that as null here
    score = nil if score.try(:nan?)
    score || 'NULL::float'
  end

  def group_score_rows
    enrollments_by_user.keys.map do |user_id|
      current = @current_groups[user_id].pluck(:global_id, :grade).to_h
      final = @final_groups[user_id].pluck(:global_id, :grade).to_h
      @groups.map do |group|
        agid = group.global_id
        enrollments_by_user[user_id].map do |enrollment|
          "(#{enrollment.id}, #{group.id}, #{number_or_null(current[agid])}, #{number_or_null(final[agid])})"
        end
      end
    end.flatten
  end

  def group_dropped_rows
    enrollments_by_user.keys.map do |user_id|
      current = @current_groups[user_id].pluck(:global_id, :dropped).to_h
      final = @final_groups[user_id].pluck(:global_id, :dropped).to_h
      @groups.map do |group|
        agid = group.global_id
        hsh = {
          current: {dropped: current[agid]},
          final: {dropped: final[agid]}
        }
        enrollments_by_user[user_id].map do |enrollment|
          "(#{enrollment.id}, #{group.id}, '#{hsh.to_json}')"
        end
      end
    end.flatten
  end

  def updated_at
    @updated_at ||= Score.connection.quote(Time.now.utc)
  end

  def current_score_column
    @ignore_muted ? 'current_score' : 'unposted_current_score'
  end

  def final_score_column
    @ignore_muted ? 'final_score' : 'unposted_final_score'
  end

  def save_scores
    return if @current_updates.empty? && @final_updates.empty?
    return if joined_enrollment_ids.blank?
    return if @grading_period && @grading_period.deleted?

    @course.touch

    save_scores_in_transaction
  end

  def save_scores_in_transaction
    Score.transaction do
      @course.shard.activate do
        save_course_and_grading_period_scores
        save_course_and_grading_period_metadata
        score_rows = group_score_rows
        if @grading_period.nil? && score_rows.any?
          dropped_rows = group_dropped_rows
          save_assignment_group_scores(score_rows.join(','), dropped_rows.join(','))
        end
      end
    end
  end

  def save_course_and_grading_period_scores
    return if @only_update_course_gp_metadata
    # Construct upsert statement to update existing Scores or create them if needed,
    # for course and grading period Scores.
    Score.connection.execute("
      UPDATE #{Score.quoted_table_name}
          SET
            #{current_score_column} = CASE enrollment_id
              #{@current_updates.map do |user_id, score|
                enrollments_by_user[user_id].map do |enrollment|
                  "WHEN #{enrollment.id} THEN #{number_or_null(score)}"
                end.join(' ')
              end.join(' ')}
              ELSE #{current_score_column}
            END,
            #{final_score_column} = CASE enrollment_id
              #{@final_updates.map do |user_id, score|
                enrollments_by_user[user_id].map do |enrollment|
                  "WHEN #{enrollment.id} THEN #{number_or_null(score)}"
                end.join(' ')
              end.join(' ')}
              ELSE #{final_score_column}
            END,
            updated_at = #{updated_at},
            -- if workflow_state was previously deleted for some reason, update it to active
            workflow_state = COALESCE(NULLIF(workflow_state, 'deleted'), 'active')
          WHERE
            enrollment_id IN (#{joined_enrollment_ids}) AND
            assignment_group_id IS NULL AND
            #{@grading_period ? "grading_period_id = #{@grading_period.id}" : 'course_score IS TRUE'};
      INSERT INTO #{Score.quoted_table_name}
          (enrollment_id, grading_period_id, #{current_score_column}, #{final_score_column}, course_score, created_at, updated_at)
          SELECT
            enrollments.id as enrollment_id,
            #{@grading_period.try(:id) || 'NULL'} as grading_period_id,
            CASE enrollments.id
              #{@current_updates.map do |user_id, score|
                enrollments_by_user[user_id].map do |enrollment|
                  "WHEN #{enrollment.id} THEN #{number_or_null(score)}"
                end.join(' ')
              end.join(' ')}
              ELSE NULL
            END :: float AS #{current_score_column},
            CASE enrollments.id
              #{@final_updates.map do |user_id, score|
                enrollments_by_user[user_id].map do |enrollment|
                  "WHEN #{enrollment.id} THEN #{number_or_null(score)}"
                end.join(' ')
              end.join(' ')}
              ELSE NULL
            END :: float AS #{final_score_column},
            #{@grading_period ? 'FALSE' : 'TRUE'} AS course_score,
            #{updated_at} as created_at,
            #{updated_at} as updated_at
          FROM #{Enrollment.quoted_table_name} enrollments
          LEFT OUTER JOIN #{Score.quoted_table_name} scores on
            scores.enrollment_id = enrollments.id AND
            scores.assignment_group_id IS NULL AND
            #{@grading_period ? "scores.grading_period_id = #{@grading_period.id}" : 'scores.course_score IS TRUE'}
          WHERE
            enrollments.id IN (#{joined_enrollment_ids}) AND
            scores.id IS NULL;
    ")
  end

  def save_course_and_grading_period_metadata
    # We only save score metadata for posted grades. This means, if we're
    # calculating unposted grades (which means @ignore_muted is false),
    # we don't want to update the score metadata. TODO: start storing the
    # score metadata for unposted grades.
    return unless @ignore_muted

    ScoreMetadata.connection.execute("
      UPDATE #{ScoreMetadata.quoted_table_name} metadata
        SET
          calculation_details = CASE enrollments.user_id
            #{@dropped_updates.map do |user_id, dropped|
              "WHEN #{user_id} THEN cast('#{dropped.to_json}' as json)"
            end.join(' ')}
            ELSE calculation_details
          END,
          updated_at = #{updated_at}
        FROM #{Score.quoted_table_name} scores
        INNER JOIN #{Enrollment.quoted_table_name} enrollments ON
          enrollments.id = scores.enrollment_id
        WHERE
          scores.enrollment_id IN (#{joined_enrollment_ids}) AND
          scores.assignment_group_id IS NULL AND
          #{@grading_period ? "scores.grading_period_id = #{@grading_period.id}" : 'scores.course_score IS TRUE'} AND
          metadata.score_id = scores.id;
      INSERT INTO #{ScoreMetadata.quoted_table_name}
        (score_id, calculation_details, created_at, updated_at)
        SELECT
          scores.id AS score_id,
          CASE enrollments.user_id
            #{@dropped_updates.map do |user_id, dropped|
              "WHEN #{user_id} THEN cast('#{dropped.to_json}' as json)"
            end.join(' ')}
            ELSE NULL
          END AS calculation_details,
          #{updated_at} AS created_at,
          #{updated_at} AS updated_at
        FROM #{Score.quoted_table_name} scores
        INNER JOIN #{Enrollment.quoted_table_name} enrollments ON
          enrollments.id = scores.enrollment_id
        LEFT OUTER JOIN #{ScoreMetadata.quoted_table_name} metadata ON
          metadata.score_id = scores.id
        WHERE
          scores.enrollment_id IN (#{joined_enrollment_ids}) AND
          scores.assignment_group_id IS NULL AND
          #{@grading_period ? "scores.grading_period_id = #{@grading_period.id}" : 'scores.course_score IS TRUE'} AND
          metadata.id IS NULL;
    ")
  end

  def save_assignment_group_scores(score_values, dropped_values)
    # Construct upsert statement to update existing Scores or create them if needed,
    # for assignment group Scores.
    Score.connection.execute("
      UPDATE #{Score.quoted_table_name} scores
          SET
            #{current_score_column} = val.current_score,
            #{final_score_column} = val.final_score,
            updated_at = #{updated_at},
            workflow_state = COALESCE(NULLIF(workflow_state, 'deleted'), 'active')
          FROM (VALUES #{score_values}) val
            (enrollment_id, assignment_group_id, current_score, final_score)
          WHERE val.enrollment_id = scores.enrollment_id AND
            val.assignment_group_id = scores.assignment_group_id;
      INSERT INTO #{Score.quoted_table_name}
          (enrollment_id, assignment_group_id, #{current_score_column}, #{final_score_column},
            course_score, created_at, updated_at)
          SELECT
            val.enrollment_id AS enrollment_id,
            val.assignment_group_id as assignment_group_id,
            val.current_score AS #{current_score_column},
            val.final_score AS #{final_score_column},
            FALSE AS course_score,
            #{updated_at} AS created_at,
            #{updated_at} AS updated_at
          FROM (VALUES #{score_values}) val
            (enrollment_id, assignment_group_id, current_score, final_score)
          LEFT OUTER JOIN #{Score.quoted_table_name} sc ON
            sc.enrollment_id = val.enrollment_id AND
            sc.assignment_group_id = val.assignment_group_id
          WHERE
            sc.id IS NULL;
    ")

    # We only save score metadata for posted grades. This means, if we're
    # calculating unposted grades (which means @ignore_muted is false),
    # we don't want to update the score metadata. TODO: start storing the
    # score metadata for unposted grades.
    if @ignore_muted
      ScoreMetadata.connection.execute("
        UPDATE #{ScoreMetadata.quoted_table_name} md
          SET
            calculation_details = CAST(val.calculation_details as json),
            updated_at = #{updated_at}
          FROM (VALUES #{dropped_values}) val
            (enrollment_id, assignment_group_id, calculation_details)
          INNER JOIN #{Score.quoted_table_name} scores ON
            scores.enrollment_id = val.enrollment_id AND
            scores.assignment_group_id = val.assignment_group_id
          WHERE
            scores.id = md.score_id;
        INSERT INTO #{ScoreMetadata.quoted_table_name}
          (score_id, calculation_details, created_at, updated_at)
          SELECT
            scores.id AS score_id,
            CAST(val.calculation_details as json) AS calculation_details,
            #{updated_at} AS created_at,
            #{updated_at} AS updated_at
          FROM (VALUES #{dropped_values}) val
            (enrollment_id, assignment_group_id, calculation_details)
          LEFT OUTER JOIN #{Score.quoted_table_name} scores ON
            scores.enrollment_id = val.enrollment_id AND
            scores.assignment_group_id = val.assignment_group_id
          LEFT OUTER JOIN #{ScoreMetadata.quoted_table_name} metadata ON
            metadata.score_id = scores.id
          WHERE
            metadata.id IS NULL;
      ")
    end
  end

  # returns information about assignments groups in the form:
  # [
  #   {
  #    :id       => 1
  #    :score    => 5,
  #    :possible => 7,
  #    :grade    => 71.42,
  #    :weight   => 50},
  #   ...]
  # each group
  def create_group_sums(submissions, user_id, ignore_ungraded: true)
    visible_assignments = @assignments.select { |assignment| assignment_visible_to_student?(assignment.id, user_id) }

    if @grading_period
      visible_assignments.select! do |assignment|
        effective_due_dates.grading_period_id_for(
          student_id: user_id,
          assignment_id: assignment.id
        ) == Shard.relative_id_for(@grading_period.id, Shard.current, @course.shard)
      end
    end

    assignments_by_group_id = visible_assignments.group_by(&:assignment_group_id)
    submissions_by_assignment_id = Hash[
      submissions.map { |s| [s.assignment_id, s] }
    ]

    @groups.map do |group|
      assignments = assignments_by_group_id[group.id] || []

      group_submissions = assignments.map do |a|
        s = submissions_by_assignment_id[a.id]

        # ignore submissions for muted assignments
        s = nil if @ignore_muted && a.muted?

        # ignore pending_review quiz submissions
        s = nil if ignore_ungraded && s.try(:pending_review?)

        {
          assignment: a,
          submission: s,
          score: s&.score,
          total: a.points_possible || 0,
          excused: s&.excused?,
        }
      end

      if enrollments_by_user[user_id].all? { |e| e.workflow_state == 'completed' }
        group_submissions.reject! { |s| s[:submission].nil? }
      end

      group_submissions.reject! { |s| s[:score].nil? } if ignore_ungraded
      group_submissions.reject! { |s| s[:excused] }
      group_submissions.reject! { |s| s[:assignment].omit_from_final_grade? }
      group_submissions.each { |s| s[:score] ||= 0 }

      logged_submissions = group_submissions.map { |s| loggable_submission(s) }
      Rails.logger.info "GRADES: calculating for assignment_group=#{group.global_id} user=#{user_id}"
      Rails.logger.info "GRADES: calculating... ignore_ungraded=#{ignore_ungraded}"
      Rails.logger.info "GRADES: calculating... submissions=#{logged_submissions.inspect}"

      kept = drop_assignments(group_submissions, group.rules_hash)
      dropped_submissions = (group_submissions - kept).map { |s| s[:submission]&.id }.compact

      score, possible = kept.reduce([0, 0]) { |(s_sum,p_sum),s|
        [s_sum + s[:score], p_sum + s[:total]]
      }

      {
        id:        group.id,
        global_id: group.global_id,
        score:     score,
        possible:  possible,
        weight:    group.group_weight,
        grade:     ((score.to_f / possible * 100).round(2) if possible > 0),
        dropped:   dropped_submissions
      }.tap { |group_grade_info|
        Rails.logger.info "GRADES: calculated #{group_grade_info.inspect}"
      }
    end
  end

  # see comments for dropAssignments in grade_calculator.coffee
  def drop_assignments(submissions, rules)
    drop_lowest    = rules[:drop_lowest] || 0
    drop_highest   = rules[:drop_highest] || 0
    never_drop_ids = rules[:never_drop] || []
    return submissions if drop_lowest.zero? && drop_highest.zero?

    Rails.logger.info "GRADES: dropping assignments! #{rules.inspect}"

    cant_drop = []
    if never_drop_ids.present? || @ignore_muted
      cant_drop, submissions = submissions.partition do |submission|
        assignment = submission[:assignment]
        (@ignore_muted && assignment.muted?) || never_drop_ids.include?(assignment.id)
      end
    end

    # fudge the drop rules if there aren't enough submissions
    return cant_drop if submissions.empty?
    drop_lowest = submissions.size - 1 if drop_lowest >= submissions.size
    drop_highest = 0 if drop_lowest + drop_highest >= submissions.size

    keep_highest = submissions.size - drop_lowest
    keep_lowest  = keep_highest - drop_highest

    submissions.sort! { |a,b| a[:assignment].id - b[:assignment].id }

    # assignment groups that have no points possible have to be dropped
    # differently (it's a simpler case, but not one that fits in with our
    # usual bisection approach)
    kept = (cant_drop + submissions).any? { |s| s[:total] > 0 } ?
      drop_pointed(submissions, cant_drop, keep_highest, keep_lowest) :
      drop_unpointed(submissions, keep_highest, keep_lowest)

    (kept + cant_drop).tap do |all_kept|
      loggable_kept = all_kept.map { |s| loggable_submission(s) }
      Rails.logger.info "GRADES.calculating... kept=#{loggable_kept.inspect}"
    end
  end

  def drop_unpointed(submissions, keep_highest, keep_lowest)
    sorted_submissions = submissions.sort_by { |s| s[:score] }
    sorted_submissions.last(keep_highest).first(keep_lowest)
  end

  def drop_pointed(submissions, cant_drop, n_highest, n_lowest)
    max_total = (submissions + cant_drop).map { |s| s[:total] }.max

    kept = keep_highest(submissions, cant_drop, n_highest, max_total)
    kept = keep_lowest(kept, cant_drop, n_lowest, max_total)
  end

  def keep_highest(submissions, cant_drop, keep, max_total)
    keep_helper(submissions, cant_drop, keep, max_total) { |*args| big_f_best(*args) }
  end

  def keep_lowest(submissions, cant_drop, keep, max_total)
    keep_helper(submissions, cant_drop, keep, max_total) { |*args| big_f_worst(*args) }
  end

  # @submissions: set of droppable submissions
  # @cant_drop: submissions that are not eligible for dropping
  # @keep: number of submissions to keep from +submissions+
  # @max_total: the highest number of points possible
  # @big_f_blk: sorting block for the big_f function
  # returns +keep+ +submissions+
  def keep_helper(submissions, cant_drop, keep, max_total, &big_f_blk)
    return submissions if submissions.size <= keep

    unpointed, pointed = (submissions + cant_drop).partition { |s|
      s[:total].zero?
    }
    grades = pointed.map { |s| s[:score].to_f / s[:total] }.sort

    q_high = estimate_q_high(pointed, unpointed, grades)
    q_low  = grades.first
    q_mid  = (q_low + q_high) / 2

    x, kept = big_f_blk.call(q_mid, submissions, cant_drop, keep)
    threshold = 1 / (2 * keep * max_total**2)
    until q_high - q_low < threshold
      x < 0 ?
        q_high = q_mid :
        q_low  = q_mid
      q_mid = (q_low + q_high) / 2

      # bail if we can't can't ever satisfy the threshold (floats!)
      break if q_mid == q_high || q_mid == q_low

      x, kept = big_f_blk.call(q_mid, submissions, cant_drop, keep)
    end

    kept
  end

  def big_f(q, submissions, cant_drop, keep, &sort_blk)
    kept = submissions.map { |s|
      rated_score = s[:score] - q * s[:total]
      [rated_score, s]
    }.sort(&sort_blk).first(keep)

    q_kept = kept.reduce(0) { |sum,(rated_score,_)| sum + rated_score }
    q_cant_drop = cant_drop.reduce(0) { |sum,s| sum + (s[:score] - q * s[:total]) }

    [q_kept + q_cant_drop, kept.map(&:last)]
  end

  # we can't use the student's highest grade as an upper-bound for bisection
  # when 0-points-possible assignments are present, so guess the best possible
  # grade the student could have earned in that case
  def estimate_q_high(pointed, unpointed, grades)
    if unpointed.present?
      points_possible = pointed.reduce(0) { |sum,s| sum + s[:total] }
      best_pointed_score = [
        points_possible,                              # 100%
        pointed.reduce(0) { |sum,s| sum + s[:score] } # ... or extra credit
      ].max
      unpointed_score = unpointed.reduce(0) { |sum,s| sum + s[:score] }
      max_score = best_pointed_score + unpointed_score
      max_score.to_f / points_possible
    else
      grades.last
    end
  end

  # determines the best +keep+ assignments from submissions for the given q
  # (suitable for use with drop_lowest)
  def big_f_best(q, submissions, cant_drop, keep)
    big_f(q, submissions, cant_drop, keep) { |(a,_),(b,_)| b <=> a }
  end

  # determines the worst +keep+ assignments from submissions for the given q
  # (suitable for use with drop_highest)
  def big_f_worst(q, submissions, cant_drop, keep)
    big_f(q, submissions, cant_drop, keep) { |(a,_),(b,_)| a <=> b }
  end

  def gather_dropped_from_group_scores(group_sums)
    dropped = group_sums.map { |sum| sum[:dropped] }
    dropped.flatten!
    dropped.uniq!
    dropped
  end

  # returns grade information from all the assignment groups
  def calculate_total_from_group_scores(group_sums)
    dropped = gather_dropped_from_group_scores(group_sums)

    if @course.group_weighting_scheme == 'percent'
      relevant_group_sums = group_sums.reject { |gs|
        gs[:possible].zero? || gs[:possible].nil?
      }
      final_grade = relevant_group_sums.reduce(0) { |grade,gs|
        grade + (gs[:score].to_f / gs[:possible]) * gs[:weight]
      }

      # scale the grade up if total weights don't add up to 100%
      full_weight = relevant_group_sums.reduce(0) { |w,gs| w + gs[:weight] }
      if full_weight.zero?
        final_grade = nil
      elsif full_weight < 100
        final_grade *= 100.0 / full_weight
      end

      {grade: final_grade.try(:round, 2), dropped: dropped}
    else
      total, possible = group_sums.reduce([0,0]) { |(m,n),gs|
        [m + gs[:score], n + gs[:possible]]
      }
      if possible > 0
        final_grade = (total.to_f / possible) * 100
        {
          grade: final_grade.round(2),
          total: total.to_f,
          possible: possible,
          dropped: dropped
        }
      else
        {grade: nil, total: total.to_f, dropped: dropped}
      end
    end
  end

  # this takes a wrapped submission (like from create_group_sums)
  def loggable_submission(wrapped_submission)
    {
      assignment_id: wrapped_submission[:assignment].id,
      score: wrapped_submission[:score],
      total: wrapped_submission[:total],
    }
  end

  # If you need to invalidate caches with associated classes, put those calls here.
  def invalidate_caches
    GradeSummaryPresenter.invalidate_cache(@course)
  end
end