array_partition.rb

class ArrayPartition
  def self.partition_counts(count, max)
    return [count] if count <= max
    group_count = (count / max) + (count % max > 0 ? 1 : 0)
    result = [0] * group_count
    count.times do |n|
      result[n % group_count] += 1
    end
    result.sort
  end
end

array_partition_spec.rb

RSpec.describe ArrayPartition do
  it 'partitions an array into optimal groups with max number of elements' do
    expect(ArrayPartition.partition_counts(5, 10)).to eq [5]
    expect(ArrayPartition.partition_counts(6, 10)).to eq [6]
    expect(ArrayPartition.partition_counts(7, 10)).to eq [7]
    expect(ArrayPartition.partition_counts(10, 10)).to eq [10]
    expect(ArrayPartition.partition_counts(11, 10)).to eq [5, 6]
    expect(ArrayPartition.partition_counts(12, 10)).to eq [6, 6]
    expect(ArrayPartition.partition_counts(13, 10)).to eq [6, 7]
    expect(ArrayPartition.partition_counts(16, 10)).to eq [8, 8]
    expect(ArrayPartition.partition_counts(20, 10)).to eq [10, 10]
    expect(ArrayPartition.partition_counts(21, 10)).to eq [7, 7, 7]
    expect(ArrayPartition.partition_counts(22, 10)).to eq [7, 7, 8]

    expect(ArrayPartition.partition_counts(5, 20)).to eq [5]
    expect(ArrayPartition.partition_counts(10, 20)).to eq [10]
    expect(ArrayPartition.partition_counts(15, 20)).to eq [15]
    expect(ArrayPartition.partition_counts(20, 20)).to eq [20]
    expect(ArrayPartition.partition_counts(21, 20)).to eq [10, 11]
    expect(ArrayPartition.partition_counts(30, 20)).to eq [15, 15]
    expect(ArrayPartition.partition_counts(40, 20)).to eq [20, 20]
    expect(ArrayPartition.partition_counts(41, 20)).to eq [13, 14, 14]
    expect(ArrayPartition.partition_counts(42, 20)).to eq [14, 14, 14]
    expect(ArrayPartition.partition_counts(43, 20)).to eq [14, 14, 15]
    expect(ArrayPartition.partition_counts(45, 20)).to eq [15, 15, 15]
    expect(ArrayPartition.partition_counts(50, 20)).to eq [16, 17, 17]
    expect(ArrayPartition.partition_counts(55, 20)).to eq [18, 18, 19]
    expect(ArrayPartition.partition_counts(60, 20)).to eq [20, 20, 20]
    expect(ArrayPartition.partition_counts(61, 20)).to eq [15, 15, 15, 16]
  end
end