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costs-table.svg
<?xml version="1.0" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg width="2570" height="400"
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink">
<style type="text/css">
<![CDATA[
@import url('https://fonts.googleapis.com/css?family=Droid+Sans+Mono');
]]>
</style>
<g id="column_group">
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d
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f
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k
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n
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b
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c
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128
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d
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100
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100
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e
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4 (a)
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80
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72
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80
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f
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0 (a)
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68
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52
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g
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64
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40
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32 (d)
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40
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64
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h
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40000000000
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20000000000
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20 (d)
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20 (e)
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36
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96
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i
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16
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84
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j
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4 (f)
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48
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k
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20
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dynamic_programming_breaks.rb
class SparseMatrix
def initialize
@data = {}
end
def set(row_idx, col_idx, value)
data[key(row_idx, col_idx)] = value
end
def get(row_idx, col_idx)
data[key(row_idx, col_idx)]
end
private
attr_reader :data
def key(row_idx, col_idx)
"#{row_idx}-#{col_idx}"
end
end
class Minima
attr_accessor :start_index, :value
def initialize(value: 10**20)
@start_index = 0
@value = value
end
end
class Minimas
def initialize(count_nodes:)
@data = [Minima.new(value: 0)] + Array.new(count_nodes){ Minima.new }
end
def update_minima(cost, start_node_idx, end_node_idx)
return if @data[end_node_idx + 1].value <= cost
@data[end_node_idx + 1].value = cost
@data[end_node_idx].start_index = start_node_idx
end
def start_nodes
@data.map(&:start_index)
end
def [](idx)
@data[idx].value
end
private
attr_reader :data
end
class Dynamic
attr_reader :word_lengths, :max_line_length, :space_length, :word_lengths_count, :line_spaces
def initialize(words:, max_line_length:)
@word_lengths = words.map(&:length)
@word_lengths_count = @word_lengths.size
@max_line_length = max_line_length
@space_length = 1
end
def breaks
@line_spaces = precalculated_possible_line_spaces
@minimas = Minimas.new(count_nodes: word_lengths_count)
(0...word_lengths_count).each do |end_word_idx|
process_possible_lines_ending_with(end_word_idx)
end
@minimas.start_nodes
end
private
def process_possible_lines_ending_with(end_word_idx)
start_word_idx = end_word_idx
while start_word_idx >= 0
process_possible_line(start_word_idx, end_word_idx)
start_word_idx -= 1
end
end
def process_possible_line(start_word_idx, end_word_idx)
cost = penality_for_line(start_word_idx, end_word_idx)
@minimas.update_minima(cost, start_word_idx, end_word_idx)
end
def penality_for_line(start_word_idx, end_word_idx)
return 10 ** 10 if line_spaces.get(start_word_idx, end_word_idx) < 0
@minimas[start_word_idx] + line_spaces.get(start_word_idx, end_word_idx) ** 2
end
def precalculated_possible_line_spaces
word_lengths.each_with_index.each_with_object(SparseMatrix.new) do |(start_word_length, start_word_idx), line_space|
remaining_space_in_line = max_line_length - start_word_length
line_space.set start_word_idx, start_word_idx, remaining_space_in_line
((start_word_idx + 1)...word_lengths_count).each do |end_word_idx|
remaining_space_in_line = line_space.get(start_word_idx, end_word_idx - 1) - word_lengths[end_word_idx] - space_length
line_space.set start_word_idx, end_word_idx, remaining_space_in_line
end
end
end
end
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greety_breaks.rb
class GreetyBreaks
attr_reader :word_lengths, :max_line_length, :space_length
def initialize(words:, max_line_length:)
@word_lengths = words.map(&:length)
@max_line_length = max_line_length
@space_length = 1
end
def breaks
current_length = -space_length
word_lengths.each_with_index.each_with_object([]) do |(word_length, idx), breaks|
if word_length + current_length >= max_line_length
breaks.push idx
current_length = -space_length
end
current_length += space_length + word_length
end
end
end
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knuth_plass_breaks.svg
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shortest_path_breaks.rb
class Minima
attr_accessor :start_index, :value
def initialize(value: 10 ** 20)
@start_index = 0
@value = value
end
end
class Minimas
def initialize(count_nodes:)
@data = [Minima.new(value: 0)] + Array.new(count_nodes) { Minima.new }
end
def update_minima(cost, start_node_idx, end_node_idx)
return if @data[end_node_idx].value <= cost
@data[end_node_idx].value = cost
@data[end_node_idx].start_index = start_node_idx
end
def start_nodes
@data.map(&:start_index)
end
def [](idx)
@data[idx].value
end
private
attr_reader :data
end
class ShortestPath
attr_reader :word_lengths, :max_line_length, :space_length, :word_lengths_count, :line_spaces
def initialize(words:, max_line_length:)
@word_lengths = words.map(&:length)
@word_lengths_count = @word_lengths.size
@max_line_length = max_line_length
@space_length = 1
end
def breaks
pre_calculate_word_offsets
@minimas = Minimas.new(count_nodes: word_lengths_count)
(0...word_lengths_count).each do |start_word_idx|
process_possible_lines(start_word_idx, start_word_idx + 1)
end
@minimas.start_nodes
end
private
def pre_calculate_word_offsets
@offsets = [0]
word_lengths.each do |word_length|
@offsets.append(@offsets[-1] + word_length)
end
end
def process_possible_lines(start_word_idx, first_end_node_idx)
end_node_idx = first_end_node_idx
while end_node_idx <= word_lengths_count
break unless process_possible_line(end_node_idx, start_word_idx)
end_node_idx += 1
end
end
def process_possible_line(end_node_idx, start_word_idx)
current_line_length = calculate_current_line_length(end_node_idx, start_word_idx)
no_space_left_in_line = current_line_length > max_line_length
return false if no_space_left_in_line
penality = (max_line_length - current_line_length) ** 2
cost = @minimas[start_word_idx] + penality
@minimas.update_minima(cost, start_word_idx, end_node_idx)
true
end
def calculate_current_line_length(end_node_idx, start_word_idx)
spaces = end_node_idx - start_word_idx - 1
@offsets[end_node_idx] - @offsets[start_word_idx] + spaces
end
end
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smawk.rb
class Minima
attr_accessor :start_index, :value
def initialize
@start_index = 0
@value = 10 ** 20
end
end
class SMAWK
attr_reader :minima_provider, :minimas, :cnt_elements
def initialize(minima_provider, cnt_elements)
@minima_provider = minima_provider
@minimas = Array.new(cnt_elements + 1) { Minima.new }
@cnt_elements = cnt_elements
@minimas[0].value = 0
end
def cost(start_idx, end_idx)
minima_provider.call(minimas[start_idx].value, start_idx, end_idx)
end
def start_index(end_index)
minimas[end_index].start_index
end
def calc
backward_facing_cursor = cnt_elements + 1
forward_facing_cursor = 0
offset = 0
loop do
rth_column = [backward_facing_cursor, 2 ** (forward_facing_cursor + 1)].min
edge_between_head_and_tail = 2 ** forward_facing_cursor + offset
calc_sub_matrix(offset...edge_between_head_and_tail, edge_between_head_and_tail...(rth_column + offset))
right_most_col_of_sub_matrix = minimas[rth_column - 1 + offset]
minimum_right_most_col_of_sub_matrix = right_most_col_of_sub_matrix.value
exited_by_break = ((2 ** forward_facing_cursor)...(rth_column - 1)).each do |start_word_idx|
current_score = cost(start_word_idx + offset, rth_column - 1 + offset)
if current_score <= minimum_right_most_col_of_sub_matrix
backward_facing_cursor -= start_word_idx
forward_facing_cursor = 0
offset += start_word_idx
break true
end
false
end
next if exited_by_break == true
break if rth_column == backward_facing_cursor
forward_facing_cursor += 1
end
end
def calc_sub_matrix(rows, columns)
rows = rows.to_a
columns = columns.to_a
rows = evaluate_sub_matrix_rows(columns, rows)
handle_leftover_columns(columns, rows)
calculate_sub_matrix_minima(columns, rows)
end
private
def calculate_sub_matrix_minima(columns, rows)
current_row = current_column = 0
while current_column < columns.size
start_row_index = if current_column + 1 < columns.size
minimas[columns[current_column + 1]].start_index
else
rows[-1]
end
current_column_cost = cost(rows[current_row], columns[current_column])
if current_column_cost < minimas[columns[current_column]].value
minimas[columns[current_column]].value = current_column_cost
minimas[columns[current_column]].start_index = rows[current_row]
end
if rows[current_row] < start_row_index
current_row += 1
else
current_column += 2
end
end
end
def handle_leftover_columns(columns, rows)
return if columns.empty?
every_second_column = columns.each_slice(2).map { |v| v[1] }.to_a.compact
new_sub_matrix = every_second_column
calc_sub_matrix(rows, new_sub_matrix)
end
def evaluate_sub_matrix_rows(columns, rows)
[].tap do |stack|
current_row = 0
while current_row < rows.size
if stack.size.positive?
current_column_cost = columns[stack.size - 1]
if cost(stack[-1], current_column_cost) < cost(rows[current_row], current_column_cost)
stack.append(rows[current_row]) if stack.size < columns.size
current_row += 1
else
stack.pop
end
else
stack.append(rows[current_row])
current_row += 1
end
end
end
end
end
class LineBreaks
NEAR_INFINITY = 10 ** 10
attr_reader :word_offsets, :max_line_length, :space_length, :word_offsets_count, :line_spaces
def initialize(words:, max_line_length:)
@word_offsets = (0...(words.size-1)).each.reduce([0]){|res, index| res.push(words[index].length + res[-1])}
@word_offsets_count = @word_offsets.size
@max_line_length = max_line_length
@space_length = 1
@smawk = SMAWK.new(lambda { |current_minima, start_idx, end_idx|
cost(current_minima, start_idx, end_idx)
}, words.size - 1 )
end
def concave_modified_infinity(current_line_width, max_line_length)
concave_modifier = current_line_width - max_line_length
NEAR_INFINITY * concave_modifier
end
def cost(current_minima, start_idx, end_idx)
white_spaces = end_idx - start_idx - 1
start_word = word_offsets[start_idx]
end_word = word_offsets[end_idx]
current_line_width = end_word - start_word + white_spaces
return concave_modified_infinity(current_line_width, max_line_length) if current_line_width > max_line_length
current_minima + (max_line_length - current_line_width) ** 2
end
def breaks
@smawk.calc
(0...word_offsets_count).map { |idx| @smawk.start_index(idx) }
end
end
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@dieter-medium
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dieter-medium commented Apr 6, 2022

Explanations: https://medium.com/@dieter.s/visualizations-with-ruby-cdc16c0cee2e

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