main
1require "spec_helper"
2
3describe "problem eleven" do
4=begin
5In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
6
7 |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
8============================================================
900|08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
1001|49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
1102|81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
1203|52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
1304|22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
1405|24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
1506|32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
1607|67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
1708|24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
1809|21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
1910|78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
2011|16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
2112|86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
2213|19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
2314|04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
2415|88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
2516|04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
2617|20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
2718|20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
2819|01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
29
30The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
31
32 What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?
33
34## design
35
36### build a grid (brute force)
37
38 [
39 [08, 02, 22, 97, 38, 15, 00, 40, 00, 75, 04, 05, 07, 78, 52, 12, 50, 77, 91, 08],
40 [49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 04, 56, 62, 00],
41 ]
42
43### build a graph
44#
45 do a traversal through the graph
46 compute the largest product from each node
47
48 08 - 49
49 / \
50 02 49
51=end
52
53 class Heading
54 attr_reader :grid
55
56 def initialize(grid)
57 @grid = grid
58 end
59
60 def max_product(digits, cell)
61 next_cell = next_cell(cell)
62 return cell.value if next_cell.nil?
63 cell.value * max_product(digits - 1, next_cell)
64 end
65 end
66
67 class North < Heading
68 def initialize(*args); super; end
69 def next_cell(cell)
70 grid.cell_at(x: cell.x - 1, y: cell.y)
71 end
72 end
73 class South < Heading
74 def initialize(*args); super; end
75 def next_cell(cell)
76 grid.cell_at(x: cell.x + 1, y: cell.y)
77 end
78 end
79 class East < Heading
80 def initialize(*args); super; end
81 def next_cell(cell)
82 grid.cell_at(x: cell.x, y: cell.y + 1)
83 end
84 end
85 class West < Heading
86 def initialize(*args); super; end
87 def next_cell(cell)
88 grid.cell_at(x: cell.x, y: cell.y - 1)
89 end
90 end
91
92 class BinaryHeading < Heading
93 def initialize(grid, left, right)
94 @left, @right = left, right
95 super(grid)
96 end
97
98 def next_cell(cell)
99 left_cell = @left.next_cell(cell)
100 return nil if left_cell.nil?
101 @right.next_cell(left_cell)
102 end
103 end
104
105 class Cell
106 attr_reader :x, :y, :value
107
108 def initialize(grid: , x:, y:, value:)
109 @grid, @x, @y, @value = grid, x, y, value
110 @north, @east, @south, @west = North.new(grid), East.new(grid), South.new(grid), West.new(grid)
111 end
112
113 def max_product(digits)
114 headings.map { |x| x.max_product(digits, self) }.max
115 end
116
117 private
118
119 def headings
120 @headings ||= [
121 @north, BinaryHeading.new(@grid, @north, @east),
122 @east, BinaryHeading.new(@grid, @south, @east),
123 @south, BinaryHeading.new(@grid, @south, @west),
124 @west, BinaryHeading.new(@grid, @north, @west),
125 ]
126 end
127 end
128
129 class Grid
130 attr_reader :cells
131
132 def initialize(cells = [])
133 @cells = cells
134 end
135
136 def add_cell(x:, y:, value:)
137 cells.push(Cell.new(grid: self, x: x, y: y, value: value))
138 end
139
140 def row_count
141 cells.map { |x| x.x }.uniq!.count
142 end
143
144 def [](row)
145 cells.find_all { |cell| cell.x == row }
146 end
147
148 def max_product(digits)
149 cells.map { |cell| cell.max_product(digits) }.max
150 end
151
152 def cell_at(x:, y:)
153 cells.find { |cell| cell.x == x && cell.y == y }
154 end
155
156 def self.build_from(items)
157 grid = Grid.new
158 items.each_with_index do |row, row_index|
159 row.each_with_index do |cell, cell_index|
160 grid.add_cell(x: row_index, y: cell_index, value: cell)
161 end
162 end
163 grid
164 end
165 end
166
167 class GreatestProduct
168 attr_reader :grid
169
170 def initialize(raw_grid)
171 @raw_grid = raw_grid
172 @grid = build_grid_from(raw_grid)
173 end
174
175 def greatest_product(digits:)
176 grid.max_product(digits)
177 end
178
179 private
180
181 def build_grid_from(raw_grid)
182 items = [].tap do |grid|
183 StringIO.new(raw_grid).each_line do |line|
184 grid.push(line.split.map(&:to_i))
185 end
186 end
187 Grid.build_from(items)
188 end
189 end
190
191 subject { GreatestProduct.new(raw_grid) }
192
193 let(:raw_grid) do
194 <<-GRID
19508 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
19649 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
19781 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
19852 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
19922 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
20024 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
20132 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
20267 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
20324 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
20421 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
20578 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
20616 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
20786 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
20819 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
20904 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
21088 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
21104 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
21220 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
21320 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
21401 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
215 GRID
216 end
217
218 it "returns the greatest product" do
219 expect(subject.greatest_product(digits: 3)).to eql([])
220 end
221
222 it 'builds a grid from the raw grid' do
223 raw_grid = <<-GRID
22408 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
22549 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
226 GRID
227 subject = GreatestProduct.new(raw_grid)
228 expect(subject.grid.row_count).to eql(2)
229 expect(subject.grid[0].map { |x| x.value }).to eql([8, 02, 22, 97, 38, 15, 0, 40, 0, 75, 04, 05, 07, 78, 52, 12, 50, 77, 91, 8])
230 expect(subject.grid[1].map { |x| x.value }).to eql([49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 04, 56, 62, 00])
231 end
232end