Problem 37: sudoku solver

problems/37-sudoku-solver/main.rb

@@ -0,0 +1,169 @@
+# @param {Character[][]} board
+# @return {Void}
+# Do not return anything, modify board in-place instead.
+def solve_sudoku(board)
+  # Find all possible options for each cell.
+  # Board may be modified.
+  # This pre-check greatly reduces the number of values to iterate over.
+  options = generate_options(board)
+
+  # Remember numbers that are already present
+  fixed_numbers = get_fixed_numbers(board)
+
+  i = 0
+  j = 0
+
+  while i <= 8
+    # Skip this cell
+    if fixed_numbers[i][j]
+      i, j = increment_indices(i, j)
+      next
+    end
+
+    # This cell is not solved
+
+    board[i][j] = options[i][j][0] if board[i][j] == '.'
+
+    # Find first good digit
+    while !cell_valid?(board, i, j) && options[i][j].include?(board[i][j])
+      board[i][j] = next_digit(board[i][j], options[i][j])
+    end
+
+    # Error somewhere else
+    if !options[i][j].include?(board[i][j])
+      board[i][j] = '.'
+      i, j = decrement_indices(i, j, fixed_numbers)
+      board[i][j] = next_digit(board[i][j], options[i][j])
+    # Looks good, move to the next cell
+    else
+      i, j = increment_indices(i, j)
+    end
+  end
+end
+
+# Returns a 3-dimensional array with all possible values for each cell.
+# Returns an empty array for cells with numbers.
+# If there is only one option, then this value is written on the board.
+def generate_options(board)
+  options = []
+
+  board.each_with_index do |row, i|
+    options.push([])
+    row.each_with_index do |cell, j|
+      options[i].push([])
+
+      # Do not generate options for filled cells
+      next unless cell == '.'
+
+      # Find values from the corresponding row, column and square
+      row = board[i]
+      column = get_column(board, j)
+      square = get_square(board, i, j)
+
+      # Find options
+      9.times do |x|
+        char = (x + 1).to_s
+        # Add number to options if doesn't repeat
+        options[i][j].push(char) unless row.include?(char) || column.include?(char) || square.include?(char)
+      end
+
+      # Only one option exists
+      if options[i][j].length == 1
+        board[i][j] = options[i][j].first
+        options[i][j] = []
+      end
+    end
+  end
+
+  options
+end
+
+# Returns 9x9 matrix with boolean values.
+# Value is true if the corresponding number is already on the board.
+def get_fixed_numbers(board)
+  fixed = []
+  board.each do |row|
+    fixed.push([])
+    row.each do |cell|
+      fixed.last.push(cell != '.')
+    end
+  end
+  fixed
+end
+
+# Returns the indices of the next cell
+def increment_indices(i, j)
+  return [i, j + 1] if j < 8
+
+  [i + 1, 0]
+end
+
+# Returns the indices of the previous cell.
+# Executes recursively until it finds a cell with no initial value.
+def decrement_indices(i, j, fixed_numbers)
+  if j.positive?
+    j -= 1
+  else
+    j = 8
+    i -= 1
+  end
+
+  return decrement_indices(i, j, fixed_numbers) if fixed_numbers[i][j]
+
+  [i, j]
+end
+
+# Checks if this cell doesn't break the rules of sudoku
+def cell_valid?(board, row_index, column_index)
+  # Check row
+  return false unless seq_valid?(board[row_index])
+  # Check column
+  return false unless seq_valid?(get_column(board, column_index))
+  # Check square
+  return false unless seq_valid?(get_square(board, row_index, column_index))
+
+  # Everything is ok
+  true
+end
+
+# Check if all values are unique (except for '.')
+def seq_valid?(cells)
+  values = []
+  cells.each do |v|
+    return false if values.include?(v)
+
+    values.push(v) if v != '.'
+  end
+  true
+end
+
+def get_column(board, column_index)
+  values = []
+  board.each do |row|
+    values.push(row[column_index])
+  end
+  values
+end
+
+def get_square(board, row_index, column_index)
+  # Calculate square location
+  a = row_index / 3 * 3
+  b = column_index / 3 * 3
+
+  # Get values
+  values = []
+  3.times do |x|
+    3.times do |y|
+      values.push(board[a + x][b + y])
+    end
+  end
+
+  values
+end
+
+def next_digit(cell, options)
+  index = options.find_index(cell)
+  return cell.next if index + 1 == options.length
+
+  options[index + 1]
+end

problems/37-sudoku-solver/test.rb

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+require_relative 'main'
+require 'test/unit'
+
+class TestSudokuSolver < Test::Unit::TestCase
+  def test_simple_sudoku
+    input = [
+      %w[5 3 . . 7 . . . .],
+      %w[6 . . 1 9 5 . . .],
+      %w[. 9 8 . . . . 6 .],
+      %w[8 . . . 6 . . . 3],
+      %w[4 . . 8 . 3 . . 1],
+      %w[7 . . . 2 . . . 6],
+      %w[. 6 . . . . 2 8 .],
+      %w[. . . 4 1 9 . . 5],
+      %w[. . . . 8 . . 7 9]
+    ]
+    output = [
+      %w[5 3 4 6 7 8 9 1 2],
+      %w[6 7 2 1 9 5 3 4 8],
+      %w[1 9 8 3 4 2 5 6 7],
+      %w[8 5 9 7 6 1 4 2 3],
+      %w[4 2 6 8 5 3 7 9 1],
+      %w[7 1 3 9 2 4 8 5 6],
+      %w[9 6 1 5 3 7 2 8 4],
+      %w[2 8 7 4 1 9 6 3 5],
+      %w[3 4 5 2 8 6 1 7 9]
+    ]
+    solve_sudoku(input)
+    assert_equal(output, input)
+  end
+
+  def test_hard_sudoku
+    input = [
+      %w[. . . . . 7 . . 9],
+      %w[. 4 . . 8 1 2 . .],
+      %w[. . . 9 . . . 1 .],
+      %w[. . 5 3 . . . 7 2],
+      %w[2 9 3 . . . . 5 .],
+      %w[. . . . . 5 3 . .],
+      %w[8 . . . 2 3 . . .],
+      %w[7 . . . 5 . . 4 .],
+      %w[5 3 1 . 7 . . . .]
+    ]
+    output = [
+      %w[3 1 2 5 4 7 8 6 9],
+      %w[9 4 7 6 8 1 2 3 5],
+      %w[6 5 8 9 3 2 7 1 4],
+      %w[1 8 5 3 6 4 9 7 2],
+      %w[2 9 3 7 1 8 4 5 6],
+      %w[4 7 6 2 9 5 3 8 1],
+      %w[8 6 4 1 2 3 5 9 7],
+      %w[7 2 9 8 5 6 1 4 3],
+      %w[5 3 1 4 7 9 6 2 8]
+    ]
+    solve_sudoku(input)
+    assert_equal(output, input)
+  end
+end