解数独小程序（Ruby实现）
某日在开一个跟我没关系的会的时候没事解手机上的数独解不出来，索性写了一段脚本来解。
大体思路是先填一个可能的数，然后进行下一轮递归，具体实现时还要想办法减少递归次数。
代码如下：
#=begin# Hardsudoku = [ # 0 1 2 3 4 5 6 7 8 [0, 0, 0, 0, 0, 3, 0, 8, 1], # 0 [2, 0, 0, 4, 0, 0, 0, 0, 0], # 1 [0, 5, 0, 0, 0, 0, 0, 0, 0], # 2 [0, 0, 0, 2, 3, 0, 7, 0, 0], # 3 [0, 1, 0, 0, 0, 0, 0, 5, 0], # 4 [0, 0, 8, 6, 0, 0, 0, 0, 0], # 5 [7, 0, 0, 0, 0, 0, 4, 0, 0], # 6 [0, 9, 0, 0, 8, 0, 0, 0, 0], # 7 [0, 0, 0, 0, 5, 0, 2, 0, 0] # 8]#=end=begin# Normalsudoku = [ # 0 1 2 3 4 5 6 7 8 [0, 5, 1, 6, 0, 0, 0, 0, 0], # 0 [0, 0, 9, 0, 0, 0, 0, 8, 2], # 1 [0, 0, 8, 0, 0, 0, 0, 0, 0], # 2 [2, 0, 0, 0, 8, 0, 0, 4, 3], # 3 [3, 0, 0, 7, 0, 0, 0, 2, 0], # 4 [0, 0, 0, 0, 0, 0, 5, 0, 0], # 5 [0, 0, 2, 1, 0, 5, 6, 0, 0], # 6 [8, 4, 0, 0, 0, 0, 2, 0, 5], # 7 [0, 0, 0, 0, 0, 0, 0, 0, 9] # 8]=end=begin# Easysudoku = [ # 0 1 2 3 4 5 6 7 8 [0, 6, 8, 7, 0, 0, 3, 0, 0], # 0 [0, 1, 4, 9, 0, 0, 0, 2, 8], # 1 [0, 0, 0, 0, 0, 8, 0, 0, 0], # 2 [8, 0, 7, 2, 0, 0, 0, 0, 0], # 3 [0, 2, 0, 0, 0, 0, 0, 6, 1], # 4 [1, 0, 0, 0, 0, 0, 0, 5, 0], # 5 [9, 0, 0, 0, 0, 2, 7, 4, 5], # 6 [4, 0, 0, 0, 5, 0, 0, 0, 0], # 7 [0, 0, 0, 4, 1, 0, 0, 0, 0] # 8]=end=begin# Testsudoku = [ # 0 1 2 3 4 5 6 7 8 [3, 2, 7, 5, 4, 6, 9, 8, 1], # 0 [1, 8, 5, 3, 9, 7, 2, 6, 4], # 1 [4, 6, 9, 2, 8, 1, 3, 7, 5], # 2 [9, 3, 1, 4, 6, 8, 5, 2, 7], # 3 [8, 5, 4, 9, 7, 2, 6, 1, 3], # 4 [2, 7, 6, 1, 3, 5, 8, 4, 9], # 5 [6, 1, 3, 7, 2, 9, 4, 5, 8], # 6 [5, 9, 8, 6, 1, 4, 7, 3, 2], # 7 [7, 4, 2, 8, 5, 3, 1, 9, 6] # 8]=end=begin# Testsudoku = [ # 0 1 2 3 4 5 6 7 8 [3, 2, 7, 5, 4, 6, 9, 8, 1], # 0 [1, 8, 5, 3, 9, 7, 2, 6, 4], # 1 [4, 6, 9, 2, 8, 1, 3, 7, 5], # 2 [9, 3, 1, 4, 6, 8, 5, 2, 7], # 3 [8, 5, 4, 9, 7, 2, 6, 1, 3], # 4 [2, 7, 6, 1, 3, 5, 8, 4, 9], # 5 [6, 1, 3, 7, 0, 0, 0, 0, 0], # 6 [5, 9, 8, 6, 0, 0, 0, 0, 0], # 7 [7, 4, 2, 8, 0, 0, 0, 0, 0] # 8]=endclass SudokuResolver attr_reader :sudoku def initialize sudoku @sudoku = sudoku.copy update_sudoku end # put sudoku into @units def update_sudoku @units = [] # row 0 - 8 0.upto(8) {|i| @units << @sudoku[i]} # column 9 - 17 0.upto(8) do |i| column = [] 0.upto(8) {|j| column << @sudoku[j][i]} @units << column end # block 18 - 26 0.upto(2) do |i| 0.upto(2) do |j| block = [] block << @sudoku[i * 3][j * 3] block << @sudoku[i * 3][j * 3 + 1] block << @sudoku[i * 3][j * 3 + 2] block << @sudoku[i * 3 + 1][j * 3] block << @sudoku[i * 3 + 1][j * 3 + 1] block << @sudoku[i * 3 + 1][j * 3 + 2] block << @sudoku[i * 3 + 2][j * 3] block << @sudoku[i * 3 + 2][j * 3 + 1] block << @sudoku[i * 3 + 2][j * 3 + 2] @units << block end end end # resolve sudoku def resolve_sudoku # step 1: Check return false unless is_vaild? return true if is_resolved? # step 2: fill definite value flag = true while flag flag = false @units.each_with_index do |unit, index| if unit.count(0) == 1 flag = true value = ([1,2,3,4,5,6,7,8,9] - unit)[0] if index >= 0 && index <= 8 @sudoku[index][unit.index(0)] = value end if index >= 9 && index <= 17 @sudoku[unit.index(0)][index - 9] = value end if index >= 18 && index <= 26 i = index - 18 #puts "value: #{value}, index: #{unit.index(0)}, i: #{(i / 3) * 3 + unit.index(0) / 3}, j: #{i % 3 * 3 + unit.index(0) % 3}" @sudoku[(i / 3) * 3 + unit.index(0) / 3][i % 3 * 3 + unit.index(0) % 3] = value end end end update_sudoku end return false unless is_vaild? return true if is_resolved? # step 3: generate marked sudoku generate_mark_sudoku # step 4: get the cell with least probable value ij_hash = {} min = 9 @mark_sudoku.each_with_index do |unit, i| unit.each_with_index do |arr, j| if arr.respond_to?("each") #puts "#{i}, #{j}" if(arr.size == 1) @sudoku[i][j] = @mark_sudoku[i][j][0] next end ij_hash[arr.size.to_s.to_sym] ||= [] ij_hash[arr.size.to_s.to_sym] << [i, j] min = arr.size if min >= arr.size end end end update_sudoku return false unless is_vaild? return true if is_resolved? return false if min == 0 # step 5: try to fill the cell getted from step 4. ij_hash[min.to_s.to_sym].each do |ij| @mark_sudoku[ij[0]][ij[1]].each do |value| temp_sudoku = @sudoku.copy temp_sudoku[ij[0]][ij[1]] = value #推导过程 #puts "sudoku, i: #{ij[0]}, j: #{ij[1]}, value: #{value}" #temp_sudoku.each {|line| line.each {|i| print "\t#{i}"};print "\r"} #puts "-----------------------------------------" #@mark_sudoku.each {|line| line.each {|i| print "\t#{i}"};print "\r"} #puts "-----------------------------------------" sub_resolver = SudokuResolver.new(temp_sudoku) if sub_resolver.resolve_sudoku @sudoku = sub_resolver.sudoku.copy return true end end return false end return false end # 如果数独被解出，则返回true。 def is_resolved? @units.each {|unit| return false if unit.include? 0} true end # 检验数独是否正确 def is_vaild? @units.each do |unit| return false unless unit.with_unique [1,2,3,4,5,6,7,8,9] end true end def generate_mark_sudoku @mark_sudoku = [] @sudoku.each_with_index do |unit, i| @mark_sudoku[i] = [] unit.each_with_index do |n, j| unless n == 0 @mark_sudoku[i][j] = -1 # -1 stands for value existing. else unit1 = @units[i] unit2 = @units[9 + j] unit3 = @units[18 + i / 3 * 3 + j / 3] @mark_sudoku[i][j] = [0,1,2,3,4,5,6,7,8,9] - unit1 - unit2 - unit3 end end end endend# add methods in class Array.class Array def count ele counter = 0 self.each {|i| counter = counter + 1 if i == ele} counter end def with_unique array self.each {|i| array.each {|j| return false if self.count(j) > 1}} true end def copy arr = [] self.each {|i| arr << i.clone} arr endendresolver = SudokuResolver.new sudokut1 = Time.nowif resolver.resolve_sudoku resolver.sudoku.each {|line| line.each {|i| print "\t#{i}"};print "\r"}else puts "No Solution"endt2 = Time.nowputs t2 - t1