写写归并排序

原理

• 将待排序元素分为前后两部分，分别调用归并排序使它们有序
• 从头开始逐个比较前后两部分的元素，根据比较结果先后放进新数组，最终返回这个新数组

联想

• 归并排序用到了递归，递归终止的条件是待排序元素数量小于 2
• 归并排序比较之后不会交换元素，而是生成新的数组

用法

#!/usr/bin/env ruby
sorted_array = MS.sort(array)

大体结构

module MS
  extend self
  def sort(arr)
    merge_sort(arr.dup)
  end

  def merge_sort(arr)
    return arr if arr.length < 2
    #将 arr 一分为二，分别调用归并排序
    #逐一比较这两部分的元素，根据比较结果生成新数组
  end
end

将待排序元素一分为二，分别调用归并排序

def merge_sort(arr)
  #...
  
  m_index = arr.length / 2
  #这两部分的命名真是头痛，原谅我英语不好
  low_part = merge_sort(arr[0...m_index]) # low_part 不包含位于 m_index 的元素
  high_part = merge_sort(arr[m_index..-1])

  #...
end

逐一比较这两部分的元素，根据比较结果生成新数组

def merge_sort(arr)
  #...
  
  l_index = 0
  h_index = 0
  new_arr = []

  while low_part[l_index] && high_part[h_index]
    if low_part[l_index] < high_part[h_index]
      new_arr << low_part[l_index]
      l_index += 1
    else
      new_arr << high_part[h_index]
      h_index += 1
    end
  end

  #如果第一部分还有未比较的元素，就放进新数组
  while low_part[l_index]
    new_arr << low_part[l_index]
    l_index += 1
  end
  
  #同上
  while high_part[h_index]
    new_arr << high_part[h_index]
    h_index += 1
  end

  new_arr

end

完整的代码，加测试用例如下：

#!usr/bin/env ruby

module MS
 extend self
 def sort(arr)
   merge_sort(arr.dup) 
   end
 def merge_sort(arr)
   return arr if arr.length < 2
   m_index = arr.length / 2
   low_part = merge_sort(arr[0...m_index])
   high_part = merge_sort(arr[m_index..-1])

   l_index = 0
   h_index = 0
   new_arr = []

   while low_part[l_index] && high_part[h_index]
     if low_part[l_index] < high_part[h_index]
       new_arr << low_part[l_index]
       l_index += 1
     else
       new_arr << high_part[h_index]
       h_index += 1
     end
   end

   #如果第一部分还有未比较的元素，就放进新数组
   while low_part[l_index]
     new_arr << low_part[l_index]
     l_index += 1
   end

   #同上
   while high_part[h_index]
     new_arr << high_part[h_index]
     h_index += 1
   end

   new_arr

  end
end

if __FILE__ == $0
  require 'test/unit'
  class TestMS < Test::Unit::TestCase
    def test_0
      input = []
      expected = []
      assert_equal MS.sort(input), expected, 'empty array not equal'
    end
    def test_1_0
      input = [0]
      expected = [0]
      assert_equal MS.sort(input), expected, 'one item array not equal'    
    end
    def test_1_1
      input = [1]
      expected = [1]
      assert_equal MS.sort(input), expected, 'one item array not equal'    
    end
    def test_2_0
      input = [0,1]
      expected = [0,1]
      assert_equal MS.sort(input), expected, 'two items array not equal'    
    end
    def test_2_1
      input = [1,0]
      expected = [0,1]
      assert_equal MS.sort(input), expected, 'two items array not equal'    
    end
    def test_2_2
      input = [1,1]
      expected = [1,1]
      assert_equal MS.sort(input), expected, 'two items array not equal'    
    end
    def test_3_0
      input = [0,1,2]
      expected = [0,1,2]
      assert_equal MS.sort(input), expected, 'three items array not equal'    
    end
    def test_3_1
      input = [0,2,1]
      expected = [0,1,2]
      assert_equal MS.sort(input), expected, 'three items array not equal'    
    end
    def test_3_2
      input = [2,1,0]
      expected = [0,1,2]
      assert_equal MS.sort(input), expected, 'three items array not equal'    
    end
    def test_3_3
      input = [2,1,1]
      expected = [1,1,2]
      assert_equal MS.sort(input), expected, 'three items array not equal'    
    end
    def test_3_4
      input = [1,1,1]
      expected = [1,1,1]
      assert_equal MS.sort(input), expected, 'three items array not equal'    
    end
    def test_4_0
      input = [0,1,2,3]
      expected = [0,1,2,3]
      assert_equal MS.sort(input), expected, 'four items array not equal'    
    end
    def test_4_1
      input = [3,1,2,0]
      expected = [0,1,2,3]
      assert_equal MS.sort(input), expected, 'four items array not equal'    
    end
    def test_4_2
      input = [3,1,2,1]
      expected = [1,1,2,3]
      assert_equal MS.sort(input), expected, 'four items array not equal'    
    end
    def test_10_0
      input = [9,8,7,6,5,4,3,2,1,0]
      expected = [0,1,2,3,4,5,6,7,8,9]
      assert_equal MS.sort(input), expected, 'ten items array not equal'    
    end
    def test_10_1
      input = [9,5,7,3,8,4,6,1,2,0]
      expected = [0,1,2,3,4,5,6,7,8,9]
      assert_equal MS.sort(input), expected, 'ten items array not equal'    
    end
  end
end

PS. 想要跑某个特定的测试，可以这样写： ruby test.rb -n test_method_name