一篇夯实一个知识点系列－－python实现十大排序算法

写在前面

干货儿

平方级排序

• 冒泡排序

  def bubble_sort(arr):
      length = len(arr)
      for i in range(length):
          for j in range(length-i-1):
              if arr[j] > arr[j+1]:
                  arr[j], arr[j+1] = arr[j+1], arr[j]
      return arr
  

• 选择排序

  def select_sort(arr):
      length = len(arr)
      for i in range(length):
          min_ix = i
          for j in range(i, length):
              if arr[j] < arr[min_ix]:
                  min_ix = j
          arr[min_ix], arr[i] = arr[i], arr[min_ix]
      return arr
  

• 插入排序

  def insert_sort(arr):
      length = len(arr)
      for i in range(length):
          for j in range(i, 0, -1):
              if arr[j] < arr[j-1]:
                  arr[j], arr[j-1] = arr[j-1], arr[j]
      return arr
  

对数级排序

• 希尔排序

  def shell_sort(arr):
      n = len(arr)
      gap = int(n/2)
      while gap > 0:
          for i in range(gap,n):
              temp = arr[i]
              j = i
              while  j >= gap and arr[j-gap] >temp:
                  arr[j] = arr[j-gap]
                  j -= gap
              arr[j] = temp
          gap = int(gap/2)
      return arr
  

• 归并排序

  def merge(left, right):
      i = j = 0
      res = []
      while i < len(left) and j < len(right):
          if left[i] < right[j]:
              res.append(left[i])
              i += 1
          else:
              res.append(right[j])
              j += 1
      if i == len(left):
          res.extend(right[j:])
      else:
          res.extend(left[i:])
      return res
  
  def merge_sort(arr):
      if len(arr) <= 1:
          return arr
      length = len(arr)
      i = int(length / 2)
      left = merge_sort(arr[:i])
      right = merge_sort(arr[i:])
      return merge(left, right)
  

• 快速排序

  def fast_sort(arr):
      if len(arr) <= 1:
          return arr
      pivot = arr.pop()
      left = [i for i in arr if i <= pivot]
      right = [i for i in arr if i > pivot]
      return fast_sort(left) + [pivot] + fast_sort(right)
  

  以上算法需要额外的空间，如果我们将小于等于基准的元素不断置于基准元素之前，大于基准的元素置于基准元素之后，那么就可以实现不需要额外空间的就地排序。

  def fast_sort_on_extra_spacing(arr):
      l = 0
      h = len(arr)-1
  
      def partition(arr, l, h):
          pivot = arr[h]
          for i in range(l, h):
              if arr[i] <= pivot:
                  arr[l], arr[i] = arr[i], arr[l]
                  l += 1
          arr[h], arr[l] = arr[l], arr[h]
          return l
  
      def fast_sort(arr, l, h):
          if l < h:
              pivot = partition(arr, l, h)
              fast_sort(arr, l, pivot-1)
              fast_sort(arr, pivot+1, h)
          return arr
      return fast_sort(arr, l, h)
  

• 堆排序

  def heapify(arr, n, i):
      # build a max root heap
      max_ix = i
      left_i = 2 * i + 1
      right_i = 2 * i + 2
  
      if left_i < n and arr[max_ix] < arr[left_i]:
          max_ix = left_i
      if right_i < n and arr[max_ix] < arr[right_i]:
          max_ix = right_i
      if max_ix != i:
          arr[max_ix], arr[i] = arr[i], arr[max_ix]
          heapify(arr, n, max_ix)
  
  def heap_sort(arr):
      for i in range(n-1, -1, -1):
          heapify(arr, n, i)
  
      for i in range(n-1, 0, -1):
          arr[i], arr[0] = arr[0], arr[i]
          heapify(arr, i, 0)
      return arr
  

线性级排序

• 计数排序

  def count_sort(arr):
      min_ix, max_ix = min(arr), max(arr)
      bucket = [0 for _ in range(max_ix+1)]
      for i in arr:
          bucket[i] += 1
      return sum([[i] * bucket[i] for i in range(len(bucket)) if bucket[i] != 0], [])
  

• 桶排序

  def bucket_sort(arr):
      min_ix, max_ix = min(arr), max(arr)
      bucket_range = (max_ix - min_ix) / len(arr)
      # +1 avoid for that max_ix - min_ix will raise a IndexError
      temp_bucket = [[] for i in range(len(arr) + 1)]
      for i in arr:
          temp_bucket[int((i-min_ix)//bucket_range)].append(i)
      return sum(temp_bucket, [])
  

• 基数排序

  def radix_sort(arr):
      max_value = max(arr)
      num_digits = len(str(max_value))
      for i in range(num_digits):
          bucket = [[] for _ in range(10)]
          for j in arr:
              bucket[j//(10**i)%10].append(j)
          arr = [j for i in bucket for j in i]
      return arr
  

笑死人不偿命排序

• 睡排序

• 猴子排序

排序算法复杂度、稳定性及通用性总结

写在最后

排序算法是算法学习中的核心。掌握排序算法及其思想是学习其它算法的基础。希望大家可以熟练掌握。欢迎关注个人博客:药少敏的博客。