diff --git a/codes/python/chapter_sorting/bubble_sort.py b/codes/python/chapter_sorting/bubble_sort.py
index 521dd8a..61f11f5 100644
--- a/codes/python/chapter_sorting/bubble_sort.py
+++ b/codes/python/chapter_sorting/bubble_sort.py
@@ -1,37 +1,47 @@
 '''
 File: bubble_sort.py
 Created Time: 2022-11-25
-Author: Krahets (krahets@163.com)
+Author: timi (xisunyy@163.com)
 '''
 
-import sys, os.path as osp
-sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
 from include import *
+import sys
+import os.path as osp
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
 
-"冒泡排序"
+"""冒泡排序"""
 def bubble_sort(nums):
-    n=len(nums)
+    n = len(nums)
     # 外循环：待排序元素数量为 n-1, n-2, ..., 1
-    for i in range(n-1,-1,-1):
+    for i in range(n-1, -1, -1):
         # 内循环：冒泡操作
         for j in range(i):
-            if nums[j]>nums[j+1]:
-                nums[j],nums[j+1]=nums[j+1],nums[j]
-"冒泡排序（标志优化）"
-def bubbleSortWithFlag(nums):
-    n=len(nums)
+            # 交换 nums[j] 与 nums[j + 1]
+            if nums[j] > nums[j+1]:
+                nums[j], nums[j+1] = nums[j+1], nums[j]
+
+
+"""冒泡排序（标志优化）"""
+def bubble_sort_with_flag(nums):
+    n = len(nums)
     # 外循环：待排序元素数量为 n-1, n-2, ..., 1
-    for i in range(n-1,-1,-1):
-        flag=False              #初始化标志位
+    for i in range(n-1, -1, -1):
+        flag = False  # 初始化标志位
         # 内循环：冒泡操作
         for j in range(i):
-            if nums[j]>nums[j+1]:
-                nums[j],nums[j+1]=nums[j+1],nums[j]
-                flag=True       #记录交换元素
-        if not flag:break
-if __name__=='__main__':
-    nums=[4,1,3,1,5,2]
+            # 交换 nums[j] 与 nums[j + 1]
+            if nums[j] > nums[j+1]:
+                nums[j], nums[j+1] = nums[j+1], nums[j]
+                flag = True  # 记录交换元素
+        if not flag:
+            break  # 此轮冒泡未交换任何元素，直接跳出
+
+
+if __name__ == '__main__':
+    nums = [4, 1, 3, 1, 5, 2]
     bubble_sort(nums)
-    print("冒泡排序后数组 nums = " ,nums)
-    bubbleSortWithFlag(nums)
-    print("冒泡排序后数组 nums = " ,nums)
\ No newline at end of file
+    print("排序后数组 nums = ", nums)
+
+    nums1 = [4, 1, 3, 1, 5, 2]
+    bubble_sort_with_flag(nums1)
+    print("排序后数组 nums = ", nums1)
diff --git a/codes/python/chapter_sorting/insertion_sort.py b/codes/python/chapter_sorting/insertion_sort.py
index 8640abc..a3b2b23 100644
--- a/codes/python/chapter_sorting/insertion_sort.py
+++ b/codes/python/chapter_sorting/insertion_sort.py
@@ -1,26 +1,28 @@
 '''
 File: insertion_sort.py
 Created Time: 2022-11-25
-Author: Krahets (krahets@163.com)
+Author: timi (xisunyy@163.com)
 '''
 
-import sys, os.path as osp
-sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
 from include import *
+import sys
+import os.path as osp
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
 
-"直接插入排序"
-def insertionSort(nums):
-    #外循环：base = nums[1], nums[2], ..., nums[n-1]
-    for i in range(1,len(nums)):
-        base=nums[i]
-        j=i-1
-        #内循环：将 base 插入到左边的正确位置
-        while j>=0 and nums[j]>base:
-            nums[j+1]=nums[j]   #1. 将 nums[j] 向右移动一位
-            j-=1
-        nums[j+1]=base          #2. 将 base 赋值到正确位置
+"""插入排序"""
+def insertion_sort(nums):
+    # 外循环：base = nums[1], nums[2], ..., nums[n-1]
+    for i in range(1, len(nums)):
+        base = nums[i]
+        j = i-1
+        # 内循环：将 base 插入到左边的正确位置
+        while j >= 0 and nums[j] > base:
+            nums[j+1] = nums[j]  # 1. 将 nums[j] 向右移动一位
+            j -= 1
+        nums[j+1] = base  # 2. 将 base 赋值到正确位置
 
-if __name__=='__main__':
-    nums=[4,1,3,1,5,2]
-    insertionSort(nums)
-    print("排序后数组 nums = " ,nums)
\ No newline at end of file
+
+if __name__ == '__main__':
+    nums = [4, 1, 3, 1, 5, 2]
+    insertion_sort(nums)
+    print("排序后数组 nums = ", nums)
diff --git a/codes/python/chapter_sorting/merge_sort.py b/codes/python/chapter_sorting/merge_sort.py
index 04c7130..f3212ef 100644
--- a/codes/python/chapter_sorting/merge_sort.py
+++ b/codes/python/chapter_sorting/merge_sort.py
@@ -1,48 +1,60 @@
 '''
 File: merge_sort.py
 Created Time: 2022-11-25
-Author: Krahets (krahets@163.com)
+Author: timi (xisunyy@163.com)
 '''
 
-import sys, os.path as osp
-sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+import copy
 from include import *
+import sys
+import os.path as osp
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
 
 
 """
-另一种 思路实现归并排序
+合并左子数组和右子数组
+左子数组区间 [left, mid]
+右子数组区间 [mid + 1, right]
 """
-def merge_sort(nums,l,r):
-    if l>=r:return 
-    mid=l+r>>1                  #划分中点
-    #进行归并
-    merge_sort(nums,l,mid)
-    merge_sort(nums,mid+1,r)
-
-    k,i,j=0,l,mid+1             #借助辅助数组 完成排序
-    while i<=mid and j<=r:  
-        if nums[i]<=nums[j]:    #这一步保证了 稳定排序
-            help_ls[k]=nums[i]
-            i+=1
+def merge(nums, left, mid, right):
+    # 初始化辅助数组 借助 copy模块
+    tmp = copy.deepcopy(nums[left:right+1])
+    # 左子数组的起始索引和结束索引
+    leftStart, leftEnd = left-left, mid - left
+    # 右子数组的起始索引和结束索引
+    rightStart, rightEnd = mid + 1 - left, right - left
+    # i, j 分别指向左子数组、右子数组的首元素
+    i, j = leftStart, rightStart
+    # 通过覆盖原数组 nums 来合并左子数组和右子数组
+    for k in range(left, right+1):
+        # 若 “左子数组已全部合并完”，则选取右子数组元素，并且 j++
+        if i > leftEnd:
+            nums[k] = tmp[j]
+            j += 1
+        # 否则，若 “右子数组已全部合并完” 或 “左子数组元素 < 右子数组元素”，则选取左子数组元素，并且 i++
+        elif j > rightEnd or tmp[i] <= tmp[j]:
+            nums[k] = tmp[i]
+            i += 1
+        # 否则，若 “左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++
         else:
-            help_ls[k]=nums[j]
-            j+=1
-        k+=1
-    
-    while i<=mid:               #对于左边区域
-        help_ls[k]=nums[i]
-        k,i=k+1,i+1
-    while j<=r:                 #对于右边区域
-        help_ls[k]=nums[j]
-        k,j=k+1,j+1
+            nums[k] = tmp[j]
+            j += 1
 
-    i,j=l,0
-    while i<=r:
-        nums[i]=help_ls[j]
-        i,j=i+1,j+1
-if __name__=='__main__':
-    nums=[4,1,3,1,5,2]
-    n=len(nums)
-    help_ls=[0 for _ in range(n)]
-    merge_sort(nums,0,n-1)
-    print("归并排序完成后 nums = ",nums)
\ No newline at end of file
+
+"""归并排序"""
+def merge_sort(nums, left, right):
+    # 终止条件
+    if left >= right:
+        return            # 当子数组长度为 1 时终止递归
+    # 划分阶段
+    mid = left + right >> 1  # 计算中点
+    merge_sort(nums, left, mid)         # 递归左子数组
+    merge_sort(nums, mid + 1, right)    # 递归右子数组
+    # 合并阶段
+    merge(nums, left, mid, right)
+
+
+if __name__ == '__main__':
+    nums = [4, 1, 3, 1, 5, 2]
+    merge_sort(nums, 0, len(nums)-1)
+    print("归并排序完成后 nums = ", nums)
diff --git a/codes/python/chapter_sorting/quick_sort.py b/codes/python/chapter_sorting/quick_sort.py
index f66ff5f..50236e4 100644
--- a/codes/python/chapter_sorting/quick_sort.py
+++ b/codes/python/chapter_sorting/quick_sort.py
@@ -1,31 +1,132 @@
 '''
 File: quick_sort.py
 Created Time: 2022-11-25
-Author: Krahets (krahets@163.com)
+Author: timi (xisunyy@163.com)
 '''
 
-import sys, os.path as osp
-sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
 from include import *
+import sys
+import os.path as osp
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
 
 
-"另一种思维 实现快速排序"
-def quick_sort(nums,l,r):
-    if l>=r:
-        return 
-    i,j,x=l-1,r+1,nums[l+r>>1]
-    while i<j:
-        while True:
-            i+=1
-            if nums[i]>=x:break
-        while True:
-            j-=1
-            if nums[j]<=x:break
-        if i<j:nums[i],nums[j]=nums[j],nums[i]
-    quick_sort(nums,l,j),quick_sort(nums,j+1,r)
-if __name__=='__main__':
-    nums=[4,1,3,1,5,2]
-    n=len(nums)
-    help_ls=[0 for _ in range(n)]
-    quick_sort(nums,0,n-1)
-    print("快速排序完成后 nums = ",nums)
+"""快速排序类"""
+class quick_sort(object):
+
+    """哨兵划分"""
+    def partition(self, nums, left, right):
+        # 以 nums[left] 作为基准数
+        i, j = left, right
+        while i < j:
+            while i < j and nums[j] >= nums[left]:
+                j -= 1   # 从右向左找首个小于基准数的元素
+            while i < j and nums[i] <= nums[left]:
+                i += 1   # 从左向右找首个大于基准数的元素
+            # 元素交换
+            nums[i], nums[j] = nums[j], nums[i]
+        # 将基准数交换至两子数组的分界线
+        nums[i], nums[left] = nums[left], nums[i]
+        return i  # 返回基准数的索引
+
+    """快速排序"""
+    def quick_sort(self, nums, left, right):
+        # 子数组长度为 1 时终止递归
+        if left >= right:
+            return
+        # 哨兵划分
+        pivot = self.partition(nums, left, right)
+        # 递归左子数组、右子数组
+        self.quick_sort(nums, left, pivot-1)
+        self.quick_sort(nums, pivot+1, right)
+
+
+"""快速排序类（中位基准数优化）"""
+class quick_sort_median():
+
+    # 选取三个元素的中位数
+    def median_three(self, nums, left, mid, right):
+        # 使用了异或操作来简化代码
+        # 异或规则为 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1
+        if (nums[left] > nums[mid]) ^ (nums[left] > nums[right]):
+            return left
+        elif (nums[mid] < nums[left]) ^ (nums[mid] > nums[right]):
+            return mid
+        return right
+
+    """哨兵划分（三数取中值）"""
+    def partition(self, nums, left, right):
+        # 以 nums[left] 作为基准数
+        med = self.median_three(nums, left, (left+right)//2, right)
+        # 将中位数交换至数组最左端
+        nums[left], nums[med] = nums[med], nums[left]
+        # 以 nums[left] 作为基准数
+        i, j = left, right
+        while i < j:
+            while i < j and nums[j] >= nums[left]:
+                j -= 1      # 从右向左找首个小于基准数的元素
+            while i < j and nums[i] <= nums[left]:
+                i += 1      # 从左向右找首个大于基准数的元素
+            # 元素交换
+            nums[i], nums[j] = nums[j], nums[i] 
+        # 将基准数交换至两子数组的分界线
+        nums[i], nums[left] = nums[left], nums[i]
+        return i            # 返回基准数的索引
+
+    """快速排序"""
+    def quick_sort(self, nums, left, right):
+        # 子数组长度为 1 时终止递归
+        if left >= right:return
+        # 哨兵划分
+        pivot = self.partition(nums, left, right)
+        # 递归左子数组、右子数组
+        self.quick_sort(nums, left, pivot-1)
+        self.quick_sort(nums, pivot+1, right)
+
+
+"""快速排序类（尾递归优化）"""
+class quick_sort_tail_call():
+
+    """哨兵划分"""
+    def partition(self, nums, left, right):
+        # 以 nums[left] 作为基准数
+        i, j = left, right
+        while i < j:
+            while i < j and nums[j] >= nums[left]:
+                j -= 1   # 从右向左找首个小于基准数的元素
+            while i < j and nums[i] <= nums[left]:
+                i += 1   # 从左向右找首个大于基准数的元素
+            # 元素交换
+            nums[i], nums[j] = nums[j], nums[i]
+        # 将基准数交换至两子数组的分界线
+        nums[i], nums[left] = nums[left], nums[i]
+        return i  # 返回基准数的索引
+
+    """快速排序（尾递归优化）"""
+    def quick_sort(self, nums, left, right):
+        # 子数组长度为 1 时终止
+        while left < right:
+            # 哨兵划分操作
+            pivot = self.partition(nums, left, right)
+            # 对两个子数组中较短的那个执行快排
+            if pivot-left < right-pivot:
+                self.quick_sort(nums, left, pivot-1)  # 递归排序左子数组
+                left = pivot+1  # 剩余待排序区间为 [pivot + 1, right]
+            else:
+                self.quick_sort(nums, pivot+1, right)  # 递归排序右子数组
+                right = pivot-1  # 剩余待排序区间为 [left, pivot - 1]
+
+if __name__ == '__main__':
+    # 快速排序 
+    nums = [4, 1, 3, 1, 5, 2]
+    quick_sort().quick_sort(nums, 0, len(nums)-1)
+    print("快速排序完成后 nums = ", nums)
+
+    # 快速排序（中位基准数优化）
+    nums1 = [4, 1, 3, 1, 5, 2]
+    quick_sort_median().quick_sort(nums1, 0, len(nums1)-1)
+    print("快速排序（中位基准数优化）完成后 nums = ", nums)
+
+    # 快速排序（尾递归优化）
+    nums2 = [4, 1, 3, 1, 5, 2]
+    quick_sort_tail_call().quick_sort(nums, 0, len(nums2)-1)
+    print("快速排序（尾递归优化）完成后 nums = ", nums)