sort
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@ -7,31 +7,32 @@ Author: timi (xisunyy@163.com)
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from include import *
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import sys
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import os.path as osp
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sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
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"""冒泡排序"""
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def bubble_sort(nums):
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n = len(nums)
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# 外循环:待排序元素数量为 n-1, n-2, ..., 1
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for i in range(n-1, -1, -1):
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for i in range(n - 1, -1, -1):
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# 内循环:冒泡操作
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for j in range(i):
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# 交换 nums[j] 与 nums[j + 1]
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if nums[j] > nums[j+1]:
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nums[j], nums[j+1] = nums[j+1], nums[j]
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if nums[j] > nums[j + 1]:
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nums[j], nums[j + 1] = nums[j + 1], nums[j]
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"""冒泡排序(标志优化)"""
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def bubble_sort_with_flag(nums):
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n = len(nums)
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# 外循环:待排序元素数量为 n-1, n-2, ..., 1
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for i in range(n-1, -1, -1):
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for i in range(n - 1, -1, -1):
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flag = False # 初始化标志位
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# 内循环:冒泡操作
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for j in range(i):
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# 交换 nums[j] 与 nums[j + 1]
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if nums[j] > nums[j+1]:
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nums[j], nums[j+1] = nums[j+1], nums[j]
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if nums[j] > nums[j + 1]:
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nums[j], nums[j + 1] = nums[j + 1], nums[j]
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flag = True # 记录交换元素
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if not flag:
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break # 此轮冒泡未交换任何元素,直接跳出
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@ -7,6 +7,7 @@ Author: timi (xisunyy@163.com)
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from include import *
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import sys
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import os.path as osp
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sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
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"""插入排序"""
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@ -14,12 +15,12 @@ def insertion_sort(nums):
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# 外循环:base = nums[1], nums[2], ..., nums[n-1]
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for i in range(1, len(nums)):
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base = nums[i]
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j = i-1
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j = i - 1
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# 内循环:将 base 插入到左边的正确位置
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while j >= 0 and nums[j] > base:
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nums[j+1] = nums[j] # 1. 将 nums[j] 向右移动一位
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nums[j + 1] = nums[j] # 1. 将 nums[j] 向右移动一位
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j -= 1
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nums[j+1] = base # 2. 将 base 赋值到正确位置
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nums[j + 1] = base # 2. 将 base 赋值到正确位置
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if __name__ == '__main__':
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@ -4,12 +4,11 @@ Created Time: 2022-11-25
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Author: timi (xisunyy@163.com)
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'''
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import copy
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from include import *
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import sys
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import os.path as osp
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sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
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sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
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"""
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合并左子数组和右子数组
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@ -18,15 +17,15 @@ sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
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"""
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def merge(nums, left, mid, right):
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# 初始化辅助数组 借助 copy模块
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tmp = copy.deepcopy(nums[left:right+1])
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tmp = nums[left:right + 1]
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# 左子数组的起始索引和结束索引
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leftStart, leftEnd = left-left, mid - left
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leftStart, leftEnd = left - left, mid - left
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# 右子数组的起始索引和结束索引
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rightStart, rightEnd = mid + 1 - left, right - left
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# i, j 分别指向左子数组、右子数组的首元素
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i, j = leftStart, rightStart
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# 通过覆盖原数组 nums 来合并左子数组和右子数组
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for k in range(left, right+1):
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for k in range(left, right + 1):
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# 若 “左子数组已全部合并完”,则选取右子数组元素,并且 j++
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if i > leftEnd:
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nums[k] = tmp[j]
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@ -45,16 +44,16 @@ def merge(nums, left, mid, right):
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def merge_sort(nums, left, right):
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# 终止条件
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if left >= right:
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return # 当子数组长度为 1 时终止递归
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return # 当子数组长度为 1 时终止递归
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# 划分阶段
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mid = left + right >> 1 # 计算中点
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merge_sort(nums, left, mid) # 递归左子数组
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merge_sort(nums, mid + 1, right) # 递归右子数组
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merge_sort(nums, left, mid) # 递归左子数组
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merge_sort(nums, mid + 1, right) # 递归右子数组
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# 合并阶段
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merge(nums, left, mid, right)
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if __name__ == '__main__':
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nums = [4, 1, 3, 1, 5, 2]
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merge_sort(nums, 0, len(nums)-1)
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merge_sort(nums, 0, len(nums) - 1)
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print("归并排序完成后 nums = ", nums)
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@ -7,21 +7,20 @@ Author: timi (xisunyy@163.com)
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from include import *
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import sys
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import os.path as osp
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sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
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sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
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"""快速排序类"""
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class quick_sort(object):
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"""哨兵划分"""
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def partition(self, nums, left, right):
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# 以 nums[left] 作为基准数
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i, j = left, right
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while i < j:
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while i < j and nums[j] >= nums[left]:
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j -= 1 # 从右向左找首个小于基准数的元素
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j -= 1 # 从右向左找首个小于基准数的元素
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while i < j and nums[i] <= nums[left]:
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i += 1 # 从左向右找首个大于基准数的元素
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i += 1 # 从左向右找首个大于基准数的元素
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# 元素交换
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nums[i], nums[j] = nums[j], nums[i]
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# 将基准数交换至两子数组的分界线
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@ -36,14 +35,14 @@ class quick_sort(object):
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# 哨兵划分
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pivot = self.partition(nums, left, right)
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# 递归左子数组、右子数组
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self.quick_sort(nums, left, pivot-1)
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self.quick_sort(nums, pivot+1, right)
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self.quick_sort(nums, left, pivot - 1)
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self.quick_sort(nums, pivot + 1, right)
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"""快速排序类(中位基准数优化)"""
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class quick_sort_median():
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# 选取三个元素的中位数
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"""选取三个元素的中位数"""
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def median_three(self, nums, left, mid, right):
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# 使用了异或操作来简化代码
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# 异或规则为 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1
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@ -56,45 +55,44 @@ class quick_sort_median():
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"""哨兵划分(三数取中值)"""
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def partition(self, nums, left, right):
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# 以 nums[left] 作为基准数
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med = self.median_three(nums, left, (left+right)//2, right)
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med = self.median_three(nums, left, (left + right) // 2, right)
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# 将中位数交换至数组最左端
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nums[left], nums[med] = nums[med], nums[left]
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# 以 nums[left] 作为基准数
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i, j = left, right
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while i < j:
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while i < j and nums[j] >= nums[left]:
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j -= 1 # 从右向左找首个小于基准数的元素
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j -= 1 # 从右向左找首个小于基准数的元素
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while i < j and nums[i] <= nums[left]:
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i += 1 # 从左向右找首个大于基准数的元素
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i += 1 # 从左向右找首个大于基准数的元素
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# 元素交换
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nums[i], nums[j] = nums[j], nums[i]
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# 将基准数交换至两子数组的分界线
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nums[i], nums[j] = nums[j], nums[i]
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# 将基准数交换至两子数组的分界线
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nums[i], nums[left] = nums[left], nums[i]
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return i # 返回基准数的索引
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return i # 返回基准数的索引
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"""快速排序"""
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def quick_sort(self, nums, left, right):
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# 子数组长度为 1 时终止递归
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if left >= right:return
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if left >= right: return
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# 哨兵划分
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pivot = self.partition(nums, left, right)
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# 递归左子数组、右子数组
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self.quick_sort(nums, left, pivot-1)
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self.quick_sort(nums, pivot+1, right)
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self.quick_sort(nums, left, pivot - 1)
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self.quick_sort(nums, pivot + 1, right)
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"""快速排序类(尾递归优化)"""
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class quick_sort_tail_call():
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"""哨兵划分"""
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def partition(self, nums, left, right):
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# 以 nums[left] 作为基准数
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i, j = left, right
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while i < j:
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while i < j and nums[j] >= nums[left]:
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j -= 1 # 从右向左找首个小于基准数的元素
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j -= 1 # 从右向左找首个小于基准数的元素
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while i < j and nums[i] <= nums[left]:
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i += 1 # 从左向右找首个大于基准数的元素
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i += 1 # 从左向右找首个大于基准数的元素
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# 元素交换
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nums[i], nums[j] = nums[j], nums[i]
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# 将基准数交换至两子数组的分界线
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@ -108,25 +106,26 @@ class quick_sort_tail_call():
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# 哨兵划分操作
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pivot = self.partition(nums, left, right)
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# 对两个子数组中较短的那个执行快排
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if pivot-left < right-pivot:
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self.quick_sort(nums, left, pivot-1) # 递归排序左子数组
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left = pivot+1 # 剩余待排序区间为 [pivot + 1, right]
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if pivot - left < right - pivot:
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self.quick_sort(nums, left, pivot - 1) # 递归排序左子数组
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left = pivot + 1 # 剩余待排序区间为 [pivot + 1, right]
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else:
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self.quick_sort(nums, pivot+1, right) # 递归排序右子数组
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right = pivot-1 # 剩余待排序区间为 [left, pivot - 1]
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self.quick_sort(nums, pivot + 1, right) # 递归排序右子数组
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right = pivot - 1 # 剩余待排序区间为 [left, pivot - 1]
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if __name__ == '__main__':
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# 快速排序
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nums = [4, 1, 3, 1, 5, 2]
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quick_sort().quick_sort(nums, 0, len(nums)-1)
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quick_sort().quick_sort(nums, 0, len(nums) - 1)
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print("快速排序完成后 nums = ", nums)
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# 快速排序(中位基准数优化)
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nums1 = [4, 1, 3, 1, 5, 2]
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quick_sort_median().quick_sort(nums1, 0, len(nums1)-1)
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quick_sort_median().quick_sort(nums1, 0, len(nums1) - 1)
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print("快速排序(中位基准数优化)完成后 nums = ", nums)
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# 快速排序(尾递归优化)
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nums2 = [4, 1, 3, 1, 5, 2]
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quick_sort_tail_call().quick_sort(nums, 0, len(nums2)-1)
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quick_sort_tail_call().quick_sort(nums, 0, len(nums2) - 1)
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print("快速排序(尾递归优化)完成后 nums = ", nums)
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