python模拟栈的操作实现非递归方式的快速排序算法
2024-04-13 09:35:18
今天在做题的时候突然想到一个问题，递归写出来的算法是否可以改成非递归的形式，查了一些资料发现：网上很多都说只要是递归可以写成的程序都是可以改成非递归形式的，关于递归的算法有很多的说法
递归的优点：
这个不用多说，递归写出来的程序和算法很清晰，甚至树的前序遍历和后序遍历这样复杂的代码都可以用不超过十行的递归代码来完成，在排序中，快速排序是一个很典型的例子，使用递归的话也可以不超过十行就实现一个功能强大的，可读性很好的排序算法，但是真的你明白递归的背后程序在干什么事情吗？程序是如何调用的，调用的层次和路线是什么，在堆栈中保存了什么？恐怕不是所有人都明白的，正如面试的时候说的：你可能很容易就使用递归的方法写出来一个树的遍历或者快排算法，但是真的改成非递归的方式的话就比较考验水平了，的确是这样的
递归的缺点：
递归的缺点也很明显，由于需要系统的堆栈那么使用的空间开销势必就会比非递归算法大很多，还需要保存一些必要信息如：保护现场，那么递归就会占用很多的资源，还有一个致命的问题就是：如果递归的深度太大的话可能是会造成栈溢出的
不过一般的学习工作中还是偏向于使用递归的代码，毕竟节省很大的精力时间和资源，如果想要加深对程序调用、执行的理解的话可是尝试一下转化递归的代码为非递归的代码，一个思路就是使用迭代或者模拟栈的操作来取代递归。迭代算法是用计算机解决问题的一种基本方法。它利用计算机运算速度快、适合做重复性操作的特点，让计算机对一组指令(或一定步骤)进行重复执行，在每次执行这组指令(或这些步骤)时，都从变量的原值推出它的一个新值。递归算法与迭代算法的设计思路区别在于：函数或算法是否具备收敛性，当且仅当一个算法存在预期的收敛效果时，采用递归算法才是可行的，否则，就不能使用递归算法。 当然，从理论上说，所有的递归函数都可以转换为迭代函数，反之亦然，然而代价通常都是比较高的。
好了，关于递归的闲聊就到了这样，今天的目的是使用模拟栈的操作来实现非递归形式的快速排序算法，做法也很简单只是模拟了栈的基本操作，使用栈的压入和弹出来取代了原始的递归调用。
下面是具体的实现：
#!usr/bin/env python
#encoding:utf-8 '''''
__Author__:沂水寒城
功能：模拟栈操作实现非递归的快速排序
''' import random
import timeclass stack(object):def __init__(self,size):'''初始化得到一个空栈'''self.size=sizeself.stack=[]def __str__(self):'''返回栈内容'''return str(self.stack)def getSize(self):'''获取栈当前的大小'''return len(self.stack)def push(self,ele):'''将一个元素压入栈中'''if self.isfull():raise Exception('Empty Stack!!!')self.stack.append(ele)def top(self):'''返回栈顶元素'''if self.isempty():raise Exception('Empty Stack!!!')return self.stack[-1]def pop(self):'''弹出栈顶元素'''if self.isempty():raise Exception('Empty Stack!!!')topElement=self.stack[-1]self.stack.remove(topElement)def isempty(self):'''判断栈是否为空'''if len(self.stack)==0:return Truereturn Falsedef isfull(self):'''判断当前栈是否已满'''if len(self.stack)==self.size:return Truereturn Falsedef random_nums_generator(max_value=1000, total_nums=20): ''''' 随机数列表生成器 一些常用函数： random随机数生成 random.random()用于生成一个0到1之间的随机数:0 <= n < 1.0； random.uniform(a, b)，用于生成一个指定范围内的随机符点数，两个参数其中一个是上限，一个是下限。min(a,b) <= n <= max(a,b)； randdom.randint(a, b), 用于生成一个指定范围内的整数，其中a是下限，b是上限： a<= n <= b； random.randrange(start, stop, step), 从指定范围内，按指定基数递增的集合获取一个随机数； random.choice(sequence), 从序列中获取一个随机元素； random.shuffle(x), 用于将一个列表中的元素打乱； random.sample(sequence, k), 从指定序列中随机获取指定长度的片断； ''' num_list=[] for i in range(total_nums): num_list.append(random.randint(0,max_value)) return num_list def quick_sort(num_list,start,end):'''模拟栈操作实现非递归的快速排序'''stackTest=stack(len(num_list))if start<end:stackTest.push(end)stackTest.push(start)while not stackTest.isempty():l=stackTest.top()stackTest.pop()r=stackTest.top()stackTest.pop()index=partition(num_list, l,r)if l<index-1:stackTest.push(index-1)stackTest.push(l)if r>index+1:stackTest.push(r)stackTest.push(index+1)return num_listdef partition(num_list,start,end):'''划分函数，返回划分出下标'''base=num_list[start]while start<end:while start<end and num_list[end]>=base:end-=1 num_list[start]=num_list[end]while start<end and num_list[start]<=base:start+=1 num_list[end]=base return startdef main_func(max_value=1000, total_nums=20):'''主调用函数'''num_list=random_nums_generator(max_value, total_nums)start_time=time.time()result_list=quick_sort(num_list,0,len(num_list)-1)end_time=time.time()print result_listreturn (end_time-start_time)*1000if __name__ == '__main__' :#测试样例# num_list=random_nums_generator(max_value=1000, total_nums=20)# print quick_sort(num_list,0,len(num_list)-1)time_list=[]one_time=main_func(max_value=100000, total_nums=20)time_list.append(one_time)print '--------------------------------------------------------'one_time=main_func(max_value=100000, total_nums=200)time_list.append(one_time)print '---------------------------------------------------------'one_time=main_func(max_value=100000, total_nums=2000)time_list.append(one_time)print '---------------------------------------------------------'one_time=main_func(max_value=100000, total_nums=20000)time_list.append(one_time)print '************************************************************'for index, one_time in enumerate(time_list):print '第{0}次运行时间为：{1}'.format(index, one_time)结果如下：
[2716, 14496, 17974, 19412, 19412, 20674, 40925, 40925, 40925, 49992, 49992, 51070, 51070, 67274, 78930, 78930, 78930, 78930, 78930, 94412]
--------------------------------------------------------
[180, 210, 210, 659, 659, 659, 659, 1633, 3184, 3831, 4275, 4275, 4275, 6070, 7250, 8700, 9362, 9362, 9362, 9362, 9362, 9373, 9373, 9373, 11634, 14098, 14098, 14098, 14098, 14098, 14098, 14098, 14098, 14098, 14098, 14098, 14098, 15254, 16308, 16308, 16308, 16308, 16308, 16498, 18573, 24588, 28759, 28759, 28759, 28759, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 29883, 30598, 30598, 30598, 30598, 30598, 30598, 32824, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 33531, 34074, 34074, 38944, 39609, 39609, 39609, 39972, 39972, 39972, 42756, 42756, 43831, 44069, 44069, 44069, 44069, 44069, 44069, 44069, 44069, 44069, 44069, 44069, 44807, 44834, 44834, 49823, 51401, 51401, 51401, 51401, 61831, 61831, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 68690, 69286, 73799, 73799, 75055, 75055, 75055, 75055, 83833, 83833, 83833, 91171, 92959, 92959, 92959, 92959, 92959, 92959, 97783]
---------------------------------------------------------
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************************************************************
第0次运行时间为：0.157833099365
第1次运行时间为：2.17199325562
第2次运行时间为：40.4109954834
第3次运行时间为：1219.03705597可以简单看一下：
数据量从20-->200-->2000->20000所用时间的消耗
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