排序算法 之 插入排序InsertionSort

介绍

插入排序的工作原理是，对于每个未排序数据，在已排序序列中从后向前扫描，找到相应位置并插入。

步骤

从第一个元素开始，该元素可以认为已经被排序

取出下一个元素，在已经排序的元素序列中从后向前扫描

如果被扫描的元素（已排序）大于新元素，将该元素后移一位

重复步骤3，直到找到已排序的元素小于或者等于新元素的位置

将新元素插入到该位置后

重复步骤2~5

代码

# -*- coding: utf-8 -*-
"""
Created on Wed Apr 27 10:41:00 2016

@author: zang
"""

from matplotlib import pyplot as plt
import random

def bubbleSort1(unsortedList):#采用递归
if len(unsortedList)<2:
return unsortedList

list_length=len(unsortedList)
for i in range(list_length - 1):
if unsortedList[i] > unsortedList[i + 1]:
unsortedList[i],unsortedList[i + 1] = unsortedList[i + 1], unsortedList[i]
max_num = unsortedList.pop()
return bubbleSort1(unsortedList) + [max_num]

def insertSort(unsortedList):
n = len(unsortedList)
for i in range(1,n):
if unsortedList[i] < unsortedList[i-1]:
temp = unsortedList[i]
index = i           #待插入的下标
for j in range(i-1,-1,-1):  #从i-1 循环到 0 (包括0)
if unsortedList[j] > temp :
unsortedList[j+1] = unsortedList[j]
index = j   #记录待插入下标
else :
break
unsortedList[index] = temp
return unsortedList

def plotScatter(inputList):
plt.scatter(range(len(inputList)),inputList)
plt.show()

if __name__ == "__main__":
num_list = range(1000)
unsortedList = random.sample(num_list, 30)
print "unsortedList:"
plotScatter(unsortedList)
print unsortedList
sortedList = insertSort(unsortedList)
print "sortedList:"
plotScatter(sortedList)
print sortedList

测试

输入

[544, 757, 514, 875, 371, 44, 538, 296, 155, 148, 612, 847, 352, 973, 654, 135, 956, 197, 655, 270, 280, 609, 175, 891, 450, 128, 75, 260, 248, 540]

输出

[44, 75, 128, 135, 148, 155, 175, 197, 248, 260, 270, 280, 296, 352, 371, 450, 514, 538, 540, 544, 609, 612, 654, 655, 757, 847, 875, 891, 956, 973]

分析

情况	性能
Worst case performance:	O(n2)
Best case performance:	O(n)
Average case performance:	O(n2)
Worst case space complexity:	O(1)

参考

http://wuchong.me/blog/2014/02/09/algorithm-sort-summary/

http://blog.jobbole.com/72850/