插入排序
原理:循环一次就移动一次元素到数组中正确的位置,通常使用在长度较小的数组的情况以及作为其它复杂排序算法的一部分,比如mergesort或quicksort。时间复杂度为 O(n2) 。
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# 1nd: 两两交换
def insertion_sort(arr):
for i in range ( 1 , len (arr)):
j = i
while j > = 0 and arr[j - 1 ] > arr[j]:
arr[j], arr[j - 1 ] = arr[j - 1 ], arr[j]
j - = 1
return arr
# 2nd: 交换,最后处理没交换的
def insertion_sort2(arr):
for i in range ( 1 , len (arr)):
j = i - 1
key = arr[i]
while j > = 0 and arr[j] > key:
arr[j + 1 ] = arr[j]
j - = 1
arr[j + 1 ] = key
return arr
# 3nd: 加速版本,利用已经排好了序的进行二分查找
def insertion_sort3(seq):
for i in range ( 1 , len (seq)):
key = seq[i]
# invariant: ``seq[:i]`` is sorted
# find the least `low' such that ``seq[low]`` is not less then `key'.
# Binary search in sorted sequence ``seq[low:up]``:
low, up = 0 , i
while up > low:
middle = (low + up) / / 2
if seq[middle] < key:
low = middle + 1
else :
up = middle
# insert key at position ``low``
seq[:] = seq[:low] + [key] + seq[low:i] + seq[i + 1 :]
return seq
# 4nd: 原理同上,使用bisect
import bisect
def insertion_sort4(seq):
for i in range ( 1 , len (seq)):
bisect.insort(seq, seq.pop(i), 0 , i) # 默认插在相同元素的左边
return seq
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选择排序
原理:每一趟都选择最小的值和当前下标的值进行交换,适用在大型的数组,时间复杂度为 O(n2)
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# 1nd: for
def select_sort(seq):
for i in range ( 0 , len (seq)):
mi = i
for j in range (i, len (seq)):
if seq[j] < seq[mi]:
mi = j
seq[mi], seq[i] = seq[i], seq[mi]
return seq
# 2nd: min
def select_sort2(seq):
for i, x in enumerate (seq):
mi = min ( range (i, len (seq)), key = seq.__getitem__)
seq[i], seq[mi] = seq[mi], x
return seq
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冒泡排序
原理:比较数组中两两相邻的数,如果第一个大于第二个,就进行交换,重复地走访过要排序的数列,达到将最小的值移动到最上面的目的,适用于小型数组,时间复杂度为O(n2)
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def bubble_sort(seq):
for i in range ( len (seq)):
for j in range ( len (seq) - 1 - i):
if seq[j] > seq[j + 1 ]:
seq[j], seq[j + 1 ] = seq[j + 1 ], seq[j]
return seq
def bubble_sort2(seq):
for i in range ( 0 , len (seq)):
for j in range (i + 1 , len (seq)):
if seq[i] > seq[j]:
seq[i], seq[j] = seq[j], seq[i]
return seq
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快速排序
原理:从数组中选择pivot,分成两个数组,一个是比pivot小,一个是比pivot大,最后将这两个数组和pivot进行合并,最好情况下时间复杂度为O(n log n),最差情况下时间复杂度为O(n2)
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def quick_sort(seq):
if len (seq) > = 1 :
pivot_idx = len (seq) / / 2
small, large = [], []
for i, val in enumerate (seq):
if i ! = pivot_idx:
if val < = seq[pivot_idx]:
small.append(val)
else :
large.append(val)
quick_sort(small)
quick_sort(large)
return small + [seq[pivot_idx]] + large
else :
return seq
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归并排序
原理:归并排序是建立在归并操作上的一种有效的排序算法,该算法是采用分治法(Divide and Conquer)的一个非常典型的应用。将已有序的子序列合并,得到完全有序的序列;即先使每个子序列有序,再使子序列段间有序。若将两个有序表合并成一个有序表,称为二路归并。
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# 1nd: 将两个有序数组合并到一个数组
def merge(left, right):
i, j = 0 , 0
result = []
while i < len (left) and j < len (right):
if left[i] < = right[j]:
result.append(left[i])
i + = 1
else :
result.append(right[j])
j + = 1
result + = left[i:]
result + = right[j:]
return result
def merge_sort(lists):
if len (lists) < = 1 :
return lists
num = len (lists) / 2
left = merge_sort(lists[:num])
right = merge_sort(lists[num:])
return merge(left, right)
# 2nd: use merge
from heapq import merge
def merge_sort2(m):
if len (m) < = 1 :
return m
middle = len (m) / / 2
left = m[:middle]
right = m[middle:]
left = merge_sort(left)
right = merge_sort(right)
return list (merge(left, right))
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堆排序
原理:堆排序(Heapsort)是指利用堆积树(堆)这种数据结构所设计的一种排序算法,它是选择排序的一种。可以利用数组的特点快速定位指定索引的元素。堆分为大根堆和小根堆,是完全二叉树。大根堆的要求是每个节点的值都不大于其父节点的值,即A[PARENT[i]] >= A[i]。在数组的非降序排序中,需要使用的就是大根堆,因为根据大根堆的要求可知,最大的值一定在堆顶。平均时间复杂度为O(n logn)
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# 1nd: normal
def swap(seq, i, j):
seq[i], seq[j] = seq[j], seq[i]
# 调整堆
def heapify(seq, end, i):
l = 2 * i + 1
r = 2 * (i + 1 )
ma = i
if l < end and seq[i] < seq[l]:
ma = l
if r < end and seq[ma] < seq[r]:
ma = r
if ma ! = i:
swap(seq, i, ma)
heapify(seq, end, ma)
def heap_sort(seq):
end = len (seq)
start = end / / 2 - 1
# 创建堆
for i in range (start, - 1 , - 1 ):
heapify(seq, end, i)
for i in range (end - 1 , 0 , - 1 ):
swap(seq, i, 0 )
heapify(seq, i, 0 )
return seq
# 2nd: use heapq
import heapq
def heap_sort2(seq):
""" Implementation of heap sort """
heapq.heapify(seq)
return [heapq.heappop(seq) for _ in range ( len (seq))]
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希尔排序
原理:希尔排序(Shell Sort)是插入排序的一种。也称缩小增量排序,是直接插入排序算法的一种更高效的改进版本。希尔排序是非稳定排序算法。希尔排序是把记录按下标的一定增量分组,对每组使用直接插入排序算法排序;随着增量逐渐减少,每组包含的关键词越来越多,当增量减至1时,整个文件恰被分成一组,算法便终止。
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def shell_sort(seq):
count = len (seq)
step = 2
group = count / / step
while group > 0 :
for i in range ( 0 , group):
j = i + group
while j < count:
k = j - group
key = seq[j]
while k > = 0 :
if seq[k] > key:
seq[k + group] = seq[k]
seq[k] = key
k - = group
j + = group
group / / = step
return seq
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区别
以上就是本文的全部内容,希望对大家的学习有所帮助,也希望大家多多支持服务器之家。
原文链接:http://www.cnblogs.com/George1994/p/7337188.html