1.[代码][Python]代码

# -*- coding: utf-8 -*-

def step_half(n):

"""Original sequence: n/2, n/4, ..., 1

a(n) = ceil(n/(2^k)), k >= 1

原始步长：从n/2开始不断减半直至1。

"""

while True:

n = n / 2

v = int(n)

yield v

if v <= 1:

return

def _step_sedgewick():

"""Sedgewick's increments: 1, 5, 19, 41, 109, ...

1, 19, 109, 505, 2161, ..., 9(4^k – 2^k) + 1, k = 0, 1, 2, 3, …

5, 41, 209, 929, 3905, ..., 2^(k+2) (2^(k+2) – 3) + 1, k = 0, 1, 2, 3, …

Sedgewick提出的步长序列：用这样步长串行的希尔排序比插入排序和堆排序都要快，

甚至在小数组中比快速排序还快，但是在涉及大量数据时希尔排序还是比快速排序慢。

"""

def step_a():

k = 0

while True:

yield 9 * (4 ** k - 2 ** k) + 1

k += 1

def step_b():

k = 0

while True:

v = 2 ** (k + 2)

yield v * (v - 3) + 1

k += 1

gen_a, gen_b = step_a(), step_b()

a, b = gen_a.next(), gen_b.next()

small = min(a, b)

yield small

while True:

if small == a:

a = gen_a.next()

else:

b = gen_b.next()

small = min(a, b)

yield small

def step_sedgewick(n):

"""限制步长序列值小于n"""

gen_step = _step_sedgewick()

while True:

v = gen_step.next()

if v < n:

yield v

else:

return

def shell_sort(A, gaps):

"""希尔排序，伪码如下：

SHELL-SORT(A, gaps)

1 n ← length[A] // 数组长度

2 foreach gap in gaps

3 ▷ 为每个步长下各列做插入排序

4 for i ← gap to n-1 // 从步长位至末位

5 do temp ← A[i]

6 j ← i

7 while j >= gap and A[j - gap] > temp // 与步长前一位比较，直至不小于它

8 do A[j] ← A[j - gap] // 大值后移

9 j ← j - gap // 再前一位

10 A[j] = temp

Args:

A (Sequence): 数组

gaps (Iterator): 步长序列

更多步长：http://en.wikipedia.org/wiki/Shellsort

"""

n = len(A)

for gap in gaps:

for i in xrange(gap, n):

temp = A[i]

j = i

while j >= gap and A[j - gap] > temp:

A[j] = A[j - gap]

j = j - gap

A[j] = temp

if __name__ == '__main__':

import random, timeit

items = range(10000)

random.shuffle(items)

def test_sorted():

# print(items)

sorted_items = sorted(items)

# print(sorted_items)

# _gaps = step_half(len(items))

_gaps = reversed([a for a in step_sedgewick(len(items))])

def test_shell_sort():

# print(items)

shell_sort(items, _gaps)

# print(items)

test_methods = [test_sorted, test_shell_sort]

for test in test_methods:

name = test.__name__ # test.func_name

t = timeit.Timer(name + '()', 'from __main__ import ' + name)

print(name + ' takes time : %f' % t.timeit(1))